Daily Papers

Learning embedding table plays a fundamental role in Click-through rate(CTR) prediction from the view of the model performance and memory usage. The embedding table is a two-dimensional tensor, with its axes indicating the number of feature values and the embedding dimension, respectively. To learn an efficient and effective embedding table, recent works either assign various embedding dimensions for feature fields and reduce the number of embeddings respectively or mask the embedding table parameters. However, all these existing works cannot get an optimal embedding table. On the one hand, various embedding dimensions still require a large amount of memory due to the vast number of features in the dataset. On the other hand, decreasing the number of embeddings usually suffers from performance degradation, which is intolerable in CTR prediction. Finally, pruning embedding parameters will lead to a sparse embedding table, which is hard to be deployed. To this end, we propose an optimal embedding table learning framework OptEmbed, which provides a practical and general method to find an optimal embedding table for various base CTR models. Specifically, we propose pruning the redundant embeddings regarding corresponding features' importance by learnable pruning thresholds. Furthermore, we consider assigning various embedding dimensions as one single candidate architecture. To efficiently search the optimal embedding dimensions, we design a uniform embedding dimension sampling scheme to equally train all candidate architectures, meaning architecture-related parameters and learnable thresholds are trained simultaneously in one supernet. We then propose an evolution search method based on the supernet to find the optimal embedding dimensions for each field. Experiments on public datasets show that OptEmbed can learn a compact embedding table which can further improve the model performance.

In this report, we introduce Piccolo2, an embedding model that surpasses other models in the comprehensive evaluation over 6 tasks on CMTEB benchmark, setting a new state-of-the-art. Piccolo2 primarily leverages an efficient multi-task hybrid loss training approach, effectively harnessing textual data and labels from diverse downstream tasks. In addition, Piccolo2 scales up the embedding dimension and uses MRL training to support more flexible vector dimensions. The latest information of piccolo models can be accessed via: https://huggingface.co/sensenova/

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.

Low-rank adaptation (LoRA) has become the default approach to fine-tune large language models (LLMs) due to its significant reduction in trainable parameters. However, trainable parameter demand for LoRA increases with increasing model embedding dimensions, leading to high compute costs. Additionally, its backward updates require storing high-dimensional intermediate activations and optimizer states, demanding high peak GPU memory. In this paper, we introduce large model fine-tuning via spectrally decomposed low-dimensional adaptation (LaMDA), a novel approach to fine-tuning large language models, which leverages low-dimensional adaptation to achieve significant reductions in trainable parameters and peak GPU memory footprint. LaMDA freezes a first projection matrix (PMA) in the adaptation path while introducing a low-dimensional trainable square matrix, resulting in substantial reductions in trainable parameters and peak GPU memory usage. LaMDA gradually freezes a second projection matrix (PMB) during the early fine-tuning stages, reducing the compute cost associated with weight updates to enhance parameter efficiency further. We also present an enhancement, LaMDA++, incorporating a ``lite-weight" adaptive rank allocation for the LoRA path via normalized spectrum analysis of pre-trained model weights. We evaluate LaMDA/LaMDA++ across various tasks, including natural language understanding with the GLUE benchmark, text summarization, natural language generation, and complex reasoning on different LLMs. Results show that LaMDA matches or surpasses the performance of existing alternatives while requiring up to 17.7x fewer parameter updates and up to 1.32x lower peak GPU memory usage during fine-tuning. Code will be publicly available.

We present Gecko, a compact and versatile text embedding model. Gecko achieves strong retrieval performance by leveraging a key idea: distilling knowledge from large language models (LLMs) into a retriever. Our two-step distillation process begins with generating diverse, synthetic paired data using an LLM. Next, we further refine the data quality by retrieving a set of candidate passages for each query, and relabeling the positive and hard negative passages using the same LLM. The effectiveness of our approach is demonstrated by the compactness of the Gecko. On the Massive Text Embedding Benchmark (MTEB), Gecko with 256 embedding dimensions outperforms all existing entries with 768 embedding size. Gecko with 768 embedding dimensions achieves an average score of 66.31, competing with 7x larger models and 5x higher dimensional embeddings.

In this paper, we show that Low Rank Adaptation (LoRA) as originally introduced in Hu et al. (2021) leads to suboptimal finetuning of models with large width (embedding dimension). This is due to the fact that adapter matrices A and B in LoRA are updated with the same learning rate. Using scaling arguments for large width networks, we demonstrate that using the same learning rate for A and B does not allow efficient feature learning. We then show that this suboptimality of LoRA can be corrected simply by setting different learning rates for the LoRA adapter matrices A and B with a well-chosen ratio. We call this proposed algorithm LoRA+. In our extensive experiments, LoRA+ improves performance (1-2 % improvements) and finetuning speed (up to sim 2X SpeedUp), at the same computational cost as LoRA.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Large Language Models (LLMs) typically represent numbers using multiple tokens, which requires the model to aggregate these tokens to interpret numerical values. This fragmentation makes both training and inference less efficient and adversely affects the model's performance on number-related tasks. Inspired by the observation that pre-trained LLMs internally learn Fourier-like features for number tokens, we propose Fourier Number Embedding (FoNE), a novel method that directly maps numbers into the embedding space with their Fourier features. FoNE encodes each number as a single token with only two embedding dimensions per digit, effectively capturing numerical values without fragmentation. This compact representation accelerates both training and inference. Compared to traditional subword and digit-wise embeddings, FoNE not only reduces computational overhead but also achieves higher accuracy across various numerical tasks including addition, subtraction and multiplication. On 6-digit decimal addition, FoNE requires 64times less data to achieve 99% accuracy than subword and digit-wise embeddings while using 3times and 6times fewer tokens per number, respectively. Furthermore, FoNE is the only method that yields 100% accuracy on over 100,000 test examples for addition, subtraction, and multiplication. The codes and visualization are available at https://fouriernumber.github.io/.

Matrix multiplication (MatMul) typically dominates the overall computational cost of large language models (LLMs). This cost only grows as LLMs scale to larger embedding dimensions and context lengths. In this work, we show that MatMul operations can be completely eliminated from LLMs while maintaining strong performance at billion-parameter scales. Our experiments show that our proposed MatMul-free models achieve performance on-par with state-of-the-art Transformers that require far more memory during inference at a scale up to at least 2.7B parameters. We investigate the scaling laws and find that the performance gap between our MatMul-free models and full precision Transformers narrows as the model size increases. We also provide a GPU-efficient implementation of this model which reduces memory usage by up to 61% over an unoptimized baseline during training. By utilizing an optimized kernel during inference, our model's memory consumption can be reduced by more than 10x compared to unoptimized models. To properly quantify the efficiency of our architecture, we build a custom hardware solution on an FPGA which exploits lightweight operations beyond what GPUs are capable of. We processed billion-parameter scale models at 13W beyond human readable throughput, moving LLMs closer to brain-like efficiency. This work not only shows how far LLMs can be stripped back while still performing effectively, but also points at the types of operations future accelerators should be optimized for in processing the next generation of lightweight LLMs. Our code implementation is available at https://github.com/ridgerchu/matmulfreellm.

Contrastive learning (CL) has emerged as a powerful technique for representation learning, with or without label supervision. However, supervised CL is prone to collapsing representations of subclasses within a class by not capturing all their features, and unsupervised CL may suppress harder class-relevant features by focusing on learning easy class-irrelevant features; both significantly compromise representation quality. Yet, there is no theoretical understanding of class collapse or feature suppression at test time. We provide the first unified theoretically rigorous framework to determine which features are learnt by CL. Our analysis indicate that, perhaps surprisingly, bias of (stochastic) gradient descent towards finding simpler solutions is a key factor in collapsing subclass representations and suppressing harder class-relevant features. Moreover, we present increasing embedding dimensionality and improving the quality of data augmentations as two theoretically motivated solutions to {feature suppression}. We also provide the first theoretical explanation for why employing supervised and unsupervised CL together yields higher-quality representations, even when using commonly-used stochastic gradient methods.

Attention based Transformer architecture has enabled significant advances in the field of natural language processing. In addition to new pre-training techniques, recent improvements crucially rely on working with a relatively larger embedding dimension for tokens. Unfortunately, this leads to models that are prohibitively large to be employed in the downstream tasks. In this paper we identify one of the important factors contributing to the large embedding size requirement. In particular, our analysis highlights that the scaling between the number of heads and the size of each head in the current architecture gives rise to a low-rank bottleneck in attention heads, causing this limitation. We further validate this in our experiments. As a solution we propose to set the head size of an attention unit to input sequence length, and independent of the number of heads, resulting in multi-head attention layers with provably more expressive power. We empirically show that this allows us to train models with a relatively smaller embedding dimension and with better performance scaling.

Lifelong user behavior sequences, comprising up to tens of thousands of history behaviors, are crucial for capturing user interests and predicting user responses in modern recommendation systems. A two-stage paradigm is typically adopted to handle these long sequences: a few relevant behaviors are first searched from the original long sequences via an attention mechanism in the first stage and then aggregated with the target item to construct a discriminative representation for prediction in the second stage. In this work, we identify and characterize, for the first time, a neglected deficiency in existing long-sequence recommendation models: a single set of embeddings struggles with learning both attention and representation, leading to interference between these two processes. Initial attempts to address this issue using linear projections -- a technique borrowed from language processing -- proved ineffective, shedding light on the unique challenges of recommendation models. To overcome this, we propose the Decoupled Attention and Representation Embeddings (DARE) model, where two distinct embedding tables are initialized and learned separately to fully decouple attention and representation. Extensive experiments and analysis demonstrate that DARE provides more accurate search of correlated behaviors and outperforms baselines with AUC gains up to 0.9% on public datasets and notable online system improvements. Furthermore, decoupling embedding spaces allows us to reduce the attention embedding dimension and accelerate the search procedure by 50% without significant performance impact, enabling more efficient, high-performance online serving.

Interpreting hierarchical structures latent in language is a key limitation of current language models (LMs). While previous research has implicitly leveraged these hierarchies to enhance LMs, approaches for their explicit encoding are yet to be explored. To address this, we introduce a novel approach to re-train transformer encoder-based LMs as Hierarchy Transformer encoders (HiTs), harnessing the expansive nature of hyperbolic space. Our method situates the output embedding space of pre-trained LMs within a Poincar\'e ball with a curvature that adapts to the embedding dimension, followed by re-training on hyperbolic cluster and centripetal losses. These losses are designed to effectively cluster related entities (input as texts) and organise them hierarchically. We evaluate HiTs against pre-trained and fine-tuned LMs, focusing on their capabilities in simulating transitive inference, predicting subsumptions, and transferring knowledge across hierarchies. The results demonstrate that HiTs consistently outperform both pre-trained and fine-tuned LMs in these tasks, underscoring the effectiveness and transferability of our re-trained hierarchy encoders.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

Training large transformer models from scratch for a target task requires lots of data and is computationally demanding. The usual practice of transfer learning overcomes this challenge by initializing the model with weights of a pretrained model of the same size and specification to increase the convergence and training speed. However, what if no pretrained model of the required size is available? In this paper, we introduce a simple yet effective technique to transfer the knowledge of a pretrained model to smaller variants. Our approach called weight subcloning expedites the training of scaled-down transformers by initializing their weights from larger pretrained models. Weight subcloning involves an operation on the pretrained model to obtain the equivalent initialized scaled-down model. It consists of two key steps: first, we introduce neuron importance ranking to decrease the embedding dimension per layer in the pretrained model. Then, we remove blocks from the transformer model to match the number of layers in the scaled-down network. The result is a network ready to undergo training, which gains significant improvements in training speed compared to random initialization. For instance, we achieve 4x faster training for vision transformers in image classification and language models designed for next token prediction.

Nearest neighbour based methods have proved to be one of the most successful self-supervised learning (SSL) approaches due to their high generalization capabilities. However, their computational efficiency decreases when more than one neighbour is used. In this paper, we propose a novel contrastive SSL approach, which we call All4One, that reduces the distance between neighbour representations using ''centroids'' created through a self-attention mechanism. We use a Centroid Contrasting objective along with single Neighbour Contrasting and Feature Contrasting objectives. Centroids help in learning contextual information from multiple neighbours whereas the neighbour contrast enables learning representations directly from the neighbours and the feature contrast allows learning representations unique to the features. This combination enables All4One to outperform popular instance discrimination approaches by more than 1% on linear classification evaluation for popular benchmark datasets and obtains state-of-the-art (SoTA) results. Finally, we show that All4One is robust towards embedding dimensionalities and augmentations, surpassing NNCLR and Barlow Twins by more than 5% on low dimensionality and weak augmentation settings. The source code would be made available soon.

Recommender systems play a significant role in information filtering and have been utilized in different scenarios, such as e-commerce and social media. With the prosperity of deep learning, deep recommender systems show superior performance by capturing non-linear information and item-user relationships. However, the design of deep recommender systems heavily relies on human experiences and expert knowledge. To tackle this problem, Automated Machine Learning (AutoML) is introduced to automatically search for the proper candidates for different parts of deep recommender systems. This survey performs a comprehensive review of the literature in this field. Firstly, we propose an abstract concept for AutoML for deep recommender systems (AutoRecSys) that describes its building blocks and distinguishes it from conventional AutoML techniques and recommender systems. Secondly, we present a taxonomy as a classification framework containing feature selection search, embedding dimension search, feature interaction search, model architecture search, and other components search. Furthermore, we put a particular emphasis on the search space and search strategy, as they are the common thread to connect all methods within each category and enable practitioners to analyze and compare various approaches. Finally, we propose four future promising research directions that will lead this line of research.

The growing computational demands posed by increasingly number of neural network's parameters necessitate low-memory-consumption training approaches. Previous memory reduction techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, suffer from the limitation of low rank and saddle point issues, particularly during intensive tasks like pre-training. In this paper, we propose Sparse Spectral Training (SST), an advanced training methodology that updates all singular values and selectively updates singular vectors of network weights, thereby optimizing resource usage while closely approximating full-rank training. SST refines the training process by employing a targeted updating strategy for singular vectors, which is determined by a multinomial sampling method weighted by the significance of the singular values, ensuring both high performance and memory reduction. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, including natural language generation, machine translation, node classification and link prediction, SST demonstrates its capability to outperform existing memory reduction training methods and is comparable with full-rank training in some cases. On OPT-125M, with rank equating to 8.3% of embedding dimension, SST reduces the perplexity gap to full-rank training by 67.6%, demonstrating a significant reduction of the performance loss with prevalent low-rank methods. This approach offers a strong alternative to traditional training techniques, paving the way for more efficient and scalable neural network training solutions.

Self-supervised speech representation learning has shown promising results in various speech processing tasks. However, the pre-trained models, e.g., HuBERT, are storage-intensive Transformers, limiting their scope of applications under low-resource settings. To this end, we propose LightHuBERT, a once-for-all Transformer compression framework, to find the desired architectures automatically by pruning structured parameters. More precisely, we create a Transformer-based supernet that is nested with thousands of weight-sharing subnets and design a two-stage distillation strategy to leverage the contextualized latent representations from HuBERT. Experiments on automatic speech recognition (ASR) and the SUPERB benchmark show the proposed LightHuBERT enables over 10^9 architectures concerning the embedding dimension, attention dimension, head number, feed-forward network ratio, and network depth. LightHuBERT outperforms the original HuBERT on ASR and five SUPERB tasks with the HuBERT size, achieves comparable performance to the teacher model in most tasks with a reduction of 29% parameters, and obtains a 3.5times compression ratio in three SUPERB tasks, e.g., automatic speaker verification, keyword spotting, and intent classification, with a slight accuracy loss. The code and pre-trained models are available at https://github.com/mechanicalsea/lighthubert.

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

Pretrained language models like BERT have achieved good results on NLP tasks, but are impractical on resource-limited devices due to memory footprint. A large fraction of this footprint comes from the input embeddings with large input vocabulary and embedding dimensions. Existing knowledge distillation methods used for model compression cannot be directly applied to train student models with reduced vocabulary sizes. To this end, we propose a distillation method to align the teacher and student embeddings via mixed-vocabulary training. Our method compresses BERT-LARGE to a task-agnostic model with smaller vocabulary and hidden dimensions, which is an order of magnitude smaller than other distilled BERT models and offers a better size-accuracy trade-off on language understanding benchmarks as well as a practical dialogue task.

Low-resource language translation is a challenging but socially valuable NLP task. Building on recent work adapting the Transformer's normalization to this setting, we propose QKNorm, a normalization technique that modifies the attention mechanism to make the softmax function less prone to arbitrary saturation without sacrificing expressivity. Specifically, we apply ell_2 normalization along the head dimension of each query and key matrix prior to multiplying them and then scale up by a learnable parameter instead of dividing by the square root of the embedding dimension. We show improvements averaging 0.928 BLEU over state-of-the-art bilingual benchmarks for 5 low-resource translation pairs from the TED Talks corpus and IWSLT'15.

