Daily Papers

While following different technical routes, both low-rank and orthogonal adaptation techniques can efficiently adapt large-scale pre-training models in specific tasks or domains based on a small piece of trainable parameters. In this study, we bridge the gap between these two techniques, proposing a simple but effective adaptation method based on Householder reflections. Given a pre-trained model, our method fine-tunes its layers by multiplying each frozen weight matrix with an orthogonal matrix constructed by a chain of learnable Householder reflections (HRs). This HR-based orthogonal fine-tuning is equivalent to an adaptive low-rank adaptation. Moreover, we show that the orthogonality of the reflection planes corresponding to the HRs impacts the model capacity and regularity. The analysis motivates us to regularize the orthogonality of the HRs, leading to different implementations of the proposed Householder reflection adaptation (HRA) method. Compared with state-of-the-art methods, HRA achieves superior performance with fewer learnable parameters when adapting large language models and conditional image generators. The code is available at https://github.com/DaShenZi721/HRA

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets.

This paper addresses the problem of cross-modal object tracking from RGB videos and event data. Rather than constructing a complex cross-modal fusion network, we explore the great potential of a pre-trained vision Transformer (ViT). Particularly, we delicately investigate plug-and-play training augmentations that encourage the ViT to bridge the vast distribution gap between the two modalities, enabling comprehensive cross-modal information interaction and thus enhancing its ability. Specifically, we propose a mask modeling strategy that randomly masks a specific modality of some tokens to enforce the interaction between tokens from different modalities interacting proactively. To mitigate network oscillations resulting from the masking strategy and further amplify its positive effect, we then theoretically propose an orthogonal high-rank loss to regularize the attention matrix. Extensive experiments demonstrate that our plug-and-play training augmentation techniques can significantly boost state-of-the-art one-stream and twostream trackers to a large extent in terms of both tracking precision and success rate. Our new perspective and findings will potentially bring insights to the field of leveraging powerful pre-trained ViTs to model cross-modal data. The code will be publicly available.

Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement that accurately recovers a latent causal model.

Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream task adaptation. Despite demonstrating good generalizability, OFT still uses a fairly large number of trainable parameters due to the high dimensionality of orthogonal matrices. To address this, we start by examining OFT from an information transmission perspective, and then identify a few key desiderata that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast Fourier transform algorithm enables efficient information transmission, we propose an efficient orthogonal parameterization using butterfly structures. We apply this parameterization to OFT, creating a novel parameter-efficient finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a special case, BOFT introduces a generalized orthogonal finetuning framework. Finally, we conduct an extensive empirical study of adapting large vision transformers, large language models, and text-to-image diffusion models to various downstream tasks in vision and language.

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width -- which govern the evolution of observables during training -- saturate at a depth of sim 20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep nonlinear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

Adapting large-scale pre-trained generative models in a parameter-efficient manner is gaining traction. Traditional methods like low rank adaptation achieve parameter efficiency by imposing constraints but may not be optimal for tasks requiring high representation capacity. We propose a novel spectrum-aware adaptation framework for generative models. Our method adjusts both singular values and their basis vectors of pretrained weights. Using the Kronecker product and efficient Stiefel optimizers, we achieve parameter-efficient adaptation of orthogonal matrices. We introduce Spectral Orthogonal Decomposition Adaptation (SODA), which balances computational efficiency and representation capacity. Extensive evaluations on text-to-image diffusion models demonstrate SODA's effectiveness, offering a spectrum-aware alternative to existing fine-tuning methods.

This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from incoherent weight and Hessian matrices, i.e., from the weights and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/jerry-chee/QuIP .

KV cache has become a de facto technique for the inference of large language models (LLMs), where tensors of shape (layer number, head number, sequence length, feature dimension) are introduced to cache historical information for self-attention. As the size of the model and data grows, the KV cache can quickly become a bottleneck within the system in both storage and memory transfer. To address this, prior studies usually focus on the first three axes of the cache tensors for compression. This paper supplements them, focusing on the feature dimension axis, by utilizing low-rank projection matrices to transform the cache features into spaces with reduced dimensions. We begin by investigating the canonical orthogonal projection method for data compression through principal component analysis (PCA). We observe the issue with PCA projection where significant performance degradation is observed at low compression rates. To bridge the gap, we propose to directly tune the orthogonal projection matrices with a distillation objective using an elaborate Matryoshka training strategy. After training, we adaptively search for the optimal compression rates for various layers and heads given varying compression budgets. Compared to previous works, our method can easily embrace pre-trained LLMs and hold a smooth tradeoff between performance and compression rate. We empirically witness the high data efficiency of our training procedure and find that our method can sustain over 90% performance with an average KV cache compression rate of 60% (and up to 75% in certain extreme scenarios) for popular LLMs like LLaMA2-7B-base and Mistral-7B-v0.3-base.

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One is to do an alternative optimization of both the dictionary and the sparse code; the other way is to optimize the dictionary by restricting it over the orthogonal group. The latter one is called orthogonal dictionary learning which has a lower complexity implementation, hence, it is more favorable for lowcost devices. However, existing schemes on orthogonal dictionary learning only work with batch data and can not be implemented online, which is not applicable for real-time applications. This paper proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. In the algorithm design, we propose a new Frank-Wolfe-based online algorithm with a convergence rate of O(ln t/t^(1/4)). The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world sensor readings demonstrate the effectiveness and efficiency of the proposed online orthogonal dictionary learning scheme.

We develop relative oscillation theory for Jacobi matrices which, rather than counting the number of eigenvalues of one single matrix, counts the difference between the number of eigenvalues of two different matrices. This is done by replacing nodes of solutions associated with one matrix by weighted nodes of Wronskians of solutions of two different matrices.

There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in parameters specifying the Schur functions. More recently similar identities have been found involving expansions in terms of characters of the symplectic group. Here these results are extended and generalised to all classical Lie groups. This is done through the derivation of explicit recurrence relations for the expansion coefficients based on the action of the Weyl groups of both the symplectic and orthogonal groups. Copious results are tabulated in the form of explicit values of the expansion coefficients as functions of highest weight parameters. An alternative approach is then based on dual pairs of symplectic and/or orthogonal groups. A byproduct of this approach is that expansions in terms of spin orthogonal group characters can always be recovered from non-spin cases.

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based bounds when the condition numbers of weight matrices are small. Especially, it is completely independent of the width of the network if the weight matrices are orthogonal. Our bound does not contradict to the existing bounds but is a complement to the existing bounds. As supported by several existing empirical results, low-rankness is not the only reason for generalization. Furthermore, our bound can be combined with the existing bounds to obtain a tighter bound. Our result sheds new light on understanding generalization of neural networks with full-rank weight matrices, and it provides a connection between operator-theoretic analysis and generalization of neural networks.

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties of orthogonal convolutional layers.We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding.We also exhibit limitations with 'valid' boundary conditions and 'same' boundary conditions with zero-padding.Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al. 2020).The second motivation of the present paper is to specify the theory behind this.We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric.The theoretical results are confirmed with experiments and the landscape of the regularization term is studied. Experiments on real data sets show that when orthogonality is used to enforce robustness, the parameter multiplying the regularization termcan be used to tune a tradeoff between accuracy and orthogonality, for the benefit of both accuracy and robustness.Altogether, the study guarantees that the regularization proposed in Wang et al. (2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.

To adapt a well-trained large model to downstream tasks, we propose constraining learning within its original latent space by leveraging linear combinations of its basis vectors. This approach ensures stable training without compromising the model's capabilities. Traditionally, constructing orthonormal bases from a matrix requires a transfer matrix, which significantly increases storage and computational overhead for parameters and feature maps. In this paper, we introduce Absorb and Decompose for Q, K, V, and O matrices, enabling their orthogonalization without the need for transfer matrices. Furthermore, the Absorb-Decompose operation eliminates redundant vectors, reducing the encoder attention parameters of Whisper-large-v3 by 46.42% without requiring additional training. For parameter-efficient and stable fine-tuning, we orthonormalized Q, K, V, and O and fine-tuned only the singular values, allowing efficient adaptation while constraining changes to the original latent space. When fine-tuning LLaMA-2-7B on eight commonsense reasoning datasets, our method outperforms LoRA by 5.4% and DoRA by 4.4%.

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of R^{n} for three symmetry groups that are missing from the machine learning literature: O(n), the orthogonal group; SO(n), the special orthogonal group; and Sp(n), the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of R^{n} when the group is O(n) or SO(n), and in the symplectic basis of R^{n} when the group is Sp(n).

This paper gives three formulas for the pseudoinverse of a matrix product A = CR. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse A^+_r may be very useful when A is a very large matrix. 1. A^+ = R^+C^+ when A = CR and C has independent columns and R has independent rows. 2. A^+ = (C^+CR)^+(CRR^+)^+ is always correct. 3. A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+ only when rank(P^TA) = rank(AQ) = rank(A) with A = CR.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Customization techniques for text-to-image models have paved the way for a wide range of previously unattainable applications, enabling the generation of specific concepts across diverse contexts and styles. While existing methods facilitate high-fidelity customization for individual concepts or a limited, pre-defined set of them, they fall short of achieving scalability, where a single model can seamlessly render countless concepts. In this paper, we address a new problem called Modular Customization, with the goal of efficiently merging customized models that were fine-tuned independently for individual concepts. This allows the merged model to jointly synthesize concepts in one image without compromising fidelity or incurring any additional computational costs. To address this problem, we introduce Orthogonal Adaptation, a method designed to encourage the customized models, which do not have access to each other during fine-tuning, to have orthogonal residual weights. This ensures that during inference time, the customized models can be summed with minimal interference. Our proposed method is both simple and versatile, applicable to nearly all optimizable weights in the model architecture. Through an extensive set of quantitative and qualitative evaluations, our method consistently outperforms relevant baselines in terms of efficiency and identity preservation, demonstrating a significant leap toward scalable customization of diffusion models.

Benefiting from massive corpora and advanced hardware, large language models (LLMs) exhibit remarkable capabilities in language understanding and generation. However, their performance degrades in scenarios where multiple tasks are encountered sequentially, also known as catastrophic forgetting. In this paper, we propose orthogonal low-rank adaptation (O-LoRA), a simple and efficient approach for continual learning in language models, effectively mitigating catastrophic forgetting while learning new tasks. Specifically, O-LoRA learns tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Our method induces only marginal additional parameter costs and requires no user data storage for replay. Experimental results on continual learning benchmarks show that our method outperforms state-of-the-art methods. Furthermore, compared to previous approaches, our method excels in preserving the generalization ability of LLMs on unseen tasks.

Recent trends in semi-supervised learning have significantly boosted the performance of 3D semi-supervised medical image segmentation. Compared with 2D images, 3D medical volumes involve information from different directions, e.g., transverse, sagittal, and coronal planes, so as to naturally provide complementary views. These complementary views and the intrinsic similarity among adjacent 3D slices inspire us to develop a novel annotation way and its corresponding semi-supervised model for effective segmentation. Specifically, we firstly propose the orthogonal annotation by only labeling two orthogonal slices in a labeled volume, which significantly relieves the burden of annotation. Then, we perform registration to obtain the initial pseudo labels for sparsely labeled volumes. Subsequently, by introducing unlabeled volumes, we propose a dual-network paradigm named Dense-Sparse Co-training (DeSCO) that exploits dense pseudo labels in early stage and sparse labels in later stage and meanwhile forces consistent output of two networks. Experimental results on three benchmark datasets validated our effectiveness in performance and efficiency in annotation. For example, with only 10 annotated slices, our method reaches a Dice up to 86.93% on KiTS19 dataset.

We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way, we solve a handful of related problems: orthogonal fold & punch, 1D fold & cut, signed 1D fold & cut, and 1D interval fold & cut.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

Federated Learning (FL) has gained significant attraction due to its ability to enable privacy-preserving training over decentralized data. Current literature in FL mostly focuses on single-task learning. However, over time, new tasks may appear in the clients and the global model should learn these tasks without forgetting previous tasks. This real-world scenario is known as Continual Federated Learning (CFL). The main challenge of CFL is Global Catastrophic Forgetting, which corresponds to the fact that when the global model is trained on new tasks, its performance on old tasks decreases. There have been a few recent works on CFL to propose methods that aim to address the global catastrophic forgetting problem. However, these works either have unrealistic assumptions on the availability of past data samples or violate the privacy principles of FL. We propose a novel method, Federated Orthogonal Training (FOT), to overcome these drawbacks and address the global catastrophic forgetting in CFL. Our algorithm extracts the global input subspace of each layer for old tasks and modifies the aggregated updates of new tasks such that they are orthogonal to the global principal subspace of old tasks for each layer. This decreases the interference between tasks, which is the main cause for forgetting. We empirically show that FOT outperforms state-of-the-art continual learning methods in the CFL setting, achieving an average accuracy gain of up to 15% with 27% lower forgetting while only incurring a minimal computation and communication cost.

Based on the Manhattan World assumption, most existing indoor layout estimation schemes focus on recovering layouts from vertically compressed 1D sequences. However, the compression procedure confuses the semantics of different planes, yielding inferior performance with ambiguous interpretability. To address this issue, we propose to disentangle this 1D representation by pre-segmenting orthogonal (vertical and horizontal) planes from a complex scene, explicitly capturing the geometric cues for indoor layout estimation. Considering the symmetry between the floor boundary and ceiling boundary, we also design a soft-flipping fusion strategy to assist the pre-segmentation. Besides, we present a feature assembling mechanism to effectively integrate shallow and deep features with distortion distribution awareness. To compensate for the potential errors in pre-segmentation, we further leverage triple attention to reconstruct the disentangled sequences for better performance. Experiments on four popular benchmarks demonstrate our superiority over existing SoTA solutions, especially on the 3DIoU metric. The code is available at https://github.com/zhijieshen-bjtu/DOPNet.