Large language models have become the cornerstone of natural language processing, but their use comes with substantial costs in terms of compute and memory resources. Sparsification provides a solution to alleviate these resource constraints, and recent works have shown that trained models can be sparsified post-hoc. Existing sparsification techniques face challenges as they need additional data structures and offer constrained speedup with current hardware. In this paper we present SliceGPT, a new post-training sparsification scheme which replaces each weight matrix with a smaller (dense) matrix, reducing the embedding dimension of the network. Through extensive experimentation, we show that SliceGPT can remove up to 25% of the model parameters (including embeddings) for LLAMA2-70B, OPT 66B and Phi-2 models while maintaining 99%, 99% and 90% zero-shot task performance of the dense model respectively. Our sliced models run on fewer GPUs and run faster without any additional code optimization: on 24GB consumer GPUs we reduce the total compute for inference on LLAMA2-70B to 64% of that of the dense model; on 40GB A100 GPUs we reduce it to 66%. We offer a new insight, computational invariance in transformer networks, which enables SliceGPT and we hope it will inspire and enable future avenues to reduce memory and computation demands for pre-trained models. Code is available at: https://github.com/microsoft/TransformerCompression

We investigate the capabilities of transformer large language models (LLMs) on relational reasoning tasks involving abstract symbols. Such tasks have long been studied in the neuroscience literature as fundamental building blocks for more complex abilities in programming, mathematics, and verbal reasoning. For (i) regression tasks, we prove that transformers generalize when trained, but require astonishingly large quantities of training data. For (ii) next-token-prediction tasks with symbolic labels, we show an "inverse scaling law": transformers fail to generalize as their embedding dimension increases. For both settings (i) and (ii), we propose subtle transformer modifications which can reduce the amount of data needed by adding two trainable parameters per head.

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

This paper proposes to model chaos in the ATM cash withdrawal time series of a big Indian bank and forecast the withdrawals using deep learning methods. It also considers the importance of day-of-the-week and includes it as a dummy exogenous variable. We first modelled the chaos present in the withdrawal time series by reconstructing the state space of each series using the lag, and embedding dimension found using an auto-correlation function and Cao's method. This process converts the uni-variate time series into multi variate time series. The "day-of-the-week" is converted into seven features with the help of one-hot encoding. Then these seven features are augmented to the multivariate time series. For forecasting the future cash withdrawals, using algorithms namely ARIMA, random forest (RF), support vector regressor (SVR), multi-layer perceptron (MLP), group method of data handling (GMDH), general regression neural network (GRNN), long short term memory neural network and 1-dimensional convolutional neural network. We considered a daily cash withdrawals data set from an Indian commercial bank. After modelling chaos and adding exogenous features to the data set, we observed improvements in the forecasting for all models. Even though the random forest (RF) yielded better Symmetric Mean Absolute Percentage Error (SMAPE) value, deep learning algorithms, namely LSTM and 1D CNN, showed similar performance compared to RF, based on t-test.

This paper presents Tiny-toxic-detector, a compact transformer-based model designed for toxic content detection. Despite having only 2.1 million parameters, Tiny-toxic-detector achieves competitive performance on benchmark datasets, with 90.97% accuracy on ToxiGen and 86.98% accuracy on the Jigsaw dataset, rivaling models over 50 times its size. This efficiency enables deployment in resource-constrained environments, addressing the need for effective content moderation tools that balance performance with computational efficiency. The model architecture features 4 transformer encoder layers, each with 2 attention heads, an embedding dimension of 64, and a feedforward dimension of 128. Trained on both public and private datasets, Tiny-toxic-detector demonstrates the potential of efficient, task-specific models for addressing online toxicity. The paper covers the model architecture, training process, performance benchmarks, and limitations, underscoring its suitability for applications such as social media monitoring and content moderation. By achieving results comparable to much larger models while significantly reducing computational demands, Tiny-toxic-detector represents progress toward more sustainable and scalable AI-driven content moderation solutions.

Attention-based mechanisms are widely used in machine learning, most prominently in transformers. However, hyperparameters such as the rank of the attention matrices and the number of heads are scaled nearly the same way in all realizations of this architecture, without theoretical justification. In this work we show that there are dramatic trade-offs between the rank and number of heads of the attention mechanism. Specifically, we present a simple and natural target function that can be represented using a single full-rank attention head for any context length, but that cannot be approximated by low-rank attention unless the number of heads is exponential in the embedding dimension, even for short context lengths. Moreover, we prove that, for short context lengths, adding depth allows the target to be approximated by low-rank attention. For long contexts, we conjecture that full-rank attention is necessary. Finally, we present experiments with off-the-shelf transformers that validate our theoretical findings.

Neural collapse (NC) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviors -- associated with generalization and robustness -- would manifest under specific conditions: models are trained towards zero loss, with noise-free labels belonging to balanced classes, which do not outnumber the model's hidden dimension. Recent studies have explored NC in the absence of one or more of these conditions to extend and capitalize on the associated benefits of ideal geometries. Language modeling presents a curious frontier, as training by token prediction constitutes a classification task where none of the conditions exist: the vocabulary is imbalanced and exceeds the embedding dimension; different tokens might correspond to similar contextual embeddings; and large language models (LLMs) in particular are typically only trained for a few epochs. This paper empirically investigates the impact of scaling the architectures and training of causal language models (CLMs) on their progression towards NC. We find that NC properties that develop with scaling are linked to generalization. Moreover, there is evidence of some relationship between NC and generalization independent of scale. Our work therefore underscores the generality of NC as it extends to the novel and more challenging setting of language modeling. Downstream, we seek to inspire further research on the phenomenon to deepen our understanding of LLMs -- and neural networks at large -- and improve existing architectures based on NC-related properties.

As opposed to scaling-up protein language models (PLMs), we seek improving performance via protein-specific optimization. Although the proportionality between the language model size and the richness of its learned representations is validated, we prioritize accessibility and pursue a path of data-efficient, cost-reduced, and knowledge-guided optimization. Through over twenty experiments ranging from masking, architecture, and pre-training data, we derive insights from protein-specific experimentation into building a model that interprets the language of life, optimally. We present Ankh, the first general-purpose PLM trained on Google's TPU-v4 surpassing the state-of-the-art performance with fewer parameters (<10% for pre-training, <7% for inference, and <30% for the embedding dimension). We provide a representative range of structure and function benchmarks where Ankh excels. We further provide a protein variant generation analysis on High-N and One-N input data scales where Ankh succeeds in learning protein evolutionary conservation-mutation trends and introducing functional diversity while retaining key structural-functional characteristics. We dedicate our work to promoting accessibility to research innovation via attainable resources.

We introduce jina-embeddings-v3, a novel text embedding model with 570 million parameters, achieves state-of-the-art performance on multilingual data and long-context retrieval tasks, supporting context lengths of up to 8192 tokens. The model includes a set of task-specific Low-Rank Adaptation (LoRA) adapters to generate high-quality embeddings for query-document retrieval, clustering, classification, and text matching. Additionally, Matryoshka Representation Learning is integrated into the training process, allowing flexible truncation of embedding dimensions without compromising performance. Evaluation on the MTEB benchmark shows that jina-embeddings-v3 outperforms the latest proprietary embeddings from OpenAI and Cohere on English tasks, while achieving superior performance compared to multilingual-e5-large-instruct across all multilingual tasks.

Common approaches rely on fixed-length embedding vectors from language models as sentence embeddings for downstream tasks such as semantic textual similarity (STS). Such methods are limited in their flexibility due to unknown computational constraints and budgets across various applications. Matryoshka Representation Learning (MRL) (Kusupati et al., 2022) encodes information at finer granularities, i.e., with lower embedding dimensions, to adaptively accommodate ad hoc tasks. Similar accuracy can be achieved with a smaller embedding size, leading to speedups in downstream tasks. Despite its improved efficiency, MRL still requires traversing all Transformer layers before obtaining the embedding, which remains the dominant factor in time and memory consumption. This prompts consideration of whether the fixed number of Transformer layers affects representation quality and whether using intermediate layers for sentence representation is feasible. In this paper, we introduce a novel sentence embedding model called Two-dimensional Matryoshka Sentence Embedding (2DMSE). It supports elastic settings for both embedding sizes and Transformer layers, offering greater flexibility and efficiency than MRL. We conduct extensive experiments on STS tasks and downstream applications. The experimental results demonstrate the effectiveness of our proposed model in dynamically supporting different embedding sizes and Transformer layers, allowing it to be highly adaptable to various scenarios.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

Transformer-based large language models (LLMs) use the key-value (KV) cache to significantly accelerate inference by storing the key and value embeddings of past tokens. However, this cache consumes significant GPU memory. In this work, we introduce HashEvict, an algorithm that uses locality-sensitive hashing (LSH) to compress the KV cache. HashEvict quickly locates tokens in the cache that are cosine dissimilar to the current query token. This is achieved by computing the Hamming distance between binarized Gaussian projections of the current token query and cached token keys, with a projection length much smaller than the embedding dimension. We maintain a lightweight binary structure in GPU memory to facilitate these calculations. Unlike existing compression strategies that compute attention to determine token retention, HashEvict makes these decisions pre-attention, thereby reducing computational costs. Additionally, HashEvict is dynamic - at every decoding step, the key and value of the current token replace the embeddings of a token expected to produce the lowest attention score. We demonstrate that HashEvict can compress the KV cache by 30%-70% while maintaining high performance across reasoning, multiple-choice, long-context retrieval and summarization tasks.

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

We propose a novel Generalized Zero-Shot learning (GZSL) method that is agnostic to both unseen images and unseen semantic vectors during training. Prior works in this context propose to map high-dimensional visual features to the semantic domain, we believe contributes to the semantic gap. To bridge the gap, we propose a novel low-dimensional embedding of visual instances that is "visually semantic." Analogous to semantic data that quantifies the existence of an attribute in the presented instance, components of our visual embedding quantifies existence of a prototypical part-type in the presented instance. In parallel, as a thought experiment, we quantify the impact of noisy semantic data by utilizing a novel visual oracle to visually supervise a learner. These factors, namely semantic noise, visual-semantic gap and label noise lead us to propose a new graphical model for inference with pairwise interactions between label, semantic data, and inputs. We tabulate results on a number of benchmark datasets demonstrating significant improvement in accuracy over state-of-the-art under both semantic and visual supervision.

Open-vocabulary querying in 3D space is challenging but essential for scene understanding tasks such as object localization and segmentation. Language-embedded scene representations have made progress by incorporating language features into 3D spaces. However, their efficacy heavily depends on neural networks that are resource-intensive in training and rendering. Although recent 3D Gaussians offer efficient and high-quality novel view synthesis, directly embedding language features in them leads to prohibitive memory usage and decreased performance. In this work, we introduce Language Embedded 3D Gaussians, a novel scene representation for open-vocabulary query tasks. Instead of embedding high-dimensional raw semantic features on 3D Gaussians, we propose a dedicated quantization scheme that drastically alleviates the memory requirement, and a novel embedding procedure that achieves smoother yet high accuracy query, countering the multi-view feature inconsistencies and the high-frequency inductive bias in point-based representations. Our comprehensive experiments show that our representation achieves the best visual quality and language querying accuracy across current language-embedded representations, while maintaining real-time rendering frame rates on a single desktop GPU.

We present a cascaded diffusion model based on a part-level implicit 3D representation. Our model achieves state-of-the-art generation quality and also enables part-level shape editing and manipulation without any additional training in conditional setup. Diffusion models have demonstrated impressive capabilities in data generation as well as zero-shot completion and editing via a guided reverse process. Recent research on 3D diffusion models has focused on improving their generation capabilities with various data representations, while the absence of structural information has limited their capability in completion and editing tasks. We thus propose our novel diffusion model using a part-level implicit representation. To effectively learn diffusion with high-dimensional embedding vectors of parts, we propose a cascaded framework, learning diffusion first on a low-dimensional subspace encoding extrinsic parameters of parts and then on the other high-dimensional subspace encoding intrinsic attributes. In the experiments, we demonstrate the outperformance of our method compared with the previous ones both in generation and part-level completion and manipulation tasks.

Knowledge graph embedding (KGE) models represent each entity and relation of a knowledge graph (KG) with low-dimensional embedding vectors. These methods have recently been applied to KG link prediction and question answering over incomplete KGs (KGQA). KGEs typically create an embedding for each entity in the graph, which results in large model sizes on real-world graphs with millions of entities. For downstream tasks these atomic entity representations often need to be integrated into a multi stage pipeline, limiting their utility. We show that an off-the-shelf encoder-decoder Transformer model can serve as a scalable and versatile KGE model obtaining state-of-the-art results for KG link prediction and incomplete KG question answering. We achieve this by posing KG link prediction as a sequence-to-sequence task and exchange the triple scoring approach taken by prior KGE methods with autoregressive decoding. Such a simple but powerful method reduces the model size up to 98% compared to conventional KGE models while keeping inference time tractable. After finetuning this model on the task of KGQA over incomplete KGs, our approach outperforms baselines on multiple large-scale datasets without extensive hyperparameter tuning.

Personalized text-to-image generation has attracted unprecedented attention in the recent few years due to its unique capability of generating highly-personalized images via using the input concept dataset and novel textual prompt. However, previous methods solely focus on the performance of the reconstruction task, degrading its ability to combine with different textual prompt. Besides, optimizing in the high-dimensional embedding space usually leads to unnecessary time-consuming training process and slow convergence. To address these issues, we propose an efficient method to explore the target embedding in a textual subspace, drawing inspiration from the self-expressiveness property. Additionally, we propose an efficient selection strategy for determining the basis vectors of the textual subspace. The experimental evaluations demonstrate that the learned embedding can not only faithfully reconstruct input image, but also significantly improves its alignment with novel input textual prompt. Furthermore, we observe that optimizing in the textual subspace leads to an significant improvement of the robustness to the initial word, relaxing the constraint that requires users to input the most relevant initial word. Our method opens the door to more efficient representation learning for personalized text-to-image generation.

Click-through rate prediction is an essential task in industrial applications, such as online advertising. Recently deep learning based models have been proposed, which follow a similar Embedding\&MLP paradigm. In these methods large scale sparse input features are first mapped into low dimensional embedding vectors, and then transformed into fixed-length vectors in a group-wise manner, finally concatenated together to fed into a multilayer perceptron (MLP) to learn the nonlinear relations among features. In this way, user features are compressed into a fixed-length representation vector, in regardless of what candidate ads are. The use of fixed-length vector will be a bottleneck, which brings difficulty for Embedding\&MLP methods to capture user's diverse interests effectively from rich historical behaviors. In this paper, we propose a novel model: Deep Interest Network (DIN) which tackles this challenge by designing a local activation unit to adaptively learn the representation of user interests from historical behaviors with respect to a certain ad. This representation vector varies over different ads, improving the expressive ability of model greatly. Besides, we develop two techniques: mini-batch aware regularization and data adaptive activation function which can help training industrial deep networks with hundreds of millions of parameters. Experiments on two public datasets as well as an Alibaba real production dataset with over 2 billion samples demonstrate the effectiveness of proposed approaches, which achieve superior performance compared with state-of-the-art methods. DIN now has been successfully deployed in the online display advertising system in Alibaba, serving the main traffic.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

Recently, a new Continual Learning (CL) paradigm was presented to control catastrophic forgetting, called Interval Continual Learning (InterContiNet), which relies on enforcing interval constraints on the neural network parameter space. Unfortunately, InterContiNet training is challenging due to the high dimensionality of the weight space, making intervals difficult to manage. To address this issue, we introduce HyperInterval, a technique that employs interval arithmetic within the embedding space and utilizes a hypernetwork to map these intervals to the target network parameter space. We train interval embeddings for consecutive tasks and train a hypernetwork to transform these embeddings into weights of the target network. An embedding for a given task is trained along with the hypernetwork, preserving the response of the target network for the previous task embeddings. Interval arithmetic works with a more manageable, lower-dimensional embedding space rather than directly preparing intervals in a high-dimensional weight space. Our model allows faster and more efficient training. Furthermore, HyperInterval maintains the guarantee of not forgetting. At the end of training, we can choose one universal embedding to produce a single network dedicated to all tasks. In such a framework, hypernetwork is used only for training and can be seen as a meta-trainer. HyperInterval obtains significantly better results than InterContiNet and gives SOTA results on several benchmarks.