Image Retrieval is a fundamental task of obtaining images similar to the query one from a database. A common image retrieval practice is to firstly retrieve candidate images via similarity search using global image features and then re-rank the candidates by leveraging their local features. Previous learning-based studies mainly focus on either global or local image representation learning to tackle the retrieval task. In this paper, we abandon the two-stage paradigm and seek to design an effective single-stage solution by integrating local and global information inside images into compact image representations. Specifically, we propose a Deep Orthogonal Local and Global (DOLG) information fusion framework for end-to-end image retrieval. It attentively extracts representative local information with multi-atrous convolutions and self-attention at first. Components orthogonal to the global image representation are then extracted from the local information. At last, the orthogonal components are concatenated with the global representation as a complementary, and then aggregation is performed to generate the final representation. The whole framework is end-to-end differentiable and can be trained with image-level labels. Extensive experimental results validate the effectiveness of our solution and show that our model achieves state-of-the-art image retrieval performances on Revisited Oxford and Paris datasets.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

Textual Inversion remains a popular method for personalizing diffusion models, in order to teach models new subjects and styles. We note that textual inversion has been underexplored using alternatives to the UNet, and experiment with textual inversion with a vision transformer. We also seek to optimize textual inversion using a strategy that does not require explicit use of the UNet and its idiosyncratic layers, so we add bonus tokens and enforce orthogonality. We find the use of the bonus token improves adherence to the source images and the use of the vision transformer improves adherence to the prompt. Code is available at https://github.com/jamesBaker361/tex_inv_plus.

Existing AI-generated image (AIGI) detection methods often suffer from limited generalization performance. In this paper, we identify a crucial yet previously overlooked asymmetry phenomenon in AIGI detection: during training, models tend to quickly overfit to specific fake patterns in the training set, while other information is not adequately captured, leading to poor generalization when faced with new fake methods. A key insight is to incorporate the rich semantic knowledge embedded within large-scale vision foundation models (VFMs) to expand the previous discriminative space (based on forgery patterns only), such that the discrimination is decided by both forgery and semantic cues, thereby reducing the overfitting to specific forgery patterns. A straightforward solution is to fully fine-tune VFMs, but it risks distorting the well-learned semantic knowledge, pushing the model back toward overfitting. To this end, we design a novel approach called Effort: Efficient orthogonal modeling for generalizable AIGI detection. Specifically, we employ Singular Value Decomposition (SVD) to construct the orthogonal semantic and forgery subspaces. By freezing the principal components and adapting the residual components (sim0.19M parameters), we preserve the original semantic subspace and use its orthogonal subspace for learning forgeries. Extensive experiments on AIGI detection benchmarks demonstrate the superior effectiveness of our approach.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Efficient attentions have greatly improved the computational efficiency of Transformers. However, most existing linear attention mechanisms suffer from an efficiency degradation problem, leading to inefficiencies in causal language modeling and hindering their application in long-range language models. This problem is more pronounced under language modeling with unbounded contexts. In this paper, we propose Linear Attention Via Orthogonal memory~(\shortname) to address these limitations, achieving strong performance while maintaining linear complexity. \shortname employs orthogonal decomposition to compress a context into a fixed-size orthogonal memory while effectively minimizing redundancy within the context. Given that orthogonal memory compresses global information, we further dissect the context to amplify fine-grained local information. Additionally, we embed the relative position encoding into \shortname to improve the extrapolation ability. Experimental results show that \shortname greatly improves the efficiency of the causal language model with the best extrapolation performance and outperforms other efficient baselines. Further, we endeavor to employ \shortname for unbounded language modeling and successfully scale the context length to 128K.

Masked Image Modeling (MIM) is a powerful self-supervised strategy for visual pre-training without the use of labels. MIM applies random crops to input images, processes them with an encoder, and then recovers the masked inputs with a decoder, which encourages the network to capture and learn structural information about objects and scenes. The intermediate feature representations obtained from MIM are suitable for fine-tuning on downstream tasks. In this paper, we propose an Image Modeling framework based on random orthogonal projection instead of binary masking as in MIM. Our proposed Random Orthogonal Projection Image Modeling (ROPIM) reduces spatially-wise token information under guaranteed bound on the noise variance and can be considered as masking entire spatial image area under locally varying masking degrees. Since ROPIM uses a random subspace for the projection that realizes the masking step, the readily available complement of the subspace can be used during unmasking to promote recovery of removed information. In this paper, we show that using random orthogonal projection leads to superior performance compared to crop-based masking. We demonstrate state-of-the-art results on several popular benchmarks.

Graph-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.

Large text-to-image diffusion models have impressive capabilities in generating photorealistic images from text prompts. How to effectively guide or control these powerful models to perform different downstream tasks becomes an important open problem. To tackle this challenge, we introduce a principled finetuning method -- Orthogonal Finetuning (OFT), for adapting text-to-image diffusion models to downstream tasks. Unlike existing methods, OFT can provably preserve hyperspherical energy which characterizes the pairwise neuron relationship on the unit hypersphere. We find that this property is crucial for preserving the semantic generation ability of text-to-image diffusion models. To improve finetuning stability, we further propose Constrained Orthogonal Finetuning (COFT) which imposes an additional radius constraint to the hypersphere. Specifically, we consider two important finetuning text-to-image tasks: subject-driven generation where the goal is to generate subject-specific images given a few images of a subject and a text prompt, and controllable generation where the goal is to enable the model to take in additional control signals. We empirically show that our OFT framework outperforms existing methods in generation quality and convergence speed.

In this paper, we introduce Knowledge-Orthogonal Reasoning (KOR), which minimizes the impact of domain-specific knowledge for a more accurate evaluation of models' reasoning abilities in out-of-distribution scenarios. Based on this concept, we propose the Knowledge-Orthogonal Reasoning Benchmark (KOR-Bench), encompassing five task categories: Operation, Logic, Cipher, Puzzle, and Counterfactual. KOR-Bench emphasizes the effectiveness of models in applying new rule descriptions to solve novel rule-driven questions, revealing that top-performing models like Claude-3.5-Sonnet and GPT-4o only achieve 58.96% and 58.00% accuracy, respectively. We conduct thorough analyses to identify bottlenecks in the Cipher task using Stepwise Prompting, discovering that two rounds of Self-Correction yield optimal results. Complex Task Processing evaluates model performance across three integrated tasks, while we also explore the impact of Tricks on the Puzzle task and visualize rule-focused attention to enhance our understanding of model behavior. We aim for KOR-Bench to be a valuable resource for enhancing models' reasoning capabilities and fostering further research in this field.

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Multi-Task Reinforcement Learning (MTRL) tackles the long-standing problem of endowing agents with skills that generalize across a variety of problems. To this end, sharing representations plays a fundamental role in capturing both unique and common characteristics of the tasks. Tasks may exhibit similarities in terms of skills, objects, or physical properties while leveraging their representations eases the achievement of a universal policy. Nevertheless, the pursuit of learning a shared set of diverse representations is still an open challenge. In this paper, we introduce a novel approach for representation learning in MTRL that encapsulates common structures among the tasks using orthogonal representations to promote diversity. Our method, named Mixture Of Orthogonal Experts (MOORE), leverages a Gram-Schmidt process to shape a shared subspace of representations generated by a mixture of experts. When task-specific information is provided, MOORE generates relevant representations from this shared subspace. We assess the effectiveness of our approach on two MTRL benchmarks, namely MiniGrid and MetaWorld, showing that MOORE surpasses related baselines and establishes a new state-of-the-art result on MetaWorld.