Hashing is an efficient method for nearest neighbor search in large-scale data space by embedding high-dimensional feature descriptors into a similarity preserving Hamming space with a low dimension. However, large-scale high-speed retrieval through binary code has a certain degree of reduction in retrieval accuracy compared to traditional retrieval methods. We have noticed that multi-view methods can well preserve the diverse characteristics of data. Therefore, we try to introduce the multi-view deep neural network into the hash learning field, and design an efficient and innovative retrieval model, which has achieved a significant improvement in retrieval performance. In this paper, we propose a supervised multi-view hash model which can enhance the multi-view information through neural networks. This is a completely new hash learning method that combines multi-view and deep learning methods. The proposed method utilizes an effective view stability evaluation method to actively explore the relationship among views, which will affect the optimization direction of the entire network. We have also designed a variety of multi-data fusion methods in the Hamming space to preserve the advantages of both convolution and multi-view. In order to avoid excessive computing resources on the enhancement procedure during retrieval, we set up a separate structure called memory network which participates in training together. The proposed method is systematically evaluated on the CIFAR-10, NUS-WIDE and MS-COCO datasets, and the results show that our method significantly outperforms the state-of-the-art single-view and multi-view hashing methods.

We describe a neural network-based system for text-to-speech (TTS) synthesis that is able to generate speech audio in the voice of many different speakers, including those unseen during training. Our system consists of three independently trained components: (1) a speaker encoder network, trained on a speaker verification task using an independent dataset of noisy speech from thousands of speakers without transcripts, to generate a fixed-dimensional embedding vector from seconds of reference speech from a target speaker; (2) a sequence-to-sequence synthesis network based on Tacotron 2, which generates a mel spectrogram from text, conditioned on the speaker embedding; (3) an auto-regressive WaveNet-based vocoder that converts the mel spectrogram into a sequence of time domain waveform samples. We demonstrate that the proposed model is able to transfer the knowledge of speaker variability learned by the discriminatively-trained speaker encoder to the new task, and is able to synthesize natural speech from speakers that were not seen during training. We quantify the importance of training the speaker encoder on a large and diverse speaker set in order to obtain the best generalization performance. Finally, we show that randomly sampled speaker embeddings can be used to synthesize speech in the voice of novel speakers dissimilar from those used in training, indicating that the model has learned a high quality speaker representation.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer architecture in which a particular embedding vector's dimension scales with its query frequency. Through theoretical analysis and systematic experiments, we demonstrate that using mixed dimensions can drastically reduce the memory usage, while maintaining and even improving the ML performance. Empirically, we show that the proposed mixed dimension layers improve accuracy by 0.1% using half as many parameters or maintain it using 16X fewer parameters for click-through rate prediction task on the Criteo Kaggle dataset.

We propose a new transformer-based image and video tokenizer with Binary Spherical Quantization (BSQ). BSQ projects the high-dimensional visual embedding to a lower-dimensional hypersphere and then applies binary quantization. BSQ is (1) parameter-efficient without an explicit codebook, (2) scalable to arbitrary token dimensions, and (3) compact: compressing visual data by up to 100times with minimal distortion. Our tokenizer uses a transformer encoder and decoder with simple block-wise causal masking to support variable-length videos as input. The resulting BSQ-ViT achieves state-of-the-art visual reconstruction quality on image and video reconstruction benchmarks with 2.4times throughput compared to the best prior methods. Furthermore, by learning an autoregressive prior for adaptive arithmetic coding, BSQ-ViT achieves comparable results on video compression with state-of-the-art video compression standards. BSQ-ViT also enables masked language models to achieve competitive image synthesis quality to GAN- and diffusion-based methods.

The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewire or infer a GNN's graph to maximize the GNN's predictive downstream performance, but it lacks solid theoretical foundations in terms of embedding-based representation guarantees. This paper addresses this issue by introducing a trainable deep learning architecture, coined neural snowflake, that can adaptively implement fractal-like metrics on R^d. We prove that any given finite weights graph can be isometrically embedded by a standard MLP encoder. Furthermore, when the latent graph can be represented in the feature space of a sufficiently regular kernel, we show that the combined neural snowflake and MLP encoder do not succumb to the curse of dimensionality by using only a low-degree polynomial number of parameters in the number of nodes. This implementation enables a low-dimensional isometric embedding of the latent graph. We conduct synthetic experiments to demonstrate the superior metric learning capabilities of neural snowflakes when compared to more familiar spaces like Euclidean space. Additionally, we carry out latent graph inference experiments on graph benchmarks. Consistently, the neural snowflake model achieves predictive performance that either matches or surpasses that of the state-of-the-art latent graph inference models. Importantly, this performance improvement is achieved without requiring random search for optimal latent geometry. Instead, the neural snowflake model achieves this enhancement in a differentiable manner.

We present WineSensed, a large multimodal wine dataset for studying the relations between visual perception, language, and flavor. The dataset encompasses 897k images of wine labels and 824k reviews of wines curated from the Vivino platform. It has over 350k unique vintages, annotated with year, region, rating, alcohol percentage, price, and grape composition. We obtained fine-grained flavor annotations on a subset by conducting a wine-tasting experiment with 256 participants who were asked to rank wines based on their similarity in flavor, resulting in more than 5k pairwise flavor distances. We propose a low-dimensional concept embedding algorithm that combines human experience with automatic machine similarity kernels. We demonstrate that this shared concept embedding space improves upon separate embedding spaces for coarse flavor classification (alcohol percentage, country, grape, price, rating) and aligns with the intricate human perception of flavor.

Artificial neural networks suffer from catastrophic forgetting when they are sequentially trained on multiple tasks. To overcome this problem, we present a novel approach based on task-conditioned hypernetworks, i.e., networks that generate the weights of a target model based on task identity. Continual learning (CL) is less difficult for this class of models thanks to a simple key feature: instead of recalling the input-output relations of all previously seen data, task-conditioned hypernetworks only require rehearsing task-specific weight realizations, which can be maintained in memory using a simple regularizer. Besides achieving state-of-the-art performance on standard CL benchmarks, additional experiments on long task sequences reveal that task-conditioned hypernetworks display a very large capacity to retain previous memories. Notably, such long memory lifetimes are achieved in a compressive regime, when the number of trainable hypernetwork weights is comparable or smaller than target network size. We provide insight into the structure of low-dimensional task embedding spaces (the input space of the hypernetwork) and show that task-conditioned hypernetworks demonstrate transfer learning. Finally, forward information transfer is further supported by empirical results on a challenging CL benchmark based on the CIFAR-10/100 image datasets.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Mining parallel document pairs poses a significant challenge because existing sentence embedding models often have limited context windows, preventing them from effectively capturing document-level information. Another overlooked issue is the lack of concrete evaluation benchmarks comprising high-quality parallel document pairs for assessing document-level mining approaches, particularly for Indic languages. In this study, we introduce Pralekha, a large-scale benchmark for document-level alignment evaluation. Pralekha includes over 2 million documents, with a 1:2 ratio of unaligned to aligned pairs, covering 11 Indic languages and English. Using Pralekha, we evaluate various document-level mining approaches across three dimensions: the embedding models, the granularity levels, and the alignment algorithm. To address the challenge of aligning documents using sentence and chunk-level alignments, we propose a novel scoring method, Document Alignment Coefficient (DAC). DAC demonstrates substantial improvements over baseline pooling approaches, particularly in noisy scenarios, achieving average gains of 20-30% in precision and 15-20% in F1 score. These results highlight DAC's effectiveness in parallel document mining for Indic languages.

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

Given the success of Large Language Models (LLMs), there has been considerable interest in studying the properties of model activations. The literature overwhelmingly agrees that LLM representations are dominated by a few ``outlier dimensions'' with exceedingly high variance and magnitude. Several studies in Natural Language Processing (NLP) have sought to mitigate the impact of such outlier dimensions and force LLMs to be isotropic (i.e., have uniform variance across all dimensions in embedding space). Isotropy is thought to be a desirable property for LLMs that improves model performance and more closely aligns textual representations with human intuition. However, many of the claims regarding isotropy in NLP have been based on the average cosine similarity of embeddings, which has recently been shown to be a flawed measure of isotropy. In this paper, we propose I-STAR: IsoScore*-based STable Anisotropic Regularization, a novel regularization method that can be used to increase or decrease levels of isotropy in embedding space during training. I-STAR uses IsoScore*, the first accurate measure of isotropy that is both differentiable and stable on mini-batch computations. In contrast to several previous works, we find that decreasing isotropy in contextualized embeddings improves performance on the majority of tasks and models considered in this paper.

Quantum embedding with transformers is a novel and promising architecture for quantum machine learning to deliver exceptional capability on near-term devices or simulators. The research incorporated a vision transformer (ViT) to advance quantum significantly embedding ability and results for a single qubit classifier with around 3 percent in the median F1 score on the BirdCLEF-2021, a challenging high-dimensional dataset. The study showcases and analyzes empirical evidence that our transformer-based architecture is a highly versatile and practical approach to modern quantum machine learning problems.

Safety backdoor attacks in large language models (LLMs) enable the stealthy triggering of unsafe behaviors while evading detection during normal interactions. The high dimensionality of potential triggers in the token space and the diverse range of malicious behaviors make this a critical challenge. We present BEEAR, a mitigation approach leveraging the insight that backdoor triggers induce relatively uniform drifts in the model's embedding space. Our bi-level optimization method identifies universal embedding perturbations that elicit unwanted behaviors and adjusts the model parameters to reinforce safe behaviors against these perturbations. Experiments show BEEAR reduces the success rate of RLHF time backdoor attacks from >95% to <1% and from 47% to 0% for instruction-tuning time backdoors targeting malicious code generation, without compromising model utility. Requiring only defender-defined safe and unwanted behaviors, BEEAR represents a step towards practical defenses against safety backdoors in LLMs, providing a foundation for further advancements in AI safety and security.

This work introduces a benchmark assessing the performance of clustering German text embeddings in different domains. This benchmark is driven by the increasing use of clustering neural text embeddings in tasks that require the grouping of texts (such as topic modeling) and the need for German resources in existing benchmarks. We provide an initial analysis for a range of pre-trained mono- and multilingual models evaluated on the outcome of different clustering algorithms. Results include strong performing mono- and multilingual models. Reducing the dimensions of embeddings can further improve clustering. Additionally, we conduct experiments with continued pre-training for German BERT models to estimate the benefits of this additional training. Our experiments suggest that significant performance improvements are possible for short text. All code and datasets are publicly available.

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x in R^d per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality epsilon-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5times fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical contributions that are tailored to the numerical properties of time-series data and allow the model to scale to large datasets, e.g., millions of temporal sequences. We adopt the Transformer architecture by first partitioning the input into non-overlapping windows. Each window is then characterized by its normalized shape and two scalar values denoting the mean and standard deviation within each window. To embed scalar values that may possess arbitrary numerical scales to high-dimensional vectors, we propose a numerically multi-scaled embedding module enumerating all possible scales for the scalar values. The model undergoes pretraining using the proposed numerically multi-scaled embedding with a simple contrastive objective on a large-scale dataset containing over a million sequences. We study its transfer performance on a number of univariate and multivariate classification benchmarks. Our method exhibits remarkable improvement against previous representation learning approaches and establishes the new state of the art, even compared with domain-specific non-learning-based methods.

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines.

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

Speaker modeling is essential for many related tasks, such as speaker recognition and speaker diarization. The dominant modeling approach is fixed-dimensional vector representation, i.e., speaker embedding. This paper introduces a research and production oriented speaker embedding learning toolkit, Wespeaker. Wespeaker contains the implementation of scalable data management, state-of-the-art speaker embedding models, loss functions, and scoring back-ends, with highly competitive results achieved by structured recipes which were adopted in the winning systems in several speaker verification challenges. The application to other downstream tasks such as speaker diarization is also exhibited in the related recipe. Moreover, CPU- and GPU-compatible deployment codes are integrated for production-oriented development. The toolkit is publicly available at https://github.com/wenet-e2e/wespeaker.

Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods.

Length extrapolation algorithms based on Rotary position embedding (RoPE) have shown promising results in extending the context length of language models. However, understanding how position embedding can capture longer-range contextual information remains elusive. Based on the intuition that different dimensions correspond to different frequency of changes in RoPE encoding, we conducted a dimension-level analysis to investigate the correlation between a hidden dimension of an attention head and its contribution to capturing long-distance dependencies. Using our correlation metric, we identified a particular type of attention heads, which we named Positional Heads, from various length-extrapolated models. These heads exhibit a strong focus on long-range information interaction and play a pivotal role in long input processing, as evidence by our ablation. We further demonstrate the correlation between the efficiency of length extrapolation and the extension of the high-dimensional attention allocation of these heads. The identification of Positional Heads provides insights for future research in long-text comprehension.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

Weakly supervised semantic segmentation (WSSS) typically utilizes limited semantic annotations to obtain initial Class Activation Maps (CAMs). However, due to the inadequate coupling between class activation responses and semantic information in high-dimensional space, the CAM is prone to object co-occurrence or under-activation, resulting in inferior recognition accuracy. To tackle this issue, we propose DOEI, Dual Optimization of Embedding Information, a novel approach that reconstructs embedding representations through semantic-aware attention weight matrices to optimize the expression capability of embedding information. Specifically, DOEI amplifies tokens with high confidence and suppresses those with low confidence during the class-to-patch interaction. This alignment of activation responses with semantic information strengthens the propagation and decoupling of target features, enabling the generated embeddings to more accurately represent target features in high-level semantic space. In addition, we propose a hybrid-feature alignment module in DOEI that combines RGB values, embedding-guided features, and self-attention weights to increase the reliability of candidate tokens. Comprehensive experiments show that DOEI is an effective plug-and-play module that empowers state-of-the-art visual transformer-based WSSS models to significantly improve the quality of CAMs and segmentation performance on popular benchmarks, including PASCAL VOC (+3.6%, +1.5%, +1.2% mIoU) and MS COCO (+1.2%, +1.6% mIoU). Code will be available at https://github.com/AIGeeksGroup/DOEI.

We propose a new character-based text classification framework for non-alphabetic languages, such as Chinese and Japanese. Our framework consists of a variational character encoder (VCE) and character-level text classifier. The VCE is composed of a beta-variational auto-encoder (beta-VAE) that learns the proposed glyph-aware disentangled character embedding (GDCE). Since our GDCE provides zero-mean unit-variance character embeddings that are dimensionally independent, it is applicable for our interpretable data augmentation, namely, semantic sub-character augmentation (SSA). In this paper, we evaluated our framework using Japanese text classification tasks at the document- and sentence-level. We confirmed that our GDCE and SSA not only provided embedding interpretability but also improved the classification performance. Our proposal achieved a competitive result to the state-of-the-art model while also providing model interpretability. Our code is available on https://github.com/IyatomiLab/GDCE-SSA

A crucial component of many deep learning applications (such as FAQ and RAG) is dense retrieval, in which embedding models are used to convert raw text to numerical vectors and then get the most similar text by MIPS (Maximum Inner Product Search). Some text embedding benchmarks (e.g. MTEB, BEIR, and AIR-Bench) have been established to evaluate embedding models accurately. Thanks to these benchmarks, we can use SOTA models; however, the deployment and application of these models in industry were hampered by their large vector dimensions and numerous parameters. To alleviate this problem, 1) we present a distillation technique that can enable a smaller student model to achieve good performance. 2) Inspired by MRL we present a training approach of reducing the vector dimensions based on its own vectors or its teacher vectors. 3) We do simple yet effective alignment training between images and text to make our model a multimodal encoder. We trained Stella and Jasper models using the technologies above and achieved high scores on the MTEB leaderboard. We release the model and data at Hugging Face Hub (https://huggingface.co/infgrad/jasper_en_vision_language_v1) and the training logs are at https://api.wandb.ai/links/dunnzhang0/z8jqoqpb.

In this study, we present an investigation into the anisotropy dynamics and intrinsic dimension of embeddings in transformer architectures, focusing on the dichotomy between encoders and decoders. Our findings reveal that the anisotropy profile in transformer decoders exhibits a distinct bell-shaped curve, with the highest anisotropy concentrations in the middle layers. This pattern diverges from the more uniformly distributed anisotropy observed in encoders. In addition, we found that the intrinsic dimension of embeddings increases in the initial phases of training, indicating an expansion into higher-dimensional space. Which is then followed by a compression phase towards the end of training with dimensionality decrease, suggesting a refinement into more compact representations. Our results provide fresh insights to the understanding of encoders and decoders embedding properties.