We present developments and applications for the diagonalization of shell-model hamiltonians in a discrete non-orthogonal basis (DNO-SM). The method, and its actual numerical implementation CARINA, based on mean-field and beyond-mean field techniques has already been applied in previous studies and is focused on basis states selection optimization. The method is benchmarked against a full set of sd shell exact diagonalizations, and is applied for the first time to the heavy deformed ^{254}No nucleus.

While the image diffusion model has made significant strides in text-driven 3D content creation, it often falls short in accurately capturing the intended meaning of the text prompt, particularly with respect to direction information. This shortcoming gives rise to the Janus problem, where multi-faced 3D models are produced with the guidance of such diffusion models. In this paper, we present a robust pipeline for generating high-fidelity 3D content with orthogonal-view image guidance. Specifically, we introduce a novel 2D diffusion model that generates an image consisting of four orthogonal-view sub-images for the given text prompt. The 3D content is then created with this diffusion model, which enhances 3D consistency and provides strong structured semantic priors. This addresses the infamous Janus problem and significantly promotes generation efficiency. Additionally, we employ a progressive 3D synthesis strategy that results in substantial improvement in the quality of the created 3D contents. Both quantitative and qualitative evaluations show that our method demonstrates a significant improvement over previous text-to-3D techniques.

Domain generalization (DG) aims to avoid the performance degradation of the model when the distribution shift between the limited training data and unseen test data occurs. Recently, foundation models with enormous parameters have been pre-trained with huge datasets, demonstrating strong generalization ability and showing promising direction for solving the DG problem. However, fully Fine-Tuning (FT) the foundation models results in unsatisfactory out-of-distribution accuracy due to the destroyed pre-trained generalized features. Recently, Parameter-Efficient Fine-Tuning (PEFT) alleviates the above problem by fine-tuning a small portion of the model parameters while keeping the rest frozen, which achieves better generalization performance compared to FT. Nevertheless, PEFT still suffers from the issue of overfitting to the training domains. To address the above issue, we propose Parameter-Efficient Group with Orthogonal regularization (PEGO) for vision transformers, which effectively preserves the generalization ability of the pre-trained network and learns more diverse knowledge compared with conventional PEFT. Specifically, we inject a group of trainable Low-Rank Adaptation (LoRA) modules into the pre-trained model and propose an orthogonal regularization loss to enhance the generalization ability of the model. Our framework achieves SOTA performance on five DG benchmarks, while only requiring training a small number of parameters without adding additional testing cost.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

Large language models (LLMs) have shown increasing power on various natural language processing (NLP) tasks. However, tuning these models for downstream tasks usually needs exorbitant costs or is unavailable due to commercial considerations. Recently, black-box tuning has been proposed to address this problem by optimizing task-specific prompts without accessing the gradients and hidden representations. However, most existing works have yet fully exploited the potential of gradient-free optimization under the scenario of few-shot learning. In this paper, we describe BBT-RGB, a suite of straightforward and complementary techniques for enhancing the efficiency and performance of black-box optimization. Specifically, our method includes three plug-and-play components: (1) Two-stage derivative-free optimization strategy that facilitates fast convergence and mitigates overfitting; (2) Automatic verbalizer construction with its novel usage under few-shot settings; (3) Better prompt initialization policy based on instruction search and auto-selected demonstration. Extensive experiments across various tasks on natural language understanding and inference demonstrate the effectiveness of our method. Our codes are publicly available at https://github.com/QiushiSun/BBT-RGB.

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.

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the iterative construction of the signal support via greedy index selection and a signal update based on solving a local data-fitting problem restricted to the current support. We show that greedy selection rules associated with popular weighted sparsity-promoting loss functions admit explicitly computable and simple formulas. Specifically, we consider ell^0 - and ell^1 -based versions of the weighted LASSO (Least Absolute Shrinkage and Selection Operator), the Square-Root LASSO (SR-LASSO) and the Least Absolute Deviations LASSO (LAD-LASSO). Through numerical experiments on Gaussian compressive sensing and high-dimensional function approximation, we demonstrate the effectiveness of the proposed algorithms and empirically show that they inherit desirable characteristics from the corresponding loss functions, such as SR-LASSO's noise-blind optimal parameter tuning and LAD-LASSO's fault tolerance. In doing so, our study sheds new light on the connection between greedy sparse recovery and convex relaxation.

With the increasingly powerful performances and enormous scales of Pretrained Language Models (PLMs), promoting parameter efficiency in fine-tuning has become a crucial need for effective and efficient adaptation to various downstream tasks. One representative line of fine-tuning methods is Orthogonal Fine-tuning (OFT), which rigorously preserves the angular distances within the parameter space to preserve the pretrained knowledge. Despite the empirical effectiveness, OFT still suffers low parameter efficiency at O(d^2) and limited capability of downstream adaptation. Inspired by Givens rotation, in this paper, we proposed quasi-Givens Orthogonal Fine-Tuning (qGOFT) to address the problems. We first use O(d) Givens rotations to accomplish arbitrary orthogonal transformation in SO(d) with provable equivalence, reducing parameter complexity from O(d^2) to O(d). Then we introduce flexible norm and relative angular adjustments under soft orthogonality regularization to enhance the adaptation capability of downstream semantic deviations. Extensive experiments on various tasks and PLMs validate the effectiveness of our methods.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10times increase in performance speed.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the Wronskian of suitable solutions of the two underlying difference equations. Until now only the case of perturbations of the main diagonal was known. We extend the known results to arbitrary perturbations, allow any (half-)open and closed spectral intervals, simplify the proof, and establish the comparison theorem.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nystr\"{o}m method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

Given only a few observed entries from a low-rank matrix X, matrix completion is the problem of imputing the missing entries, and it formalizes a wide range of real-world settings that involve estimating missing data. However, when there are too few observed entries to complete the matrix, what other aspects of the underlying matrix can be reliably recovered? We study one such problem setting, that of "one-sided" matrix completion, where our goal is to recover the right singular vectors of X, even in the regime where recovering the left singular vectors is impossible, which arises when there are more rows than columns and very few observations. We propose a natural algorithm that involves imputing the missing values of the matrix X^TX and show that even with only two observations per row in X, we can provably recover X^TX as long as we have at least Omega(r^2 d log d) rows, where r is the rank and d is the number of columns. We evaluate our algorithm on one-sided recovery of synthetic data and low-coverage genome sequencing. In these settings, our algorithm substantially outperforms standard matrix completion and a variety of direct factorization methods.

Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new closed-form predictor variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at 100 and 300 epochs (top-1 linear accuracy on ImageNet).

We study the matrix models pi:C(S_N^+)to M_N(C(X)) which are flat, in the sense that the standard generators of C(S_N^+) are mapped to rank 1 projections. Our first result is a generalization of the Pauli matrix construction at N=4, using finite groups and 2-cocycles. Our second result is the construction of a universal representation of C(S_N^+), inspired from the Sinkhorn algorithm, that we conjecture to be inner faithful.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

Low-rank adaptation~(LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices A and B to represent the weight change, i.e., Delta W=BA. Despite LoRA's progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats Delta W as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover Delta W. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. Our code is released at https://github.com/Chaos96/fourierft.

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.

We show how the Schur-Weyl duality that exists between the partition algebra and the symmetric group results in a stronger theoretical foundation for characterising all of the possible permutation equivariant neural networks whose layers are some tensor power of the permutation representation M_n of the symmetric group S_n. In doing so, we unify two separate bodies of literature, and we correct some of the major results that are now widely quoted by the machine learning community. In particular, we find a basis of matrices for the learnable, linear, permutation equivariant layer functions between such tensor power spaces in the standard basis of M_n by using an elegant graphical representation of a basis of set partitions for the partition algebra and its related vector spaces. Also, we show how we can calculate the number of weights that must appear in these layer functions by looking at certain paths through the McKay quiver for M_n. Finally, we describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Exceptional text-to-image (T2I) generation results of Stable Diffusion models (SDMs) come with substantial computational demands. To resolve this issue, recent research on efficient SDMs has prioritized reducing the number of sampling steps and utilizing network quantization. Orthogonal to these directions, this study highlights the power of classical architectural compression for general-purpose T2I synthesis by introducing block-removed knowledge-distilled SDMs (BK-SDMs). We eliminate several residual and attention blocks from the U-Net of SDMs, obtaining over a 30% reduction in the number of parameters, MACs per sampling step, and latency. We conduct distillation-based pretraining with only 0.22M LAION pairs (fewer than 0.1% of the full training pairs) on a single A100 GPU. Despite being trained with limited resources, our compact models can imitate the original SDM by benefiting from transferred knowledge and achieve competitive results against larger multi-billion parameter models on the zero-shot MS-COCO benchmark. Moreover, we demonstrate the applicability of our lightweight pretrained models in personalized generation with DreamBooth finetuning.

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an undisputed principle of diffusion models. We consider that such a uniform assumption is not the optimal solution in practice; i.e., we can find different optimal time steps for different models. Therefore, we propose to search the optimal time steps sequence and compressed model architecture in a unified framework to achieve effective image generation for diffusion models without any further training. Specifically, we first design a unified search space that consists of all possible time steps and various architectures. Then, a two stage evolutionary algorithm is introduced to find the optimal solution in the designed search space. To further accelerate the search process, we employ FID score between generated and real samples to estimate the performance of the sampled examples. As a result, the proposed method is (i).training-free, obtaining the optimal time steps and model architecture without any training process; (ii). orthogonal to most advanced diffusion samplers and can be integrated to gain better sample quality. (iii). generalized, where the searched time steps and architectures can be directly applied on different diffusion models with the same guidance scale. Experimental results show that our method achieves excellent performance by using only a few time steps, e.g. 17.86 FID score on ImageNet 64 times 64 with only four steps, compared to 138.66 with DDIM. The code is available at https://github.com/lilijiangg/AutoDiffusion.

Self-alignment, whereby models learn to improve themselves without human annotation, is a rapidly growing research area. However, existing techniques often fail to improve complex reasoning tasks due to the difficulty of assigning correct rewards. An orthogonal approach that is known to improve correctness is self-consistency, a method applied at inference time based on multiple sampling in order to find the most consistent answer. In this work, we extend the self-consistency concept to help train models. We thus introduce self-consistency preference optimization (ScPO), which iteratively trains consistent answers to be preferred over inconsistent ones on unsupervised new problems. We show ScPO leads to large improvements over conventional reward model training on reasoning tasks such as GSM8K and MATH, closing the gap with supervised training with gold answers or preferences, and that combining ScPO with standard supervised learning improves results even further. On ZebraLogic, ScPO finetunes Llama-3 8B to be superior to Llama-3 70B, Gemma-2 27B, and Claude-3 Haiku.

While LLMs have demonstrated impressive performance across various domains and tasks, their security issues have become increasingly severe. Machine unlearning (MU) has emerged as a promising solution to address these issues by removing the influence of undesired data on the target model without compromising its utility in other aspects. MU typically assumes full access to the original training data to preserve utility, which is difficult to achieve in LLM unlearning. Existing LLM unlearning methods often assume access to data most affected by undesired data unlearning. However, this assumption underestimates the entanglement among various LLM capabilities and ignores data access limitations due to various issues. Moreover, these LLM unlearning methods do not sufficiently consider that unlearning requests in real-world scenarios are continuously emerging. To overcome these challenges and achieve practical LLM unlearning, we propose the O3 framework. The O3 framework includes an Out-Of-Distribution (OOD) detector to measure the similarity between input and unlearning data, and an Orthogonal low-rank adapter (LoRA) for continuously unlearning requested data. The OOD detector is trained with a novel contrastive entropy loss and utilizes a local-global layer-aggregated scoring mechanism. The orthogonal LoRA achieves parameter disentanglement among continual unlearning requests. During inference, our O3 framework can smartly decide whether and to what extent to load the unlearning LoRA based on the OOD detector's predictions. Notably, O3's effectiveness does not rely on any retained data. We conducted extensive experiments on O3 and state-of-the-art LLM unlearning methods across three tasks and seven datasets. The results indicate that O3 consistently achieves the best trade-off between unlearning effectiveness and utility preservation, especially when facing continuous unlearning requests.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~muas yr^{-1}. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~muas yr^{-1} in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 muas yr^{-1} over 150degr on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5,sigma significance level.

Current fake audio detection algorithms have achieved promising performances on most datasets. However, their performance may be significantly degraded when dealing with audio of a different dataset. The orthogonal weight modification to overcome catastrophic forgetting does not consider the similarity of genuine audio across different datasets. To overcome this limitation, we propose a continual learning algorithm for fake audio detection to overcome catastrophic forgetting, called Regularized Adaptive Weight Modification (RAWM). When fine-tuning a detection network, our approach adaptively computes the direction of weight modification according to the ratio of genuine utterances and fake utterances. The adaptive modification direction ensures the network can effectively detect fake audio on the new dataset while preserving its knowledge of old model, thus mitigating catastrophic forgetting. In addition, genuine audio collected from quite different acoustic conditions may skew their feature distribution, so we introduce a regularization constraint to force the network to remember the old distribution in this regard. Our method can easily be generalized to related fields, like speech emotion recognition. We also evaluate our approach across multiple datasets and obtain a significant performance improvement on cross-dataset experiments.