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

Large-scale embedding-based retrieval (EBR) is the cornerstone of search-related industrial applications. Given a user query, the system of EBR aims to identify relevant information from a large corpus of documents that may be tens or hundreds of billions in size. The storage and computation turn out to be expensive and inefficient with massive documents and high concurrent queries, making it difficult to further scale up. To tackle the challenge, we propose a binary embedding-based retrieval (BEBR) engine equipped with a recurrent binarization algorithm that enables customized bits per dimension. Specifically, we compress the full-precision query and document embeddings, formulated as float vectors in general, into a composition of multiple binary vectors using a lightweight transformation model with residual multilayer perception (MLP) blocks. We can therefore tailor the number of bits for different applications to trade off accuracy loss and cost savings. Importantly, we enable task-agnostic efficient training of the binarization model using a new embedding-to-embedding strategy. We also exploit the compatible training of binary embeddings so that the BEBR engine can support indexing among multiple embedding versions within a unified system. To further realize efficient search, we propose Symmetric Distance Calculation (SDC) to achieve lower response time than Hamming codes. We successfully employed the introduced BEBR to Tencent products, including Sogou, Tencent Video, QQ World, etc. The binarization algorithm can be seamlessly generalized to various tasks with multiple modalities. Extensive experiments on offline benchmarks and online A/B tests demonstrate the efficiency and effectiveness of our method, significantly saving 30%~50% index costs with almost no loss of accuracy at the system level.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and/or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2% vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning.

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).

We develop a portfolio allocation framework that leverages deep learning techniques to address challenges arising from high-dimensional, non-stationary, and low-signal-to-noise market information. Our approach includes a dynamic embedding method that reduces the non-stationary, high-dimensional state space into a lower-dimensional representation. We design a reinforcement learning (RL) framework that integrates generative autoencoders and online meta-learning to dynamically embed market information, enabling the RL agent to focus on the most impactful parts of the state space for portfolio allocation decisions. Empirical analysis based on the top 500 U.S. stocks demonstrates that our framework outperforms common portfolio benchmarks and the predict-then-optimize (PTO) approach using machine learning, particularly during periods of market stress. Traditional factor models do not fully explain this superior performance. The framework's ability to time volatility reduces its market exposure during turbulent times. Ablation studies confirm the robustness of this performance across various reinforcement learning algorithms. Additionally, the embedding and meta-learning techniques effectively manage the complexities of high-dimensional, noisy, and non-stationary financial data, enhancing both portfolio performance and risk management.

In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is a methodology designed for mapping observations of the same object, related by rigid transformations, into a single low-dimensional linear subspace. This process yields a transformation-invariant representation of the observations, with its matrix form representation being covariant (i.e. equivariant) with the transformation. We extend the UME framework by introducing a UME-compatible feature extraction method augmented with a unique UME contrastive loss and a sampling equalizer. These components are integrated into a comprehensive and robust registration pipeline, named UMERegRobust. We propose the RotKITTI registration benchmark, specifically tailored to evaluate registration methods for scenarios involving large rotations. UMERegRobust achieves better than state-of-the-art performance on the KITTI benchmark, especially when strict precision of (1{\deg}, 10cm) is considered (with an average gain of +9%), and notably outperform SOTA methods on the RotKITTI benchmark (with +45% gain compared the most recent SOTA method).

While Rotary Position Embedding (RoPE) and its variants are widely adopted for their long-context capabilities, the extension of the 1D RoPE to video, with its complex spatio-temporal structure, remains an open challenge. This work first introduces a comprehensive analysis that identifies four key characteristics essential for the effective adaptation of RoPE to video, which have not been fully considered in prior work. As part of our analysis, we introduce a challenging V-NIAH-D (Visual Needle-In-A-Haystack with Distractors) task, which adds periodic distractors into V-NIAH. The V-NIAH-D task demonstrates that previous RoPE variants, lacking appropriate temporal dimension allocation, are easily misled by distractors. Based on our analysis, we introduce VideoRoPE, with a 3D structure designed to preserve spatio-temporal relationships. VideoRoPE features low-frequency temporal allocation to mitigate periodic oscillations, a diagonal layout to maintain spatial symmetry, and adjustable temporal spacing to decouple temporal and spatial indexing. VideoRoPE consistently surpasses previous RoPE variants, across diverse downstream tasks such as long video retrieval, video understanding, and video hallucination. Our code will be available at https://github.com/Wiselnn570/VideoRoPE{https://github.com/Wiselnn570/VideoRoPE}.

Predicting high-dimensional or extreme multilabels, such as in medical coding, requires both accuracy and interpretability. Existing works often rely on local interpretability methods, failing to provide comprehensive explanations of the overall mechanism behind each label prediction within a multilabel set. We propose a mechanistic interpretability module called DIctionary Label Attention (\method) that disentangles uninterpretable dense embeddings into a sparse embedding space, where each nonzero element (a dictionary feature) represents a globally learned medical concept. Through human evaluations, we show that our sparse embeddings are more human understandable than its dense counterparts by at least 50 percent. Our automated dictionary feature identification pipeline, leveraging large language models (LLMs), uncovers thousands of learned medical concepts by examining and summarizing the highest activating tokens for each dictionary feature. We represent the relationships between dictionary features and medical codes through a sparse interpretable matrix, enhancing the mechanistic and global understanding of the model's predictions while maintaining competitive performance and scalability without extensive human annotation.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

Image clustering is one of the most important computer vision applications, which has been extensively studied in literature. However, current clustering methods mostly suffer from lack of efficiency and scalability when dealing with large-scale and high-dimensional data. In this paper, we propose a new clustering model, called DEeP Embedded RegularIzed ClusTering (DEPICT), which efficiently maps data into a discriminative embedding subspace and precisely predicts cluster assignments. DEPICT generally consists of a multinomial logistic regression function stacked on top of a multi-layer convolutional autoencoder. We define a clustering objective function using relative entropy (KL divergence) minimization, regularized by a prior for the frequency of cluster assignments. An alternating strategy is then derived to optimize the objective by updating parameters and estimating cluster assignments. Furthermore, we employ the reconstruction loss functions in our autoencoder, as a data-dependent regularization term, to prevent the deep embedding function from overfitting. In order to benefit from end-to-end optimization and eliminate the necessity for layer-wise pretraining, we introduce a joint learning framework to minimize the unified clustering and reconstruction loss functions together and train all network layers simultaneously. Experimental results indicate the superiority and faster running time of DEPICT in real-world clustering tasks, where no labeled data is available for hyper-parameter tuning.

This work presents a novel framework for training Arabic nested embedding models through Matryoshka Embedding Learning, leveraging multilingual, Arabic-specific, and English-based models, to highlight the power of nested embeddings models in various Arabic NLP downstream tasks. Our innovative contribution includes the translation of various sentence similarity datasets into Arabic, enabling a comprehensive evaluation framework to compare these models across different dimensions. We trained several nested embedding models on the Arabic Natural Language Inference triplet dataset and assessed their performance using multiple evaluation metrics, including Pearson and Spearman correlations for cosine similarity, Manhattan distance, Euclidean distance, and dot product similarity. The results demonstrate the superior performance of the Matryoshka embedding models, particularly in capturing semantic nuances unique to the Arabic language. Results demonstrated that Arabic Matryoshka embedding models have superior performance in capturing semantic nuances unique to the Arabic language, significantly outperforming traditional models by up to 20-25\% across various similarity metrics. These results underscore the effectiveness of language-specific training and highlight the potential of Matryoshka models in enhancing semantic textual similarity tasks for Arabic NLP.

Embedding models have been crucial in enabling various downstream tasks such as semantic similarity, information retrieval, and clustering. Recently, there has been a surge of interest in developing universal text embedding models that can generalize across tasks (e.g., MTEB). However, progress in learning universal multimodal embedding models has been relatively slow despite their importance. In this work, we aim to explore the potential for building universal embeddings capable of handling a wide range of downstream tasks. Our contributions are twofold: (1) MMEB (Massive Multimodal Embedding Benchmark), which covers 4 meta-tasks (i.e. classification, visual question answering, multimodal retrieval, and visual grounding) and 36 datasets, including 20 training and 16 evaluation datasets, and (2) VLM2Vec (Vision-Language Model -> Vector), a contrastive training framework that converts any state-of-the-art vision-language model into an embedding model via training on MMEB. Unlike previous models such as CLIP and BLIP, VLM2Vec can process any combination of images and text to generate a fixed-dimensional vector based on task instructions. We build a series of VLM2Vec models on Phi-3.5-V and evaluate them on MMEB's evaluation split. Our results show that \model achieves an absolute average improvement of 10% to 20% over existing multimodal embedding models on both in-distribution and out-of-distribution datasets in MMEB.

In recent years, exploiting the domain-specific underlying structure of data and its generative factors for representation learning has shown success in various use-case agnostic applications. However, the diversity and complexity of tabular data have made it challenging to represent these structures in a latent space through multi-dimensional vectors. We design an autoencoder-based framework for building general purpose embeddings, we assess the performance of different autoencoder architectures, and show simpler models outperform complex ones in embedding highly complex tabular data. We apply our framework to produce plug-and-play, rich, and anonymized embeddings representing AWS customers for usage in any model, saving up to 45% of development time, and observe significant improvements in downstream models. Moreover, we propose a significant improvement to the calculation of reconstruction loss for multi-layer contractive autoencoders (CAE) by calculating the Jacobian of the entire encoder leading to a 15% improvement in reconstruction quality when compared to a stacked CAE.

Vector search systems, pivotal in AI applications, often rely on the Hierarchical Navigable Small Worlds (HNSW) algorithm. However, the behaviour of HNSW under real-world scenarios using vectors generated with deep learning models remains under-explored. Existing Approximate Nearest Neighbours (ANN) benchmarks and research typically has an over-reliance on simplistic datasets like MNIST or SIFT1M and fail to reflect the complexity of current use-cases. Our investigation focuses on HNSW's efficacy across a spectrum of datasets, including synthetic vectors tailored to mimic specific intrinsic dimensionalities, widely-used retrieval benchmarks with popular embedding models, and proprietary e-commerce image data with CLIP models. We survey the most popular HNSW vector databases and collate their default parameters to provide a realistic fixed parameterisation for the duration of the paper. We discover that the recall of approximate HNSW search, in comparison to exact K Nearest Neighbours (KNN) search, is linked to the vector space's intrinsic dimensionality and significantly influenced by the data insertion sequence. Our methodology highlights how insertion order, informed by measurable properties such as the pointwise Local Intrinsic Dimensionality (LID) or known categories, can shift recall by up to 12 percentage points. We also observe that running popular benchmark datasets with HNSW instead of KNN can shift rankings by up to three positions for some models. This work underscores the need for more nuanced benchmarks and design considerations in developing robust vector search systems using approximate vector search algorithms. This study presents a number of scenarios with varying real world applicability which aim to better increase understanding and future development of ANN algorithms and embedding

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

It is challenging for humans -- particularly those living with physical disabilities -- to control high-dimensional, dexterous robots. Prior work explores learning embedding functions that map a human's low-dimensional inputs (e.g., via a joystick) to complex, high-dimensional robot actions for assistive teleoperation; however, a central problem is that there are many more high-dimensional actions than available low-dimensional inputs. To extract the correct action and maximally assist their human controller, robots must reason over their context: for example, pressing a joystick down when interacting with a coffee cup indicates a different action than when interacting with knife. In this work, we develop assistive robots that condition their latent embeddings on visual inputs. We explore a spectrum of visual encoders and show that incorporating object detectors pretrained on small amounts of cheap, easy-to-collect structured data enables i) accurately and robustly recognizing the current context and ii) generalizing control embeddings to new objects and tasks. In user studies with a high-dimensional physical robot arm, participants leverage this approach to perform new tasks with unseen objects. Our results indicate that structured visual representations improve few-shot performance and are subjectively preferred by users.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Rotary Position Embedding (RoPE) enables each attention head to capture multi-frequency information along the sequence dimension and is widely applied in foundation models. However, the nonlinearity introduced by RoPE complicates optimization of the key state in the Key-Value (KV) cache for RoPE-based attention. Existing KV cache compression methods typically store key state before rotation and apply the transformation during decoding, introducing additional computational overhead. This paper introduces EliteKV, a flexible modification framework for RoPE-based models supporting variable KV cache compression ratios. EliteKV first identifies the intrinsic frequency preference of each head using RoPElite, selectively restoring linearity to certain dimensions of key within attention computation. Building on this, joint low-rank compression of key and value enables partial cache sharing. Experimental results show that with minimal uptraining on only 0.6% of the original training data, RoPE-based models achieve a 75% reduction in KV cache size while preserving performance within a negligible margin. Furthermore, EliteKV consistently performs well across models of different scales within the same family.

Instruction-following is crucial for building AI agents with large language models (LLMs), as these models must adhere strictly to user-provided constraints and guidelines. However, LLMs often fail to follow even simple and clear instructions. To improve instruction-following behavior and prevent undesirable outputs, a deeper understanding of how LLMs' internal states relate to these outcomes is required. Our analysis of LLM internal states reveal a dimension in the input embedding space linked to successful instruction-following. We demonstrate that modifying representations along this dimension improves instruction-following success rates compared to random changes, without compromising response quality. Further investigation reveals that this dimension is more closely related to the phrasing of prompts rather than the inherent difficulty of the task or instructions. This discovery also suggests explanations for why LLMs sometimes fail to follow clear instructions and why prompt engineering is often effective, even when the content remains largely unchanged. This work provides insight into the internal workings of LLMs' instruction-following, paving the way for reliable LLM agents.

While static word embedding models are known to represent linguistic analogies as parallel lines in high-dimensional space, the underlying mechanism as to why they result in such geometric structures remains obscure. We find that an elementary contrastive-style method employed over distributional information performs competitively with popular word embedding models on analogy recovery tasks, while achieving dramatic speedups in training time. Further, we demonstrate that a contrastive loss is sufficient to create these parallel structures in word embeddings, and establish a precise relationship between the co-occurrence statistics and the geometric structure of the resulting word embeddings.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

3D point clouds play a pivotal role in outdoor scene perception, especially in the context of autonomous driving. Recent advancements in 3D LiDAR segmentation often focus intensely on the spatial positioning and distribution of points for accurate segmentation. However, these methods, while robust in variable conditions, encounter challenges due to sole reliance on coordinates and point intensity, leading to poor isometric invariance and suboptimal segmentation. To tackle this challenge, our work introduces Range-Aware Pointwise Distance Distribution (RAPiD) features and the associated RAPiD-Seg architecture. Our RAPiD features exhibit rigid transformation invariance and effectively adapt to variations in point density, with a design focus on capturing the localized geometry of neighboring structures. They utilize inherent LiDAR isotropic radiation and semantic categorization for enhanced local representation and computational efficiency, while incorporating a 4D distance metric that integrates geometric and surface material reflectivity for improved semantic segmentation. To effectively embed high-dimensional RAPiD features, we propose a double-nested autoencoder structure with a novel class-aware embedding objective to encode high-dimensional features into manageable voxel-wise embeddings. Additionally, we propose RAPiD-Seg which incorporates a channel-wise attention fusion and two effective RAPiD-Seg variants, further optimizing the embedding for enhanced performance and generalization. Our method outperforms contemporary LiDAR segmentation work in terms of mIoU on SemanticKITTI (76.1) and nuScenes (83.6) datasets.

By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all d--dimensional Grassmannians into a stratified space of covariance matrices. We observe that Grassmannians constitute the lowest dimensional skeleton of the stratification while it is possible to define a Riemaniann metric on the highest dimensional and dense stratum, such a metric being compatible with the global stratification. With such a Riemaniann metric at hand, it is possible to look for geodesics between two linear subspaces of different dimensions that do not go through higher dimensional linear subspaces as would euclidean geodesics. Building upon the proposed embedding of Grassmannians into the stratified space of covariance matrices, we generalize the concept of varifolds to what we call flagfolds in order to model multi-dimensional shapes.

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

Conversational systems often rely on embedding models for intent classification and intent clustering tasks. The advent of Large Language Models (LLMs), which enable instructional embeddings allowing one to adjust semantics over the embedding space using prompts, are being viewed as a panacea for these downstream conversational tasks. However, traditional evaluation benchmarks rely solely on task metrics that don't particularly measure gaps related to semantic understanding. Thus, we propose an intent semantic toolkit that gives a more holistic view of intent embedding models by considering three tasks -- (1) intent classification, (2) intent clustering, and (3) a novel triplet task. The triplet task gauges the model's understanding of two semantic concepts paramount in real-world conversational systems -- negation and implicature. We observe that current embedding models fare poorly in semantic understanding of these concepts. To address this, we propose a pre-training approach to improve the embedding model by leveraging augmentation with data generated by an auto-regressive model and a contrastive loss term. Our approach improves the semantic understanding of the intent embedding model on the aforementioned linguistic dimensions while slightly effecting their performance on downstream task metrics.