The capabilities and adoption of deep neural networks (DNNs) grow at an exhilarating pace: Vision models accurately classify human actions in videos and identify cancerous tissue in medical scans as precisely than human experts; large language models answer wide-ranging questions, generate code, and write prose, becoming the topic of everyday dinner-table conversations. Even though their uses are exhilarating, the continually increasing model sizes and computational complexities have a dark side. The economic cost and negative environmental externalities of training and serving models is in evident disharmony with financial viability and climate action goals. Instead of pursuing yet another increase in predictive performance, this dissertation is dedicated to the improvement of neural network efficiency. Specifically, a core contribution addresses the efficiency aspects during online inference. Here, the concept of Continual Inference Networks (CINs) is proposed and explored across four publications. CINs extend prior state-of-the-art methods developed for offline processing of spatio-temporal data and reuse their pre-trained weights, improving their online processing efficiency by an order of magnitude. These advances are attained through a bottom-up computational reorganization and judicious architectural modifications. The benefit to online inference is demonstrated by reformulating several widely used network architectures into CINs, including 3D CNNs, ST-GCNs, and Transformer Encoders. An orthogonal contribution tackles the concurrent adaptation and computational acceleration of a large source model into multiple lightweight derived models. Drawing on fusible adapter networks and structured pruning, Structured Pruning Adapters achieve superior predictive accuracy under aggressive pruning using significantly fewer learned weights compared to fine-tuning with pruning.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves extensive sampling at inference time guided by an external LLM verifier, resulting in a two-player system. Despite external guidance, the effectiveness of this system demonstrates the potential of a single LLM to tackle complex tasks. Thus, we pose a new research problem: Can we internalize the searching capabilities to fundamentally enhance the reasoning abilities of a single LLM? This work explores an orthogonal direction focusing on post-training LLMs for autoregressive searching (i.e., an extended reasoning process with self-reflection and self-exploration of new strategies). To achieve this, we propose the Chain-of-Action-Thought (COAT) reasoning and a two-stage training paradigm: 1) a small-scale format tuning stage to internalize the COAT reasoning format and 2) a large-scale self-improvement stage leveraging reinforcement learning. Our approach results in Satori, a 7B LLM trained on open-source models and data. Extensive empirical evaluations demonstrate that Satori achieves state-of-the-art performance on mathematical reasoning benchmarks while exhibits strong generalization to out-of-domain tasks. Code, data, and models will be fully open-sourced.

Improvements in language models' capabilities have pushed their applications towards longer contexts, making long-context evaluation and development an active research area. However, many disparate use-cases are grouped together under the umbrella term of "long-context", defined simply by the total length of the model's input, including - for example - Needle-in-a-Haystack tasks, book summarization, and information aggregation. Given their varied difficulty, in this position paper we argue that conflating different tasks by their context length is unproductive. As a community, we require a more precise vocabulary to understand what makes long-context tasks similar or different. We propose to unpack the taxonomy of long-context based on the properties that make them more difficult with longer contexts. We propose two orthogonal axes of difficulty: (I) Diffusion: How hard is it to find the necessary information in the context? (II) Scope: How much necessary information is there to find? We survey the literature on long-context, provide justification for this taxonomy as an informative descriptor, and situate the literature with respect to it. We conclude that the most difficult and interesting settings, whose necessary information is very long and highly diffused within the input, is severely under-explored. By using a descriptive vocabulary and discussing the relevant properties of difficulty in long-context, we can implement more informed research in this area. We call for a careful design of tasks and benchmarks with distinctly long context, taking into account the characteristics that make it qualitatively different from shorter context.

Neural Radiance Fields (NeRFs) have proven to be powerful 3D representations, capable of high quality novel view synthesis of complex scenes. While NeRFs have been applied to graphics, vision, and robotics, problems with slow rendering speed and characteristic visual artifacts prevent adoption in many use cases. In this work, we investigate combining an autoencoder (AE) with a NeRF, in which latent features (instead of colours) are rendered and then convolutionally decoded. The resulting latent-space NeRF can produce novel views with higher quality than standard colour-space NeRFs, as the AE can correct certain visual artifacts, while rendering over three times faster. Our work is orthogonal to other techniques for improving NeRF efficiency. Further, we can control the tradeoff between efficiency and image quality by shrinking the AE architecture, achieving over 13 times faster rendering with only a small drop in performance. We hope that our approach can form the basis of an efficient, yet high-fidelity, 3D scene representation for downstream tasks, especially when retaining differentiability is useful, as in many robotics scenarios requiring continual learning.

Transformers rely on both content-based and position-based addressing mechanisms to make predictions, but existing positional encoding techniques often diminish the effectiveness of position-based addressing. Many current methods enforce rigid patterns in attention maps, limiting the ability to model long-range dependencies and adapt to diverse tasks. Additionally, most positional encodings are learned as general biases, lacking the specialization required for different instances within a dataset. To address this, we propose conTextualized equivariAnt Position Embedding (TAPE), a novel framework that enhances positional embeddings by incorporating sequence content across layers. TAPE introduces dynamic, context-aware positional encodings, overcoming the constraints of traditional fixed patterns. By enforcing permutation and orthogonal equivariance, TAPE ensures the stability of positional encodings during updates, improving robustness and adaptability. Our method can be easily integrated into pre-trained transformers, offering parameter-efficient fine-tuning with minimal overhead. Extensive experiments shows that TAPE achieves superior performance in language modeling, arithmetic reasoning, and long-context retrieval tasks compared to existing positional embedding techniques.

We introduce XFT, a simple yet powerful training scheme, by simply merging upcycled Mixture-of-Experts (MoE) to unleash the performance limit of instruction-tuned code Large Language Models (LLMs). While vanilla sparse upcycling fails to improve instruction tuning, XFT introduces a shared expert mechanism with a novel routing weight normalization strategy into sparse upcycling, which significantly boosts instruction tuning. After fine-tuning the upcycled MoE model, XFT introduces a learnable model merging mechanism to compile the upcycled MoE model back to a dense model, achieving upcycled MoE-level performance with only dense-model compute. By applying XFT to a 1.3B model, we create a new state-of-the-art tiny code LLM (<3B) with 67.1 and 64.6 pass@1 on HumanEval and HumanEval+ respectively. With the same data and model architecture, XFT improves supervised fine-tuning (SFT) by 13% on HumanEval+, along with consistent improvements from 2% to 13% on MBPP+, MultiPL-E, and DS-1000, demonstrating its generalizability. XFT is fully orthogonal to existing techniques such as Evol-Instruct and OSS-Instruct, opening a new dimension for improving code instruction tuning. Codes are available at https://github.com/ise-uiuc/xft .

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

Large language models (LLMs) represent a groundbreaking advancement in the domain of natural language processing due to their impressive reasoning abilities. Recently, there has been considerable interest in increasing the context lengths for these models to enhance their applicability to complex tasks. However, at long context lengths and large batch sizes, the key-value (KV) cache, which stores the attention keys and values, emerges as the new bottleneck in memory usage during inference. To address this, we propose Eigen Attention, which performs the attention operation in a low-rank space, thereby reducing the KV cache memory overhead. Our proposed approach is orthogonal to existing KV cache compression techniques and can be used synergistically with them. Through extensive experiments over OPT, MPT, and Llama model families, we demonstrate that Eigen Attention results in up to 40% reduction in KV cache sizes and up to 60% reduction in attention operation latency with minimal drop in performance.

With the tremendous success of large transformer models in natural language understanding, down-sizing them for cost-effective deployments has become critical. Recent studies have explored the low-rank weight factorization techniques which are efficient to train, and apply out-of-the-box to any transformer architecture. Unfortunately, the low-rank assumption tends to be over-restrictive and hinders the expressiveness of the compressed model. This paper proposes, DSFormer, a simple alternative factorization scheme which expresses a target weight matrix as the product of a small dense and a semi-structured sparse matrix. The resulting approximation is more faithful to the weight distribution in transformers and therefore achieves a stronger efficiency-accuracy trade-off. Another concern with existing factorizers is their dependence on a task-unaware initialization step which degrades the accuracy of the resulting model. DSFormer addresses this issue through a novel Straight-Through Factorizer (STF) algorithm that jointly learns all the weight factorizations to directly maximize the final task accuracy. Extensive experiments on multiple natural language understanding benchmarks demonstrate that DSFormer obtains up to 40% better compression than the state-of-the-art low-rank factorizers, leading semi-structured sparsity baselines and popular knowledge distillation approaches. Our approach is also orthogonal to mainstream compressors and offers up to 50% additional compression when added to popular distilled, layer-shared and quantized transformers. We empirically evaluate the benefits of STF over conventional optimization practices.