We introduce StyleGaussian, a novel 3D style transfer technique that allows instant transfer of any image's style to a 3D scene at 10 frames per second (fps). Leveraging 3D Gaussian Splatting (3DGS), StyleGaussian achieves style transfer without compromising its real-time rendering ability and multi-view consistency. It achieves instant style transfer with three steps: embedding, transfer, and decoding. Initially, 2D VGG scene features are embedded into reconstructed 3D Gaussians. Next, the embedded features are transformed according to a reference style image. Finally, the transformed features are decoded into the stylized RGB. StyleGaussian has two novel designs. The first is an efficient feature rendering strategy that first renders low-dimensional features and then maps them into high-dimensional features while embedding VGG features. It cuts the memory consumption significantly and enables 3DGS to render the high-dimensional memory-intensive features. The second is a K-nearest-neighbor-based 3D CNN. Working as the decoder for the stylized features, it eliminates the 2D CNN operations that compromise strict multi-view consistency. Extensive experiments show that StyleGaussian achieves instant 3D stylization with superior stylization quality while preserving real-time rendering and strict multi-view consistency. Project page: https://kunhao-liu.github.io/StyleGaussian/

This paper describes RETVec, an efficient, resilient, and multilingual text vectorizer designed for neural-based text processing. RETVec combines a novel character encoding with an optional small embedding model to embed words into a 256-dimensional vector space. The RETVec embedding model is pre-trained using pair-wise metric learning to be robust against typos and character-level adversarial attacks. In this paper, we evaluate and compare RETVec to state-of-the-art vectorizers and word embeddings on popular model architectures and datasets. These comparisons demonstrate that RETVec leads to competitive, multilingual models that are significantly more resilient to typos and adversarial text attacks. RETVec is available under the Apache 2 license at https://github.com/google-research/retvec.

Modern image retrieval methods typically rely on fine-tuning pre-trained encoders to extract image-level descriptors. However, the most widely used models are pre-trained on ImageNet-1K with limited classes. The pre-trained feature representation is therefore not universal enough to generalize well to the diverse open-world classes. In this paper, we first cluster the large-scale LAION400M into one million pseudo classes based on the joint textual and visual features extracted by the CLIP model. Due to the confusion of label granularity, the automatically clustered dataset inevitably contains heavy inter-class conflict. To alleviate such conflict, we randomly select partial inter-class prototypes to construct the margin-based softmax loss. To further enhance the low-dimensional feature representation, we randomly select partial feature dimensions when calculating the similarities between embeddings and class-wise prototypes. The dual random partial selections are with respect to the class dimension and the feature dimension of the prototype matrix, making the classification conflict-robust and the feature embedding compact. Our method significantly outperforms state-of-the-art unsupervised and supervised image retrieval approaches on multiple benchmarks. The code and pre-trained models are released to facilitate future research https://github.com/deepglint/unicom.

Effective approaches that can scale embedding model depth (i.e. layers) and embedding size allow for the creation of models that are highly scalable across different computational resources and task requirements. While the recently proposed 2D Matryoshka training approach can efficiently produce a single embedding model such that its sub-layers and sub-dimensions can measure text similarity, its effectiveness is significantly worse than if smaller models were trained separately. To address this issue, we propose Starbucks, a new training strategy for Matryoshka-like embedding models, which encompasses both the fine-tuning and pre-training phases. For the fine-tuning phase, we discover that, rather than sampling a random sub-layer and sub-dimensions for each training steps, providing a fixed list of layer-dimension pairs, from small size to large sizes, and computing the loss across all pairs significantly improves the effectiveness of 2D Matryoshka embedding models, bringing them on par with their separately trained counterparts. To further enhance performance, we introduce a new pre-training strategy, which applies masked autoencoder language modelling to sub-layers and sub-dimensions during pre-training, resulting in a stronger backbone for subsequent fine-tuning of the embedding model. Experimental results on both semantic text similarity and retrieval benchmarks demonstrate that the proposed pre-training and fine-tuning strategies significantly improved the effectiveness over 2D Matryoshka models, enabling Starbucks models to perform more efficiently and effectively than separately trained models.

This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering logical comparison questions (e.g., Was Cristiano born before Messi?). We first identified these subspaces using partial least squares regression, which effectively encodes the numerical attributes associated with the entities in comparison prompts. Further, we demonstrate causality by intervening in these subspaces to manipulate hidden states, thereby altering the LLM's comparison outcomes. Experimental results show that our findings hold for different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning.

We ask whether multilingual language models trained on unbalanced, English-dominated corpora use English as an internal pivot language -- a question of key importance for understanding how language models function and the origins of linguistic bias. Focusing on the Llama-2 family of transformer models, our study uses carefully constructed non-English prompts with a unique correct single-token continuation. From layer to layer, transformers gradually map an input embedding of the final prompt token to an output embedding from which next-token probabilities are computed. Tracking intermediate embeddings through their high-dimensional space reveals three distinct phases, whereby intermediate embeddings (1) start far away from output token embeddings; (2) already allow for decoding a semantically correct next token in the middle layers, but give higher probability to its version in English than in the input language; (3) finally move into an input-language-specific region of the embedding space. We cast these results into a conceptual model where the three phases operate in "input space", "concept space", and "output space", respectively. Crucially, our evidence suggests that the abstract "concept space" lies closer to English than to other languages, which may have important consequences regarding the biases held by multilingual language models.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

Despite recent successes in hair acquisition that fits a high-dimensional hair model to a specific input subject, generative hair models, which establish general embedding spaces for encoding, editing, and sampling diverse hairstyles, are way less explored. In this paper, we present GroomGen, the first generative model designed for hair geometry composed of highly-detailed dense strands. Our approach is motivated by two key ideas. First, we construct hair latent spaces covering both individual strands and hairstyles. The latent spaces are compact, expressive, and well-constrained for high-quality and diverse sampling. Second, we adopt a hierarchical hair representation that parameterizes a complete hair model to three levels: single strands, sparse guide hairs, and complete dense hairs. This representation is critical to the compactness of latent spaces, the robustness of training, and the efficiency of inference. Based on this hierarchical latent representation, our proposed pipeline consists of a strand-VAE and a hairstyle-VAE that encode an individual strand and a set of guide hairs to their respective latent spaces, and a hybrid densification step that populates sparse guide hairs to a dense hair model. GroomGen not only enables novel hairstyle sampling and plausible hairstyle interpolation, but also supports interactive editing of complex hairstyles, or can serve as strong data-driven prior for hairstyle reconstruction from images. We demonstrate the superiority of our approach with qualitative examples of diverse sampled hairstyles and quantitative evaluation of generation quality regarding every single component and the entire pipeline.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric prediction. In this paper, we provide one of the first comprehensive investigations into embedding-based regression and demonstrate that LLM embeddings as features can be better for high-dimensional regression tasks than using traditional feature engineering. This regression performance can be explained in part due to LLM embeddings over numeric data inherently preserving Lipschitz continuity over the feature space. Furthermore, we quantify the contribution of different model effects, most notably model size and language understanding, which we find surprisingly do not always improve regression performance.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Human biases are ubiquitous but not uniform: disparities exist across linguistic, cultural, and societal borders. As large amounts of recent literature suggest, language models (LMs) trained on human data can reflect and often amplify the effects of these social biases. However, the vast majority of existing studies on bias are heavily skewed towards Western and European languages. In this work, we scale the Word Embedding Association Test (WEAT) to 24 languages, enabling broader studies and yielding interesting findings about LM bias. We additionally enhance this data with culturally relevant information for each language, capturing local contexts on a global scale. Further, to encompass more widely prevalent societal biases, we examine new bias dimensions across toxicity, ableism, and more. Moreover, we delve deeper into the Indian linguistic landscape, conducting a comprehensive regional bias analysis across six prevalent Indian languages. Finally, we highlight the significance of these social biases and the new dimensions through an extensive comparison of embedding methods, reinforcing the need to address them in pursuit of more equitable language models. All code, data and results are available here: https://github.com/iamshnoo/weathub.

We study how multilingual sentence representations capture European countries and occupations and how this differs across European languages. We prompt the models with templated sentences that we machine-translate into 12 European languages and analyze the most prominent dimensions in the embeddings.Our analysis reveals that the most prominent feature in the embedding is the geopolitical distinction between Eastern and Western Europe and the country's economic strength in terms of GDP. When prompted specifically for job prestige, the embedding space clearly distinguishes high and low-prestige jobs. The occupational dimension is uncorrelated with the most dominant country dimensions in three out of four studied models. The exception is a small distilled model that exhibits a connection between occupational prestige and country of origin, which is a potential source of nationality-based discrimination. Our findings are consistent across languages.

Language models pre-trained on biomedical corpora, such as BioBERT, have recently shown promising results on downstream biomedical tasks. Many existing pre-trained models, on the other hand, are resource-intensive and computationally heavy owing to factors such as embedding size, hidden dimension, and number of layers. The natural language processing (NLP) community has developed numerous strategies to compress these models utilising techniques such as pruning, quantisation, and knowledge distillation, resulting in models that are considerably faster, smaller, and subsequently easier to use in practice. By the same token, in this paper we introduce six lightweight models, namely, BioDistilBERT, BioTinyBERT, BioMobileBERT, DistilBioBERT, TinyBioBERT, and CompactBioBERT which are obtained either by knowledge distillation from a biomedical teacher or continual learning on the Pubmed dataset via the Masked Language Modelling (MLM) objective. We evaluate all of our models on three biomedical tasks and compare them with BioBERT-v1.1 to create efficient lightweight models that perform on par with their larger counterparts. All the models will be publicly available on our Huggingface profile at https://huggingface.co/nlpie and the codes used to run the experiments will be available at https://github.com/nlpie-research/Compact-Biomedical-Transformers.

Large pre-trained transformers are on top of contemporary semantic segmentation benchmarks, but come with high computational cost and a lengthy training. To lift this constraint, we look at efficient semantic segmentation from a perspective of comprehensive knowledge distillation and consider to bridge the gap between multi-source knowledge extractions and transformer-specific patch embeddings. We put forward the Transformer-based Knowledge Distillation (TransKD) framework which learns compact student transformers by distilling both feature maps and patch embeddings of large teacher transformers, bypassing the long pre-training process and reducing the FLOPs by >85.0%. Specifically, we propose two fundamental and two optimization modules: (1) Cross Selective Fusion (CSF) enables knowledge transfer between cross-stage features via channel attention and feature map distillation within hierarchical transformers; (2) Patch Embedding Alignment (PEA) performs dimensional transformation within the patchifying process to facilitate the patch embedding distillation; (3) Global-Local Context Mixer (GL-Mixer) extracts both global and local information of a representative embedding; (4) Embedding Assistant (EA) acts as an embedding method to seamlessly bridge teacher and student models with the teacher's number of channels. Experiments on Cityscapes, ACDC, and NYUv2 datasets show that TransKD outperforms state-of-the-art distillation frameworks and rivals the time-consuming pre-training method. Code is available at https://github.com/RuipingL/TransKD.

Whitening loss offers a theoretical guarantee against feature collapse in self-supervised learning (SSL) with joint embedding architectures. Typically, it involves a hard whitening approach, transforming the embedding and applying loss to the whitened output. In this work, we introduce Spectral Transformation (ST), a framework to modulate the spectrum of embedding and to seek for functions beyond whitening that can avoid dimensional collapse. We show that whitening is a special instance of ST by definition, and our empirical investigations unveil other ST instances capable of preventing collapse. Additionally, we propose a novel ST instance named IterNorm with trace loss (INTL). Theoretical analysis confirms INTL's efficacy in preventing collapse and modulating the spectrum of embedding toward equal-eigenvalues during optimization. Our experiments on ImageNet classification and COCO object detection demonstrate INTL's potential in learning superior representations. The code is available at https://github.com/winci-ai/INTL.

We present a meta-learning framework for learning new visual concepts quickly, from just one or a few examples, guided by multiple naturally occurring data streams: simultaneously looking at images, reading sentences that describe the objects in the scene, and interpreting supplemental sentences that relate the novel concept with other concepts. The learned concepts support downstream applications, such as answering questions by reasoning about unseen images. Our model, namely FALCON, represents individual visual concepts, such as colors and shapes, as axis-aligned boxes in a high-dimensional space (the "box embedding space"). Given an input image and its paired sentence, our model first resolves the referential expression in the sentence and associates the novel concept with particular objects in the scene. Next, our model interprets supplemental sentences to relate the novel concept with other known concepts, such as "X has property Y" or "X is a kind of Y". Finally, it infers an optimal box embedding for the novel concept that jointly 1) maximizes the likelihood of the observed instances in the image, and 2) satisfies the relationships between the novel concepts and the known ones. We demonstrate the effectiveness of our model on both synthetic and real-world datasets.

Many NLP models operate over sequences of subword tokens produced by hand-crafted tokenization rules and heuristic subword induction algorithms. A simple universal alternative is to represent every computerized text as a sequence of bytes via UTF-8, obviating the need for an embedding layer since there are fewer token types (256) than dimensions. Surprisingly, replacing the ubiquitous embedding layer with one-hot representations of each byte does not hurt performance; experiments on byte-to-byte machine translation from English to 10 different languages show a consistent improvement in BLEU, rivaling character-level and even standard subword-level models. A deeper investigation reveals that the combination of embeddingless models with decoder-input dropout amounts to token dropout, which benefits byte-to-byte models in particular.

LLMs are seeing growing use for applications such as document analysis and summarization which require large context windows, and with these large context windows KV cache activations surface as the dominant contributor to memory consumption during inference. Quantization is a promising approach for compressing KV cache activations; however, existing solutions fail to represent activations accurately in ultra-low precisions, such as sub-4-bit. In this work, we present KVQuant, which addresses this problem by incorporating novel methods for quantizing cached KV activations, including: (i) Per-Channel Key Quantization, where we adjust the dimension along which we quantize the Key activations to better match the distribution; (ii) Pre-RoPE Key Quantization, where we quantize Key activations before the rotary positional embedding to mitigate its impact on quantization; (iii) Non-Uniform KV Cache Quantization, where we derive per-layer sensitivity-weighted non-uniform datatypes that better represent the distributions; (iv) Per-Vector Dense-and-Sparse Quantization, where we isolate outliers separately for each vector to minimize skews in quantization ranges; and (v) Q-Norm, where we normalize quantization centroids in order to mitigate distribution shift, providing additional benefits for 2-bit quantization. By applying our method to the LLaMA, LLaMA-2, and Mistral models, we achieve <0.1 perplexity degradation with 3-bit quantization on both Wikitext-2 and C4, outperforming existing approaches. Our method enables serving the LLaMA-7B model with a context length of up to 1 million on a single A100-80GB GPU and up to 10 million on an 8-GPU system.

Fairness and environmental impact are important research directions for the sustainable development of artificial intelligence. However, while each topic is an active research area in natural language processing (NLP), there is a surprising lack of research on the interplay between the two fields. This lacuna is highly problematic, since there is increasing evidence that an exclusive focus on fairness can actually hinder environmental sustainability, and vice versa. In this work, we shed light on this crucial intersection in NLP by (1) investigating the efficiency of current fairness approaches through surveying example methods for reducing unfair stereotypical bias from the literature, and (2) evaluating a common technique to reduce energy consumption (and thus environmental impact) of English NLP models, knowledge distillation (KD), for its impact on fairness. In this case study, we evaluate the effect of important KD factors, including layer and dimensionality reduction, with respect to: (a) performance on the distillation task (natural language inference and semantic similarity prediction), and (b) multiple measures and dimensions of stereotypical bias (e.g., gender bias measured via the Word Embedding Association Test). Our results lead us to clarify current assumptions regarding the effect of KD on unfair bias: contrary to other findings, we show that KD can actually decrease model fairness.

We propose Meta-Prod2vec, a novel method to compute item similarities for recommendation that leverages existing item metadata. Such scenarios are frequently encountered in applications such as content recommendation, ad targeting and web search. Our method leverages past user interactions with items and their attributes to compute low-dimensional embeddings of items. Specifically, the item metadata is in- jected into the model as side information to regularize the item embeddings. We show that the new item representa- tions lead to better performance on recommendation tasks on an open music dataset.

Electronic health records (EHR) contain narrative notes that provide extensive details on the medical condition and management of patients. Natural language processing (NLP) of clinical notes can use observed frequencies of clinical terms as predictive features for downstream applications such as clinical decision making and patient trajectory prediction. However, due to the vast number of highly similar and related clinical concepts, a more effective modeling strategy is to represent clinical terms as semantic embeddings via representation learning and use the low dimensional embeddings as feature vectors for predictive modeling. To achieve efficient representation, fine-tuning pretrained language models with biomedical knowledge graphs may generate better embeddings for biomedical terms than those from standard language models alone. These embeddings can effectively discriminate synonymous pairs of from those that are unrelated. However, they often fail to capture different degrees of similarity or relatedness for concepts that are hierarchical in nature. To overcome this limitation, we propose HiPrBERT, a novel biomedical term representation model trained on additionally complied data that contains hierarchical structures for various biomedical terms. We modify an existing contrastive loss function to extract information from these hierarchies. Our numerical experiments demonstrate that HiPrBERT effectively learns the pair-wise distance from hierarchical information, resulting in a substantially more informative embeddings for further biomedical applications

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

This paper investigates discrepancies in how neural networks learn from different imaging domains, which are commonly overlooked when adopting computer vision techniques from the domain of natural images to other specialized domains such as medical images. Recent works have found that the generalization error of a trained network typically increases with the intrinsic dimension (d_{data}) of its training set. Yet, the steepness of this relationship varies significantly between medical (radiological) and natural imaging domains, with no existing theoretical explanation. We address this gap in knowledge by establishing and empirically validating a generalization scaling law with respect to d_{data}, and propose that the substantial scaling discrepancy between the two considered domains may be at least partially attributed to the higher intrinsic ``label sharpness'' (K_F) of medical imaging datasets, a metric which we propose. Next, we demonstrate an additional benefit of measuring the label sharpness of a training set: it is negatively correlated with the trained model's adversarial robustness, which notably leads to models for medical images having a substantially higher vulnerability to adversarial attack. Finally, we extend our d_{data} formalism to the related metric of learned representation intrinsic dimension (d_{repr}), derive a generalization scaling law with respect to d_{repr}, and show that d_{data} serves as an upper bound for d_{repr}. Our theoretical results are supported by thorough experiments with six models and eleven natural and medical imaging datasets over a range of training set sizes. Our findings offer insights into the influence of intrinsic dataset properties on generalization, representation learning, and robustness in deep neural networks. Code link: https://github.com/mazurowski-lab/intrinsic-properties

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Although pretrained language models can be fine-tuned to produce state-of-the-art results for a very wide range of language understanding tasks, the dynamics of this process are not well understood, especially in the low data regime. Why can we use relatively vanilla gradient descent algorithms (e.g., without strong regularization) to tune a model with hundreds of millions of parameters on datasets with only hundreds or thousands of labeled examples? In this paper, we argue that analyzing fine-tuning through the lens of intrinsic dimension provides us with empirical and theoretical intuitions to explain this remarkable phenomenon. We empirically show that common pre-trained models have a very low intrinsic dimension; in other words, there exists a low dimension reparameterization that is as effective for fine-tuning as the full parameter space. For example, by optimizing only 200 trainable parameters randomly projected back into the full space, we can tune a RoBERTa model to achieve 90\% of the full parameter performance levels on MRPC. Furthermore, we empirically show that pre-training implicitly minimizes intrinsic dimension and, perhaps surprisingly, larger models tend to have lower intrinsic dimension after a fixed number of pre-training updates, at least in part explaining their extreme effectiveness. Lastly, we connect intrinsic dimensionality with low dimensional task representations and compression based generalization bounds to provide intrinsic-dimension-based generalization bounds that are independent of the full parameter count.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Document retrieval is a core component of question-answering systems, as it enables conditioning answer generation on new and large-scale corpora. While effective, the standard practice of encoding documents into high-dimensional embeddings for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. In this paper, we propose a tree-based method for organizing and representing reference documents at various granular levels, which offers the flexibility to balance cost and utility, and eases the inspection of the corpus content and retrieval operations. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches, hence directly optimizing for retrieval performance. Our evaluations show that ReTreever generally preserves full representation accuracy. Its hierarchical structure further provides strong coarse representations and enhances transparency by indirectly learning meaningful semantic groupings. Among hierarchical retrieval methods, ReTreever achieves the best retrieval accuracy at the lowest latency, proving that this family of techniques can be viable in practical applications.

The long-standing dominance of gradient-boosted decision trees on tabular data is currently challenged by tabular foundation models using In-Context Learning (ICL): setting the training data as context for the test data and predicting in a single forward pass without parameter updates. While the very recent TabPFNv2 foundation model (2025) excels on tables with up to 10K samples, its alternating column- and row-wise attentions make handling large training sets computationally prohibitive. So, can ICL be effectively scaled and deliver a benefit for larger tables? We introduce TabICL, a tabular foundation model for classification, pretrained on synthetic datasets with up to 60K samples and capable of handling 500K samples on affordable resources. This is enabled by a novel two-stage architecture: a column-then-row attention mechanism to build fixed-dimensional embeddings of rows, followed by a transformer for efficient ICL. Across 200 classification datasets from the TALENT benchmark, TabICL is on par with TabPFNv2 while being systematically faster (up to 10 times), and significantly outperforms all other approaches. On 56 datasets with over 10K samples, TabICL surpasses both TabPFNv2 and CatBoost, demonstrating the potential of ICL for large data.

In this research, we present a novel approach to motion customization in video generation, addressing the widespread gap in the thorough exploration of motion representation within video generative models. Recognizing the unique challenges posed by video's spatiotemporal nature, our method introduces Motion Embeddings, a set of explicit, temporally coherent one-dimensional embeddings derived from a given video. These embeddings are designed to integrate seamlessly with the temporal transformer modules of video diffusion models, modulating self-attention computations across frames without compromising spatial integrity. Our approach offers a compact and efficient solution to motion representation and enables complex manipulations of motion characteristics through vector arithmetic in the embedding space. Furthermore, we identify the Temporal Discrepancy in video generative models, which refers to variations in how different motion modules process temporal relationships between frames. We leverage this understanding to optimize the integration of our motion embeddings. Our contributions include the introduction of a tailored motion embedding for customization tasks, insights into the temporal processing differences in video models, and a demonstration of the practical advantages and effectiveness of our method through extensive experiments.

Machine learning models often learn latent embedding representations that capture the domain semantics of their training data. These embedding representations are valuable for interpreting trained models, building new models, and analyzing new datasets. However, interpreting and using embeddings can be challenging due to their opaqueness, high dimensionality, and the large size of modern datasets. To tackle these challenges, we present WizMap, an interactive visualization tool to help researchers and practitioners easily explore large embeddings. With a novel multi-resolution embedding summarization method and a familiar map-like interaction design, WizMap enables users to navigate and interpret embedding spaces with ease. Leveraging modern web technologies such as WebGL and Web Workers, WizMap scales to millions of embedding points directly in users' web browsers and computational notebooks without the need for dedicated backend servers. WizMap is open-source and available at the following public demo link: https://poloclub.github.io/wizmap.

Word embeddings are one of the most fundamental technologies used in natural language processing. Existing word embeddings are high-dimensional and consume considerable computational resources. In this study, we propose WordTour, unsupervised one-dimensional word embeddings. To achieve the challenging goal, we propose a decomposition of the desiderata of word embeddings into two parts, completeness and soundness, and focus on soundness in this paper. Owing to the single dimensionality, WordTour is extremely efficient and provides a minimal means to handle word embeddings. We experimentally confirmed the effectiveness of the proposed method via user study and document classification.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Contrastive learning is a highly successful technique for learning representations of data from labeled tuples, specifying the distance relations within the tuple. We study the sample complexity of contrastive learning, i.e. the minimum number of labeled tuples sufficient for getting high generalization accuracy. We give tight bounds on the sample complexity in a variety of settings, focusing on arbitrary distance functions, both general ell_p-distances, and tree metrics. Our main result is an (almost) optimal bound on the sample complexity of learning ell_p-distances for integer p. For any p ge 1 we show that tilde Theta(min(nd,n^2)) labeled tuples are necessary and sufficient for learning d-dimensional representations of n-point datasets. Our results hold for an arbitrary distribution of the input samples and are based on giving the corresponding bounds on the Vapnik-Chervonenkis/Natarajan dimension of the associated problems. We further show that the theoretical bounds on sample complexity obtained via VC/Natarajan dimension can have strong predictive power for experimental results, in contrast with the folklore belief about a substantial gap between the statistical learning theory and the practice of deep learning.

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes. However, we believe that the potential offered by this paradigm is not yet fully exploited. In this work, we propose to utilize the structure of the space spanned by the attributes using a set of relations. We devise objective functions to preserve these relations in the embedding space, thereby inducing semanticity to the embedding space. Through extensive experimental evaluation on five benchmark datasets, we demonstrate that inducing semanticity to the embedding space is beneficial for zero-shot learning. The proposed approach outperforms the state-of-the-art on the standard zero-shot setting as well as the more realistic generalized zero-shot setting. We also demonstrate how the proposed approach can be useful for making approximate semantic inferences about an image belonging to a category for which attribute information is not available.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Transformer models encounter challenges in scaling hidden dimensions efficiently, as uniformly increasing them inflates computational and memory costs while failing to emphasize the most relevant features for each token. For further understanding, we study hidden dimension sparsity and observe that trained Transformers utilize only a small fraction of token dimensions, revealing an "activation flow" pattern. Notably, there are shared sub-dimensions with sustained activation across multiple consecutive tokens and specialized sub-dimensions uniquely activated for each token. To better model token-relevant sub-dimensions, we propose MoHD (Mixture of Hidden Dimensions), a sparse conditional activation architecture. Particularly, MoHD employs shared sub-dimensions for common token features and a routing mechanism to dynamically activate specialized sub-dimensions. To mitigate potential information loss from sparsity, we design activation scaling and group fusion mechanisms to preserve activation flow. In this way, MoHD expands hidden dimensions with negligible increases in computation or parameters, efficient training and inference while maintaining performance. Evaluations across 10 NLP tasks show that MoHD surpasses Vanilla Transformers in parameter efficiency and task performance. It achieves 1.7% higher performance with 50% fewer activation parameters and 3.7% higher performance with a 3x parameter expansion at constant activation cost. MOHD offers a new perspective for scaling the model, showcasing the potential of hidden dimension sparsity to boost efficiency

A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedding layer, transforming a sequence of tokens into vector representations. While the robustness with respect to changes of continuous inputs is well-understood, the situation is less clear when considering discrete changes, for instance replacing a word by another in an input sentence. Our work formally proves that popular embedding schemes, such as concatenation, TF-IDF, and Paragraph Vector (a.k.a. doc2vec), exhibit robustness in the H\"older or Lipschitz sense with respect to the Hamming distance. We provide quantitative bounds for these schemes and demonstrate how the constants involved are affected by the length of the document. These findings are exemplified through a series of numerical examples.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

Large-scale language-agnostic sentence embedding models such as LaBSE (Feng et al., 2022) obtain state-of-the-art performance for parallel sentence alignment. However, these large-scale models can suffer from inference speed and computation overhead. This study systematically explores learning language-agnostic sentence embeddings with lightweight models. We demonstrate that a thin-deep encoder can construct robust low-dimensional sentence embeddings for 109 languages. With our proposed distillation methods, we achieve further improvements by incorporating knowledge from a teacher model. Empirical results on Tatoeba, United Nations, and BUCC show the effectiveness of our lightweight models. We release our lightweight language-agnostic sentence embedding models LEALLA on TensorFlow Hub.

This paper presents a new technique for creating monolingual and cross-lingual meta-embeddings. Our method integrates multiple word embeddings created from complementary techniques, textual sources, knowledge bases and languages. Existing word vectors are projected to a common semantic space using linear transformations and averaging. With our method the resulting meta-embeddings maintain the dimensionality of the original embeddings without losing information while dealing with the out-of-vocabulary problem. An extensive empirical evaluation demonstrates the effectiveness of our technique with respect to previous work on various intrinsic and extrinsic multilingual evaluations, obtaining competitive results for Semantic Textual Similarity and state-of-the-art performance for word similarity and POS tagging (English and Spanish). The resulting cross-lingual meta-embeddings also exhibit excellent cross-lingual transfer learning capabilities. In other words, we can leverage pre-trained source embeddings from a resource-rich language in order to improve the word representations for under-resourced languages.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Several techniques have been proposed to detect vulnerable Spectre gadgets in widely deployed commercial software. Unfortunately, detection techniques proposed so far rely on hand-written rules which fall short in covering subtle variations of known Spectre gadgets as well as demand a huge amount of time to analyze each conditional branch in software. Moreover, detection tool evaluations are based only on a handful of these gadgets, as it requires arduous effort to craft new gadgets manually. In this work, we employ both fuzzing and deep learning techniques to automate the generation and detection of Spectre gadgets. We first create a diverse set of Spectre-V1 gadgets by introducing perturbations to the known gadgets. Using mutational fuzzing, we produce a data set with more than 1 million Spectre-V1 gadgets which is the largest Spectre gadget data set built to date. Next, we conduct the first empirical usability study of Generative Adversarial Networks (GANs) in the context of assembly code generation without any human interaction. We introduce SpectreGAN which leverages masking implementation of GANs for both learning the gadget structures and generating new gadgets. This provides the first scalable solution to extend the variety of Spectre gadgets. Finally, we propose FastSpec which builds a classifier with the generated Spectre gadgets based on a novel high dimensional Neural Embeddings technique (BERT). For the case studies, we demonstrate that FastSpec discovers potential gadgets with a high success rate in OpenSSL libraries and Phoronix benchmarks. Further, FastSpec offers much greater flexibility and time-related performance gain compared to the existing tools and therefore can be used for gadget detection in large-scale software.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at https://github.com/zknus/Hamiltonian-GNN.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing image classifier and a semantic word embedding model, which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

Contrastive learning, a prominent approach to representation learning, traditionally assumes positive pairs are closely related samples (the same image or class) and negative pairs are distinct samples. We challenge this assumption by proposing to learn from arbitrary pairs, allowing any pair of samples to be positive within our framework.The primary challenge of the proposed approach lies in applying contrastive learning to disparate pairs which are semantically distant. Motivated by the discovery that SimCLR can separate given arbitrary pairs (e.g., garter snake and table lamp) in a subspace, we propose a feature filter in the condition of class pairs that creates the requisite subspaces by gate vectors selectively activating or deactivating dimensions. This filter can be optimized through gradient descent within a conventional contrastive learning mechanism. We present Hydra, a universal contrastive learning framework for visual representations that extends conventional contrastive learning to accommodate arbitrary pairs. Our approach is validated using IN1K, where 1K diverse classes compose 500,500 pairs, most of them being distinct. Surprisingly, Hydra achieves superior performance in this challenging setting. Additional benefits include the prevention of dimensional collapse and the discovery of class relationships. Our work highlights the value of learning common features of arbitrary pairs and potentially broadens the applicability of contrastive learning techniques on the sample pairs with weak relationships.

For convolutional neural network models that optimize an image embedding, we propose a method to highlight the regions of images that contribute most to pairwise similarity. This work is a corollary to the visualization tools developed for classification networks, but applicable to the problem domains better suited to similarity learning. The visualization shows how similarity networks that are fine-tuned learn to focus on different features. We also generalize our approach to embedding networks that use different pooling strategies and provide a simple mechanism to support image similarity searches on objects or sub-regions in the query image.

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many real-life datasets, however, are of increasingly high dimensionality, where a large number of features may be irrelevant for both supervised and unsupervised learning tasks. The inclusion of such features would not only introduce unwanted noise but also increase computational complexity. Furthermore, due to high non-linearity and dependency among a large number of features, DNN models tend to be unavoidably opaque and perceived as black-box methods because of their not well-understood internal functioning. Their algorithmic complexity is often simply beyond the capacities of humans to understand the interplay among myriads of hyperparameters. A well-interpretable model can identify statistically significant features and explain the way they affect the model's outcome. In this paper, we propose an efficient method to improve the interpretability of black-box models for classification tasks in the case of high-dimensional datasets. First, we train a black-box model on a high-dimensional dataset to learn the embeddings on which the classification is performed. To decompose the inner working principles of the black-box model and to identify top-k important features, we employ different probing and perturbing techniques. We then approximate the behavior of the black-box model by means of an interpretable surrogate model on the top-k feature space. Finally, we derive decision rules and local explanations from the surrogate model to explain individual decisions. Our approach outperforms state-of-the-art methods like TabNet and XGboost when tested on different datasets with varying dimensionality between 50 and 20,000 w.r.t metrics and explainability.

Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream conclusions drawn from word embedding statistics has remained challenging. When using only point estimates for embeddings, researchers have no streamlined way of assessing the degree to which their model selection criteria or scientific conclusions are subject to noise due to sparsity in the underlying data used to generate the embeddings. We introduce a method to obtain approximate, easy-to-use, and scalable reconstruction error variance estimates for GloVe (Pennington et al., 2014), one of the most widely used word embedding models, using an analytical approximation to a multivariate normal model. To demonstrate the value of embeddings with variance (GloVe-V), we illustrate how our approach enables principled hypothesis testing in core word embedding tasks, such as comparing the similarity between different word pairs in vector space, assessing the performance of different models, and analyzing the relative degree of ethnic or gender bias in a corpus using different word lists.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains.