The performance of Large Language Models (LLMs) in reasoning tasks depends heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency being critical methods that enhance this ability. However, these methods do not fully exploit the answers generated by the LLM to guide subsequent responses. This paper proposes a new prompting method, named Progressive-Hint Prompting (PHP), that enables automatic multiple interactions between users and LLMs by using previously generated answers as hints to progressively guide toward the correct answers. PHP is orthogonal to CoT and self-consistency, making it easy to combine with state-of-the-art techniques to further improve performance. We conducted extensive and comprehensive experiments on seven benchmarks. The results show that PHP significantly improves accuracy while remaining highly efficient. For instance, with text-davinci-003, we observed a 4.2% improvement on GSM8K with greedy decoding compared to Complex CoT, and a 46.17% reduction in sample paths with self-consistency. With GPT-4 and PHP, we achieve state-of-the-art performances on SVAMP (89.1% -> 91.9%), GSM8K (92% -> 95.5%), AQuA (76.4% -> 79.9%) and MATH (50.3% -> 53.9%).

Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in model complexity and in the computational resources invested in training these models. Our work questions the underlying paradigm of compressing large training data into ever growing parametric representations. We rather present an orthogonal, semi-parametric approach. We complement comparably small diffusion or autoregressive models with a separate image database and a retrieval strategy. During training we retrieve a set of nearest neighbors from this external database for each training instance and condition the generative model on these informative samples. While the retrieval approach is providing the (local) content, the model is focusing on learning the composition of scenes based on this content. As demonstrated by our experiments, simply swapping the database for one with different contents transfers a trained model post-hoc to a novel domain. The evaluation shows competitive performance on tasks which the generative model has not been trained on, such as class-conditional synthesis, zero-shot stylization or text-to-image synthesis without requiring paired text-image data. With negligible memory and computational overhead for the external database and retrieval we can significantly reduce the parameter count of the generative model and still outperform the state-of-the-art.

Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal. To this end, we train Generative Adversarial Networks at the largest scale yet attempted, and study the instabilities specific to such scale. We find that applying orthogonal regularization to the generator renders it amenable to a simple "truncation trick," allowing fine control over the trade-off between sample fidelity and variety by reducing the variance of the Generator's input. Our modifications lead to models which set the new state of the art in class-conditional image synthesis. When trained on ImageNet at 128x128 resolution, our models (BigGANs) achieve an Inception Score (IS) of 166.5 and Frechet Inception Distance (FID) of 7.4, improving over the previous best IS of 52.52 and FID of 18.6.

In this work, we introduce FlexGen, a flexible framework designed to generate controllable and consistent multi-view images, conditioned on a single-view image, or a text prompt, or both. FlexGen tackles the challenges of controllable multi-view synthesis through additional conditioning on 3D-aware text annotations. We utilize the strong reasoning capabilities of GPT-4V to generate 3D-aware text annotations. By analyzing four orthogonal views of an object arranged as tiled multi-view images, GPT-4V can produce text annotations that include 3D-aware information with spatial relationship. By integrating the control signal with proposed adaptive dual-control module, our model can generate multi-view images that correspond to the specified text. FlexGen supports multiple controllable capabilities, allowing users to modify text prompts to generate reasonable and corresponding unseen parts. Additionally, users can influence attributes such as appearance and material properties, including metallic and roughness. Extensive experiments demonstrate that our approach offers enhanced multiple controllability, marking a significant advancement over existing multi-view diffusion models. This work has substantial implications for fields requiring rapid and flexible 3D content creation, including game development, animation, and virtual reality. Project page: https://xxu068.github.io/flexgen.github.io/.

Large Language Models (LLMs) have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical reasoning processes. To mitigate this problem, we introduced Hint-before-Solving Prompting (HSP), which guides the model to generate hints (e.g., specific knowledge or key ideas) for solving the problem and then generate solutions containing intermediate reasoning steps. Since HSP is orthogonal to prompting methods (e.g., Chain-of-Thought (CoT)), we applied HSP to CoT, Least-to-Most, Plan-and-Solve, and Standard promptings. The results of extensive experiments on 6 reasoning benchmarks and 4 open-source LLMs demonstrate that HSP can effectively improve the accuracy of reasoning tasks: (1) By applying high-quality hint-enhanced HSP to CoT prompting, Llama2-70B-Chat shows an improvement of 9.7. (2) Beyond exploring training-free LLM capabilities, we built the HSPMATH dataset based on HSP and fine-tuned Llemma-7B, reaching 64.3 accuracy, surpassing GPT-3.5 and WizardMath-13B. We make our code and dataset publicly available at https://github.com/jinlanfu/HSP.

The objective of this paper is to develop a functional system for translating spoken languages into sign languages, referred to as Spoken2Sign translation. The Spoken2Sign task is orthogonal and complementary to traditional sign language to spoken language (Sign2Spoken) translation. To enable Spoken2Sign translation, we present a simple baseline consisting of three steps: 1) creating a gloss-video dictionary using existing Sign2Spoken benchmarks; 2) estimating a 3D sign for each sign video in the dictionary; 3) training a Spoken2Sign model, which is composed of a Text2Gloss translator, a sign connector, and a rendering module, with the aid of the yielded gloss-3D sign dictionary. The translation results are then displayed through a sign avatar. As far as we know, we are the first to present the Spoken2Sign task in an output format of 3D signs. In addition to its capability of Spoken2Sign translation, we also demonstrate that two by-products of our approach-3D keypoint augmentation and multi-view understanding-can assist in keypoint-based sign language understanding. Code and models are available at https://github.com/FangyunWei/SLRT.

Natural image matting algorithms aim to predict the transparency map (alpha-matte) with the trimap guidance. However, the production of trimaps often requires significant labor, which limits the widespread application of matting algorithms on a large scale. To address the issue, we propose Matte Anything model (MatAny), an interactive natural image matting model which could produce high-quality alpha-matte with various simple hints. The key insight of MatAny is to generate pseudo trimap automatically with contour and transparency prediction. We leverage task-specific vision models to enhance the performance of natural image matting. Specifically, we use the segment anything model (SAM) to predict high-quality contour with user interaction and an open-vocabulary (OV) detector to predict the transparency of any object. Subsequently, a pretrained image matting model generates alpha mattes with pseudo trimaps. MatAny is the interactive matting algorithm with the most supported interaction methods and the best performance to date. It consists of orthogonal vision models without any additional training. We evaluate the performance of MatAny against several current image matting algorithms, and the results demonstrate the significant potential of our approach.