Deep neural networks have been demonstrated to achieve phenomenal success in many domains, and yet their inner mechanisms are not well understood. In this paper, we investigate the curvature of image manifolds, i.e., the manifold deviation from being flat in its principal directions. We find that state-of-the-art trained convolutional neural networks for image classification have a characteristic curvature profile along layers: an initial steep increase, followed by a long phase of a plateau, and followed by another increase. In contrast, this behavior does not appear in untrained networks in which the curvature flattens. We also show that the curvature gap between the last two layers has a strong correlation with the generalization capability of the network. Moreover, we find that the intrinsic dimension of latent codes is not necessarily indicative of curvature. Finally, we observe that common regularization methods such as mixup yield flatter representations when compared to other methods. Our experiments show consistent results over a variety of deep learning architectures and multiple data sets. Our code is publicly available at https://github.com/azencot-group/CRLM

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

Previous work has shown that the representations output by contextual language models are more anisotropic than static type embeddings, and typically display outlier dimensions. This seems to be true for both monolingual and multilingual models, although much less work has been done on the multilingual context. Why these outliers occur and how they affect the representations is still an active area of research. We investigate outlier dimensions and their relationship to anisotropy in multiple pre-trained multilingual language models. We focus on cross-lingual semantic similarity tasks, as these are natural tasks for evaluating multilingual representations. Specifically, we examine sentence representations. Sentence transformers which are fine-tuned on parallel resources (that are not always available) perform better on this task, and we show that their representations are more isotropic. However, we aim to improve multilingual representations in general. We investigate how much of the performance difference can be made up by only transforming the embedding space without fine-tuning, and visualise the resulting spaces. We test different operations: Removing individual outlier dimensions, cluster-based isotropy enhancement, and ZCA whitening. We publish our code for reproducibility.

Growing amount and quality of AI-generated texts makes detecting such content more difficult. In most real-world scenarios, the domain (style and topic) of generated data and the generator model are not known in advance. In this work, we focus on the robustness of classifier-based detectors of AI-generated text, namely their ability to transfer to unseen generators or semantic domains. We investigate the geometry of the embedding space of Transformer-based text encoders and show that clearing out harmful linear subspaces helps to train a robust classifier, ignoring domain-specific spurious features. We investigate several subspace decomposition and feature selection strategies and achieve significant improvements over state of the art methods in cross-domain and cross-generator transfer. Our best approaches for head-wise and coordinate-based subspace removal increase the mean out-of-distribution (OOD) classification score by up to 9% and 14% in particular setups for RoBERTa and BERT embeddings respectively. We release our code and data: https://github.com/SilverSolver/RobustATD

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

Fine-grained and instance-level recognition methods are commonly trained and evaluated on specific domains, in a model per domain scenario. Such an approach, however, is impractical in real large-scale applications. In this work, we address the problem of universal image embedding, where a single universal model is trained and used in multiple domains. First, we leverage existing domain-specific datasets to carefully construct a new large-scale public benchmark for the evaluation of universal image embeddings, with 241k query images, 1.4M index images and 2.8M training images across 8 different domains and 349k classes. We define suitable metrics, training and evaluation protocols to foster future research in this area. Second, we provide a comprehensive experimental evaluation on the new dataset, demonstrating that existing approaches and simplistic extensions lead to worse performance than an assembly of models trained for each domain separately. Finally, we conducted a public research competition on this topic, leveraging industrial datasets, which attracted the participation of more than 1k teams worldwide. This exercise generated many interesting research ideas and findings which we present in detail. Project webpage: https://cmp.felk.cvut.cz/univ_emb/

In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often found, largely by focusing on extremal filter responses. In this paper, we show that this approach can favor easy-to-interpret cases that are not necessarily representative of the average behavior of a representation. A more realistic but harder-to-study hypothesis is that semantic representations are distributed, and thus filters must be studied in conjunction. In order to investigate this idea while enabling systematic visualization and quantification of multiple filter responses, we introduce the Net2Vec framework, in which semantic concepts are mapped to vectorial embeddings based on corresponding filter responses. By studying such embeddings, we are able to show that 1., in most cases, multiple filters are required to code for a concept, that 2., often filters are not concept specific and help encode multiple concepts, and that 3., compared to single filter activations, filter embeddings are able to better characterize the meaning of a representation and its relationship to other concepts.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in fully-connected layers with Hamilton products of Quaternions, both enjoy parameter savings with only 1/4 learnable parameters and achieve comparable performance in various applications. However, one key caveat is that hypercomplex space only exists at very few predefined dimensions (4D, 8D, and 16D). This restricts the flexibility of models that leverage hypercomplex multiplications. To this end, we propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space, providing more architectural flexibility using arbitrarily 1/n learnable parameters compared with the fully-connected layer counterpart. Experiments of applications to the LSTM and Transformer models on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate architectural flexibility and effectiveness of the proposed approach.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

This paper proposes an unsupervised method that leverages topological characteristics of data manifolds to estimate class separability of the data without requiring labels. Experiments conducted in this paper on several datasets demonstrate a clear correlation and consistency between the class separability estimated by the proposed method with supervised metrics like Fisher Discriminant Ratio~(FDR) and cross-validation of a classifier, which both require labels. This can enable implementing learning paradigms aimed at learning from both labeled and unlabeled data, like semi-supervised and transductive learning. This would be particularly useful when we have limited labeled data and a relatively large unlabeled dataset that can be used to enhance the learning process. The proposed method is implemented for language model fine-tuning with automated stopping criterion by monitoring class separability of the embedding-space manifold in an unsupervised setting. The proposed methodology has been first validated on synthetic data, where the results show a clear consistency between class separability estimated by the proposed method and class separability computed by FDR. The method has been also implemented on both public and internal data. The results show that the proposed method can effectively aid -- without the need for labels -- a decision on when to stop or continue the fine-tuning of a language model and which fine-tuning iteration is expected to achieve a maximum classification performance through quantification of the class separability of the embedding manifold.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Building a scalable and real-time recommendation system is vital for many businesses driven by time-sensitive customer feedback, such as short-videos ranking or online ads. Despite the ubiquitous adoption of production-scale deep learning frameworks like TensorFlow or PyTorch, these general-purpose frameworks fall short of business demands in recommendation scenarios for various reasons: on one hand, tweaking systems based on static parameters and dense computations for recommendation with dynamic and sparse features is detrimental to model quality; on the other hand, such frameworks are designed with batch-training stage and serving stage completely separated, preventing the model from interacting with customer feedback in real-time. These issues led us to reexamine traditional approaches and explore radically different design choices. In this paper, we present Monolith, a system tailored for online training. Our design has been driven by observations of our application workloads and production environment that reflects a marked departure from other recommendations systems. Our contributions are manifold: first, we crafted a collisionless embedding table with optimizations such as expirable embeddings and frequency filtering to reduce its memory footprint; second, we provide an production-ready online training architecture with high fault-tolerance; finally, we proved that system reliability could be traded-off for real-time learning. Monolith has successfully landed in the BytePlus Recommend product.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Document embeddings and similarity measures underpin content-based recommender systems, whereby a document is commonly represented as a single generic embedding. However, similarity computed on single vector representations provides only one perspective on document similarity that ignores which aspects make two documents alike. To address this limitation, aspect-based similarity measures have been developed using document segmentation or pairwise multi-class document classification. While segmentation harms the document coherence, the pairwise classification approach scales poorly to large scale corpora. In this paper, we treat aspect-based similarity as a classical vector similarity problem in aspect-specific embedding spaces. We represent a document not as a single generic embedding but as multiple specialized embeddings. Our approach avoids document segmentation and scales linearly w.r.t.the corpus size. In an empirical study, we use the Papers with Code corpus containing 157,606 research papers and consider the task, method, and dataset of the respective research papers as their aspects. We compare and analyze three generic document embeddings, six specialized document embeddings and a pairwise classification baseline in the context of research paper recommendations. As generic document embeddings, we consider FastText, SciBERT, and SPECTER. To compute the specialized document embeddings, we compare three alternative methods inspired by retrofitting, fine-tuning, and Siamese networks. In our experiments, Siamese SciBERT achieved the highest scores. Additional analyses indicate an implicit bias of the generic document embeddings towards the dataset aspect and against the method aspect of each research paper. Our approach of aspect-based document embeddings mitigates potential risks arising from implicit biases by making them explicit.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

The performance of algorithms for neural architecture search strongly depends on the parametrization of the search space. We use contrastive learning to identify networks across different initializations based on their data Jacobians, and automatically produce the first architecture embeddings independent from the parametrization of the search space. Using our contrastive embeddings, we show that traditional black-box optimization algorithms, without modification, can reach state-of-the-art performance in Neural Architecture Search. As our method provides a unified embedding space, we perform for the first time transfer learning between search spaces. Finally, we show the evolution of embeddings during training, motivating future studies into using embeddings at different training stages to gain a deeper understanding of the networks in a search space.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique. Code for our experiments can be found at github.com/edwardjhu/TP4.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

With the ever-increasing volumes of the Earth observation data present in the archives of large programmes such as Copernicus, there is a growing need for efficient vector representations of the underlying raw data. The approach of extracting feature representations from pretrained deep neural networks is a powerful approach that can provide semantic abstractions of the input data. However, the way this is done for imagery archives containing geospatial data has not yet been defined. In this work, an extension is proposed to an existing community project, Major TOM, focused on the provision and standardization of open and free AI-ready datasets for Earth observation. Furthermore, four global and dense embedding datasets are released openly and for free along with the publication of this manuscript, resulting in the most comprehensive global open dataset of geospatial visual embeddings in terms of covered Earth's surface.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Self-supervised representation learning follows a paradigm of withholding some part of the data and tasking the network to predict it from the remaining part. Among many techniques, data augmentation lies at the core for creating the information gap. Towards this end, masking has emerged as a generic and powerful tool where content is withheld along the sequential dimension, e.g., spatial in images, temporal in audio, and syntactic in language. In this paper, we explore the orthogonal channel dimension for generic data augmentation by exploiting precision redundancy. The data for each channel is quantized through a non-uniform quantizer, with the quantized value sampled randomly within randomly sampled quantization bins. From another perspective, quantization is analogous to channel-wise masking, as it removes the information within each bin, but preserves the information across bins. Our approach significantly surpasses existing generic data augmentation methods, while showing on par performance against modality-specific augmentations. We comprehensively evaluate our approach on vision, audio, 3D point clouds, as well as the DABS benchmark which is comprised of various data modalities. The code is available at https: //github.com/microsoft/random_quantize.

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, e.g., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in https://github.com/wdayang/Manifoldron for free download and evaluation.

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional filters. The proposed algorithm combines dense embeddings with discrete filtering attributes, enabling fast retrieval in high-dimensional spaces. Designed specifically for CPU-based systems, our disk-based approach offers a cost-effective solution for large-scale similarity search. We demonstrate the effectiveness of our method through a case study, showcasing its potential for various practical uses.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

Generative Adversarial Networks (GANs) have shown compelling results in various tasks and applications in recent years. However, mode collapse remains a critical problem in GANs. In this paper, we propose a novel training pipeline to address the mode collapse issue of GANs. Different from existing methods, we propose to generalize the discriminator as feature embedding and maximize the entropy of distributions in the embedding space learned by the discriminator. Specifically, two regularization terms, i.e., Deep Local Linear Embedding (DLLE) and Deep Isometric feature Mapping (DIsoMap), are designed to encourage the discriminator to learn the structural information embedded in the data, such that the embedding space learned by the discriminator can be well-formed. Based on the well-learned embedding space supported by the discriminator, a non-parametric entropy estimator is designed to efficiently maximize the entropy of embedding vectors, playing as an approximation of maximizing the entropy of the generated distribution. By improving the discriminator and maximizing the distance of the most similar samples in the embedding space, our pipeline effectively reduces the mode collapse without sacrificing the quality of generated samples. Extensive experimental results show the effectiveness of our method, which outperforms the GAN baseline, MaF-GAN on CelebA (9.13 vs. 12.43 in FID) and surpasses the recent state-of-the-art energy-based model on the ANIME-FACE dataset (2.80 vs. 2.26 in Inception score). The code is available at https://github.com/HaozheLiu-ST/MEE

Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel data-driven supervision for tabular data by introducing a characteristic -- scale -- as data labels. By representing varied sub-vectors of data instances, we define scale as the relationship between the dimensionality of original sub-vectors and that of representations. Scales serve as labels attached to transformed representations, thus offering ample labeled data for neural network training. This paper further proposes a scale learning-based anomaly detection method. Supervised by the learning objective of scale distribution alignment, our approach learns the ranking of representations converted from varied subspaces of each data instance. Through this proxy task, our approach models inherent regularities and patterns within data, which well describes data "normality". Abnormal degrees of testing instances are obtained by measuring whether they fit these learned patterns. Extensive experiments show that our approach leads to significant improvement over state-of-the-art generative/contrastive anomaly detection methods.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.

Nonlinear sufficient dimension reductionlibing_generalSDR, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean random objects, which are frequently encountered in many recent statistical applications. In this paper, we introduce a new statistical dependence measure termed Fr\'echet Cumulative Covariance (FCCov) and develop a novel nonlinear SDR framework based on FCCov. Our approach is not only applicable to complex non-Euclidean data, but also exhibits robustness against outliers. We further incorporate Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to estimate nonlinear sufficient directions in the sample level. Theoretically, we prove that our method with squared Frobenius norm regularization achieves unbiasedness at the sigma-field level. Furthermore, we establish non-asymptotic convergence rates for our estimators based on FNNs and ResNet-type CNNs, which match the minimax rate of nonparametric regression up to logarithmic factors. Intensive simulation studies verify the performance of our methods in both Euclidean and non-Euclidean settings. We apply our method to facial expression recognition datasets and the results underscore more realistic and broader applicability of our proposal.

Causal representation learning has showed a variety of settings in which we can disentangle latent variables with identifiability guarantees (up to some reasonable equivalence class). Common to all of these approaches is the assumption that (1) the latent variables are represented as d-dimensional vectors, and (2) that the observations are the output of some injective generative function of these latent variables. While these assumptions appear benign, we show that when the observations are of multiple objects, the generative function is no longer injective and disentanglement fails in practice. We can address this failure by combining recent developments in object-centric learning and causal representation learning. By modifying the Slot Attention architecture arXiv:2006.15055, we develop an object-centric architecture that leverages weak supervision from sparse perturbations to disentangle each object's properties. This approach is more data-efficient in the sense that it requires significantly fewer perturbations than a comparable approach that encodes to a Euclidean space and we show that this approach successfully disentangles the properties of a set of objects in a series of simple image-based disentanglement experiments.

Modern retrieval system often requires recomputing the representation of every piece of data in the gallery when updating to a better representation model. This process is known as backfilling and can be especially costly in the real world where the gallery often contains billions of samples. Recently, researchers have proposed the idea of Backward Compatible Training (BCT) where the new representation model can be trained with an auxiliary loss to make it backward compatible with the old representation. In this way, the new representation can be directly compared with the old representation, in principle avoiding the need for any backfilling. However, followup work shows that there is an inherent tradeoff where a backward compatible representation model cannot simultaneously maintain the performance of the new model itself. This paper reports our ``not-so-surprising'' finding that adding extra dimensions to the representation can help here. However, we also found that naively increasing the dimension of the representation did not work. To deal with this, we propose Backward-compatible Training with a novel Basis Transformation (BT^2). A basis transformation (BT) is basically a learnable set of parameters that applies an orthonormal transformation. Such a transformation possesses an important property whereby the original information contained in its input is retained in its output. We show in this paper how a BT can be utilized to add only the necessary amount of additional dimensions. We empirically verify the advantage of BT^2 over other state-of-the-art methods in a wide range of settings. We then further extend BT^2 to other challenging yet more practical settings, including significant change in model architecture (CNN to Transformers), modality change, and even a series of updates in the model architecture mimicking the evolution of deep learning models.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy~(VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

Despite significant recent advances in the field of face recognition, implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors. Our method uses a deep convolutional network trained to directly optimize the embedding itself, rather than an intermediate bottleneck layer as in previous deep learning approaches. To train, we use triplets of roughly aligned matching / non-matching face patches generated using a novel online triplet mining method. The benefit of our approach is much greater representational efficiency: we achieve state-of-the-art face recognition performance using only 128-bytes per face. On the widely used Labeled Faces in the Wild (LFW) dataset, our system achieves a new record accuracy of 99.63%. On YouTube Faces DB it achieves 95.12%. Our system cuts the error rate in comparison to the best published result by 30% on both datasets. We also introduce the concept of harmonic embeddings, and a harmonic triplet loss, which describe different versions of face embeddings (produced by different networks) that are compatible to each other and allow for direct comparison between each other.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent work has shown that a zero-pass approach, where parameters are interpreted directly without a forward/backward pass is feasible for some Transformer parameters, and for two-layer attention networks. In this work, we present a theoretical analysis where all parameters of a trained Transformer are interpreted by projecting them into the embedding space, that is, the space of vocabulary items they operate on. We derive a simple theoretical framework to support our arguments and provide ample evidence for its validity. First, an empirical analysis showing that parameters of both pretrained and fine-tuned models can be interpreted in embedding space. Second, we present two applications of our framework: (a) aligning the parameters of different models that share a vocabulary, and (b) constructing a classifier without training by ``translating'' the parameters of a fine-tuned classifier to parameters of a different model that was only pretrained. Overall, our findings open the door to interpretation methods that, at least in part, abstract away from model specifics and operate in the embedding space only.

Embedding index that enables fast approximate nearest neighbor(ANN) search, serves as an indispensable component for state-of-the-art deep retrieval systems. Traditional approaches, often separating the two steps of embedding learning and index building, incur additional indexing time and decayed retrieval accuracy. In this paper, we propose a novel method called Poeem, which stands for product quantization based embedding index jointly trained with deep retrieval model, to unify the two separate steps within an end-to-end training, by utilizing a few techniques including the gradient straight-through estimator, warm start strategy, optimal space decomposition and Givens rotation. Extensive experimental results show that the proposed method not only improves retrieval accuracy significantly but also reduces the indexing time to almost none. We have open sourced our approach for the sake of comparison and reproducibility.

Zero-shot learning (ZSL) models rely on learning a joint embedding space where both textual/semantic description of object classes and visual representation of object images can be projected to for nearest neighbour search. Despite the success of deep neural networks that learn an end-to-end model between text and images in other vision problems such as image captioning, very few deep ZSL model exists and they show little advantage over ZSL models that utilise deep feature representations but do not learn an end-to-end embedding. In this paper we argue that the key to make deep ZSL models succeed is to choose the right embedding space. Instead of embedding into a semantic space or an intermediate space, we propose to use the visual space as the embedding space. This is because that in this space, the subsequent nearest neighbour search would suffer much less from the hubness problem and thus become more effective. This model design also provides a natural mechanism for multiple semantic modalities (e.g., attributes and sentence descriptions) to be fused and optimised jointly in an end-to-end manner. Extensive experiments on four benchmarks show that our model significantly outperforms the existing models. Code is available at https://github.com/lzrobots/DeepEmbeddingModel_ZSL

Collecting large-scale medical datasets with fully annotated samples for training of deep networks is prohibitively expensive, especially for 3D volume data. Recent breakthroughs in self-supervised learning (SSL) offer the ability to overcome the lack of labeled training samples by learning feature representations from unlabeled data. However, most current SSL techniques in the medical field have been designed for either 2D images or 3D volumes. In practice, this restricts the capability to fully leverage unlabeled data from numerous sources, which may include both 2D and 3D data. Additionally, the use of these pre-trained networks is constrained to downstream tasks with compatible data dimensions. In this paper, we propose a novel framework for unsupervised joint learning on 2D and 3D data modalities. Given a set of 2D images or 2D slices extracted from 3D volumes, we construct an SSL task based on a 2D contrastive clustering problem for distinct classes. The 3D volumes are exploited by computing vectored embedding at each slice and then assembling a holistic feature through deformable self-attention mechanisms in Transformer, allowing incorporating long-range dependencies between slices inside 3D volumes. These holistic features are further utilized to define a novel 3D clustering agreement-based SSL task and masking embedding prediction inspired by pre-trained language models. Experiments on downstream tasks, such as 3D brain segmentation, lung nodule detection, 3D heart structures segmentation, and abnormal chest X-ray detection, demonstrate the effectiveness of our joint 2D and 3D SSL approach. We improve plain 2D Deep-ClusterV2 and SwAV by a significant margin and also surpass various modern 2D and 3D SSL approaches.

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these sources, inductive biases take a paramount role in enabling disentanglement. In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. Concretely, we do this by (i) quantizing the latent space into discrete code vectors with a separate learnable scalar codebook per dimension and (ii) applying strong model regularization via an unusually high weight decay. Intuitively, the latent space design forces the encoder to combinatorially construct codes from a small number of distinct scalar values, which in turn enables the decoder to assign a consistent meaning to each value. Regularization then serves to drive the model towards this parsimonious strategy. We demonstrate the broad applicability of this approach by adding it to both basic data-reconstructing (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models. For reliable evaluation, we also propose InfoMEC, a new set of metrics for disentanglement that is cohesively grounded in information theory and fixes well-established shortcomings in previous metrics. Together with regularization, latent quantization dramatically improves the modularity and explicitness of learned representations on a representative suite of benchmark datasets. In particular, our quantized-latent autoencoder (QLAE) consistently outperforms strong methods from prior work in these key disentanglement properties without compromising data reconstruction.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals p_d(y) can shift across domains but the class conditionals p(x|y) do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to p(d|x) suffices to identify p_d(y) and p_d(y|x) up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator p(d|x); (ii) discretize the data by clustering examples in p(d|x) space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered p(y|d) with the discriminator outputs p(d|x) to compute p_d(y|x) ; forall d. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve upon competitive unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.

Today, transformer language models serve as a core component for majority of natural language processing tasks. Industrial application of such models requires minimization of computation time and memory footprint. Knowledge distillation is one of approaches to address this goal. Existing methods in this field are mainly focused on reducing the number of layers or dimension of embeddings/hidden representations. Alternative option is to reduce the number of tokens in vocabulary and therefore the embeddings matrix of the student model. The main problem with vocabulary minimization is mismatch between input sequences and output class distributions of a teacher and a student models. As a result, it is impossible to directly apply KL-based knowledge distillation. We propose two simple yet effective alignment techniques to make knowledge distillation to the students with reduced vocabulary. Evaluation of distilled models on a number of common benchmarks for Russian such as Russian SuperGLUE, SberQuAD, RuSentiment, ParaPhaser, Collection-3 demonstrated that our techniques allow to achieve compression from 17times to 49times, while maintaining quality of 1.7times compressed student with the full-sized vocabulary, but reduced number of Transformer layers only. We make our code and distilled models available.

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large image dimension, circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging key empirical observations: (i) the low intrinsic dimensionality of image data, (ii) a union of manifold structure of image data, and (iii) the low-rank property of the denoising autoencoder in trained diffusion models. These observations motivate us to assume the underlying data distribution of image data as a mixture of low-rank Gaussians and to parameterize the denoising autoencoder as a low-rank model according to the score function of the assumed distribution. With these setups, we rigorously show that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples. Based on this equivalence, we further show that the minimal number of samples required to learn the underlying distribution scales linearly with the intrinsic dimensions under the above data and model assumptions. This insight sheds light on why diffusion models can break the curse of dimensionality and exhibit the phase transition in learning distributions. Moreover, we empirically establish a correspondence between the subspaces and the semantic representations of image data, facilitating image editing. We validate these results with corroborated experimental results on both simulated distributions and image datasets.

Ad-hoc search calls for the selection of appropriate answers from a massive-scale corpus. Nowadays, the embedding-based retrieval (EBR) becomes a promising solution, where deep learning based document representation and ANN search techniques are allied to handle this task. However, a major challenge is that the ANN index can be too large to fit into memory, given the considerable size of answer corpus. In this work, we tackle this problem with Bi-Granular Document Representation, where the lightweight sparse embeddings are indexed and standby in memory for coarse-grained candidate search, and the heavyweight dense embeddings are hosted in disk for fine-grained post verification. For the best of retrieval accuracy, a Progressive Optimization framework is designed. The sparse embeddings are learned ahead for high-quality search of candidates. Conditioned on the candidate distribution induced by the sparse embeddings, the dense embeddings are continuously learned to optimize the discrimination of ground-truth from the shortlisted candidates. Besides, two techniques: the contrastive quantization and the locality-centric sampling are introduced for the learning of sparse and dense embeddings, which substantially contribute to their performances. Thanks to the above features, our method effectively handles massive-scale EBR with strong advantages in accuracy: with up to +4.3% recall gain on million-scale corpus, and up to +17.5% recall gain on billion-scale corpus. Besides, Our method is applied to a major sponsored search platform with substantial gains on revenue (+1.95%), Recall (+1.01%) and CTR (+0.49%). Our code is available at https://github.com/microsoft/BiDR.

Attributes act as intermediate representations that enable parameter sharing between classes, a must when training data is scarce. We propose to view attribute-based image classification as a label-embedding problem: each class is embedded in the space of attribute vectors. We introduce a function that measures the compatibility between an image and a label embedding. The parameters of this function are learned on a training set of labeled samples to ensure that, given an image, the correct classes rank higher than the incorrect ones. Results on the Animals With Attributes and Caltech-UCSD-Birds datasets show that the proposed framework outperforms the standard Direct Attribute Prediction baseline in a zero-shot learning scenario. Label embedding enjoys a built-in ability to leverage alternative sources of information instead of or in addition to attributes, such as e.g. class hierarchies or textual descriptions. Moreover, label embedding encompasses the whole range of learning settings from zero-shot learning to regular learning with a large number of labeled examples.

Training visual embeddings with labeled data supervision has been the de facto setup for representation learning in computer vision. Inspired by recent success of adopting masked image modeling (MIM) in self-supervised representation learning, we propose a simple yet effective setup that can easily integrate MIM into existing supervised training paradigms. In our design, in addition to the original classification task applied to a vision transformer image encoder, we add a shallow transformer-based decoder on top of the encoder and introduce an MIM task which tries to reconstruct image tokens based on masked image inputs. We show with minimal change in architecture and no overhead in inference that this setup is able to improve the quality of the learned representations for downstream tasks such as classification, image retrieval, and semantic segmentation. We conduct a comprehensive study and evaluation of our setup on public benchmarks. On ImageNet-1k, our ViT-B/14 model achieves 81.72% validation accuracy, 2.01% higher than the baseline model. On K-Nearest-Neighbor image retrieval evaluation with ImageNet-1k, the same model outperforms the baseline by 1.32%. We also show that this setup can be easily scaled to larger models and datasets. Code and checkpoints will be released.

In this paper, we present a new embedding model, called M3-Embedding, which is distinguished for its versatility in Multi-Linguality, Multi-Functionality, and Multi-Granularity. It can support more than 100 working languages, leading to new state-of-the-art performances on multi-lingual and cross-lingual retrieval tasks. It can simultaneously perform the three common retrieval functionalities of embedding model: dense retrieval, multi-vector retrieval, and sparse retrieval, which provides a unified model foundation for real-world IR applications. It is able to process inputs of different granularities, spanning from short sentences to long documents of up to 8192 tokens. The effective training of M3-Embedding involves the following technical contributions. We propose a novel self-knowledge distillation approach, where the relevance scores from different retrieval functionalities can be integrated as the teacher signal to enhance the training quality. We also optimize the batching strategy, enabling a large batch size and high training throughput to ensure the discriminativeness of embeddings. To the best of our knowledge, M3-Embedding is the first embedding model which realizes such a strong versatility. The model and code will be publicly available at https://github.com/FlagOpen/FlagEmbedding.

Joint-Embedding Self Supervised Learning (JE-SSL) has seen a rapid development, with the emergence of many method variations but only few principled guidelines that would help practitioners to successfully deploy them. The main reason for that pitfall comes from JE-SSL's core principle of not employing any input reconstruction therefore lacking visual cues of unsuccessful training. Adding non informative loss values to that, it becomes difficult to deploy SSL on a new dataset for which no labels can help to judge the quality of the learned representation. In this study, we develop a simple unsupervised criterion that is indicative of the quality of the learned JE-SSL representations: their effective rank. Albeit simple and computationally friendly, this method -- coined RankMe -- allows one to assess the performance of JE-SSL representations, even on different downstream datasets, without requiring any labels. A further benefit of RankMe is that it does not have any training or hyper-parameters to tune. Through thorough empirical experiments involving hundreds of training episodes, we demonstrate how RankMe can be used for hyperparameter selection with nearly no reduction in final performance compared to the current selection method that involve a dataset's labels. We hope that RankMe will facilitate the deployment of JE-SSL towards domains that do not have the opportunity to rely on labels for representations' quality assessment.

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less. Code: https://github.com/google/svcca/

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

Deep metric learning has been widely applied in many computer vision tasks, and recently, it is more attractive in zero-shot image retrieval and clustering(ZSRC) where a good embedding is requested such that the unseen classes can be distinguished well. Most existing works deem this 'good' embedding just to be the discriminative one and thus race to devise powerful metric objectives or hard-sample mining strategies for leaning discriminative embedding. However, in this paper, we first emphasize that the generalization ability is a core ingredient of this 'good' embedding as well and largely affects the metric performance in zero-shot settings as a matter of fact. Then, we propose the Energy Confused Adversarial Metric Learning(ECAML) framework to explicitly optimize a robust metric. It is mainly achieved by introducing an interesting Energy Confusion regularization term, which daringly breaks away from the traditional metric learning idea of discriminative objective devising, and seeks to 'confuse' the learned model so as to encourage its generalization ability by reducing overfitting on the seen classes. We train this confusion term together with the conventional metric objective in an adversarial manner. Although it seems weird to 'confuse' the network, we show that our ECAML indeed serves as an efficient regularization technique for metric learning and is applicable to various conventional metric methods. This paper empirically and experimentally demonstrates the importance of learning embedding with good generalization, achieving state-of-the-art performances on the popular CUB, CARS, Stanford Online Products and In-Shop datasets for ZSRC tasks. \textcolor[rgb]{1, 0, 0}{Code available at http://www.bhchen.cn/}.

Text embeddings are useful features in many applications such as semantic search and computing text similarity. Previous work typically trains models customized for different use cases, varying in dataset choice, training objective and model architecture. In this work, we show that contrastive pre-training on unsupervised data at scale leads to high quality vector representations of text and code. The same unsupervised text embeddings that achieve new state-of-the-art results in linear-probe classification also display impressive semantic search capabilities and sometimes even perform competitively with fine-tuned models. On linear-probe classification accuracy averaging over 7 tasks, our best unsupervised model achieves a relative improvement of 4% and 1.8% over previous best unsupervised and supervised text embedding models respectively. The same text embeddings when evaluated on large-scale semantic search attains a relative improvement of 23.4%, 14.7%, and 10.6% over previous best unsupervised methods on MSMARCO, Natural Questions and TriviaQA benchmarks, respectively. Similarly to text embeddings, we train code embedding models on (text, code) pairs, obtaining a 20.8% relative improvement over prior best work on code search.

Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems. That changed with the recent development of approximate algorithms that leverage the distributional properties of sparse embeddings to speed up retrieval. Nonetheless, in much of the existing literature, evaluation has been limited to datasets with only a few million documents such as MSMARCO. It remains unclear how these systems behave on much larger datasets and what challenges lurk in larger scales. To bridge that gap, we investigate the behavior of state-of-the-art retrieval algorithms on massive datasets. We compare and contrast the recently-proposed Seismic and graph-based solutions adapted from dense retrieval. We extensively evaluate Splade embeddings of 138M passages from MsMarco-v2 and report indexing time and other efficiency and effectiveness metrics.

We introduce the Granite Embedding models, a family of encoder-based embedding models designed for retrieval tasks, spanning dense-retrieval and sparse retrieval architectures, with both English and Multilingual capabilities. This report provides the technical details of training these highly effective 12 layer embedding models, along with their efficient 6 layer distilled counterparts. Extensive evaluations show that the models, developed with techniques like retrieval oriented pretraining, contrastive finetuning, knowledge distillation, and model merging significantly outperform publicly available models of similar sizes on both internal IBM retrieval and search tasks, and have equivalent performance on widely used information retrieval benchmarks, while being trained on high-quality data suitable for enterprise use. We publicly release all our Granite Embedding models under the Apache 2.0 license, allowing both research and commercial use at https://huggingface.co/collections/ibm-granite.

This article introduces byteSteady -- a fast model for classification using byte-level n-gram embeddings. byteSteady assumes that each input comes as a sequence of bytes. A representation vector is produced using the averaged embedding vectors of byte-level n-grams, with a pre-defined set of n. The hashing trick is used to reduce the number of embedding vectors. This input representation vector is then fed into a linear classifier. A straightforward application of byteSteady is text classification. We also apply byteSteady to one type of non-language data -- DNA sequences for gene classification. For both problems we achieved competitive classification results against strong baselines, suggesting that byteSteady can be applied to both language and non-language data. Furthermore, we find that simple compression using Huffman coding does not significantly impact the results, which offers an accuracy-speed trade-off previously unexplored in machine learning.