Prompting methods such as Chain-of-Thought (CoT) have shed new light on enhancing the reasoning capabilities of large language models, and researchers have extensively explored the generation process of rationales and answers. However, they have overlooked the potential challenges posed by the poor quality of reasoning problems, which may influence the reasoning performance significantly. In this work, we propose Self-Polish (SP), a novel method that facilitates the model's problem-solving process by prompting them to progressively refine the given problems to be more comprehensible and solvable. Specifically, the method teaches models to eliminate irrelevant information, rearrange the logic structure and organize local conditions into new ones parallelly. SP is orthogonal to all other prompting methods, making it convenient to integrate with state-of-the-art techniques for further improvement. We conduct thorough experiments on five benchmarks to illustrate the effectiveness of the proposed method. For example, with Text-davinci-003, our method boosts the performance of standard few-shot prompting by 8.0% on GSM8K and 17.8% on MultiArith; it also improves the performance of CoT by 6.0% on GSM8K and 6.0% on MathQA, respectively. Furthermore, our method also showcases impressive performance on robustness evaluation.

Domain shift across crowd data severely hinders crowd counting models to generalize to unseen scenarios. Although domain adaptive crowd counting approaches close this gap to a certain extent, they are still dependent on the target domain data to adapt (e.g. finetune) their models to the specific domain. In this paper, we aim to train a model based on a single source domain which can generalize well on any unseen domain. This falls into the realm of domain generalization that remains unexplored in crowd counting. We first introduce a dynamic sub-domain division scheme which divides the source domain into multiple sub-domains such that we can initiate a meta-learning framework for domain generalization. The sub-domain division is dynamically refined during the meta-learning. Next, in order to disentangle domain-invariant information from domain-specific information in image features, we design the domain-invariant and -specific crowd memory modules to re-encode image features. Two types of losses, i.e. feature reconstruction and orthogonal losses, are devised to enable this disentanglement. Extensive experiments on several standard crowd counting benchmarks i.e. SHA, SHB, QNRF, and NWPU, show the strong generalizability of our method.

This paper describes a new technique for finding disentangled semantic directions in the latent space of StyleGAN. Our method identifies meaningful orthogonal subspaces that allow editing of one human face attribute, while minimizing undesired changes in other attributes. Our model is capable of editing a single attribute in multiple directions, resulting in a range of possible generated images. We compare our scheme with three state-of-the-art models and show that our method outperforms them in terms of face editing and disentanglement capabilities. Additionally, we suggest quantitative measures for evaluating attribute separation and disentanglement, and exhibit the superiority of our model with respect to those measures.

We consider distributed image transmission over a noisy multiple access channel (MAC) using deep joint source-channel coding (DeepJSCC). It is known that Shannon's separation theorem holds when transmitting independent sources over a MAC in the asymptotic infinite block length regime. However, we are interested in the practical finite block length regime, in which case separate source and channel coding is known to be suboptimal. We introduce a novel joint image compression and transmission scheme, where the devices send their compressed image representations in a non-orthogonal manner. While non-orthogonal multiple access (NOMA) is known to achieve the capacity region, to the best of our knowledge, non-orthogonal joint source channel coding (JSCC) scheme for practical systems has not been studied before. Through extensive experiments, we show significant improvements in terms of the quality of the reconstructed images compared to orthogonal transmission employing current DeepJSCC approaches particularly for low bandwidth ratios. We publicly share source code to facilitate further research and reproducibility.

Modern machine learning research relies on relatively few carefully curated datasets. Even in these datasets, and typically in `untidy' or raw data, practitioners are faced with significant issues of data quality and diversity which can be prohibitively labor intensive to address. Existing methods for dealing with these challenges tend to make strong assumptions about the particular issues at play, and often require a priori knowledge or metadata such as domain labels. Our work is orthogonal to these methods: we instead focus on providing a unified and efficient framework for Metadata Archaeology -- uncovering and inferring metadata of examples in a dataset. We curate different subsets of data that might exist in a dataset (e.g. mislabeled, atypical, or out-of-distribution examples) using simple transformations, and leverage differences in learning dynamics between these probe suites to infer metadata of interest. Our method is on par with far more sophisticated mitigation methods across different tasks: identifying and correcting mislabeled examples, classifying minority-group samples, prioritizing points relevant for training and enabling scalable human auditing of relevant examples.

Uplink (UL) dominated sporadic transmission and stringent latency requirement of massive machine type communication (mMTC) forces researchers to abandon complicated grant-acknowledgment based legacy networks. UL grant-free non-orthogonal multiple access (NOMA) provides an array of features which can be harnessed to efficiently solve the problem of massive random connectivity and latency. Because of the inherent sparsity in user activity pattern in mMTC, the trend of existing literature specifically revolves around compressive sensing based multi user detection (CS-MUD) and Bayesian framework paradigm which employs either random or Zadoff-Chu spreading sequences for non-orthogonal multiple access. In this work, we propose sinusoidal code as candidate spreading sequences. We show that, sinusoidal codes allow some non-iterative algorithms to be employed in context of active user detection, channel estimation and data detection in a UL grant-free mMTC system. This relaxes the requirement of several impractical assumptions considered in the state-of-art algorithms with added advantages of performance guarantees and lower computational cost. Extensive simulation results validate the performance potential of sinusoidal codes in realistic mMTC environments.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are big(mathcal{O}big(frac 1nbig),,, mathcal{O}big(1{min{m,n}}big)big)-DP under some reasonable restrictions, where m and n are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural networks (SSNs). We show that techniques to properly identify the contributions of the different model components in SSNs, however, lead to suboptimal network estimation, slower convergence, and degenerated or erroneous predictions. In order to solve these problems while preserving favorable model properties, we propose a non-invasive post-hoc orthogonalization (PHO) that guarantees identifiability of model components and provides better estimation and prediction quality. Our theoretical findings are supported by numerical experiments, a benchmark comparison as well as a real-world application to COVID-19 infections.

This paper studies the problem of recovering cameras from a set of fundamental matrices. A set of fundamental matrices is said to be compatible if a set of cameras exists for which they are the fundamental matrices. We focus on the complete graph, where fundamental matrices for each pair of cameras are given. Previous work has established necessary and sufficient conditions for compatibility as rank and eigenvalue conditions on the n-view fundamental matrix obtained by concatenating the individual fundamental matrices. In this work, we show that the eigenvalue condition is redundant. We provide explicit homogeneous polynomials that describe necessary and sufficient conditions for compatibility in terms of the fundamental matrices and their epipoles. In this direction, we find that quadruple-wise compatibility is enough to ensure global compatibility for any number of cameras. We demonstrate that for four cameras, compatibility is generically described by triple-wise conditions and one additional equation involving all fundamental matrices.

Diffusion models have opened up new avenues for the field of image generation, resulting in the proliferation of high-quality models shared on open-source platforms. However, a major challenge persists in current text-to-image systems are often unable to handle diverse inputs, or are limited to single model results. Current unified attempts often fall into two orthogonal aspects: i) parse Diverse Prompts in input stage; ii) activate expert model to output. To combine the best of both worlds, we propose DiffusionGPT, which leverages Large Language Models (LLM) to offer a unified generation system capable of seamlessly accommodating various types of prompts and integrating domain-expert models. DiffusionGPT constructs domain-specific Trees for various generative models based on prior knowledge. When provided with an input, the LLM parses the prompt and employs the Trees-of-Thought to guide the selection of an appropriate model, thereby relaxing input constraints and ensuring exceptional performance across diverse domains. Moreover, we introduce Advantage Databases, where the Tree-of-Thought is enriched with human feedback, aligning the model selection process with human preferences. Through extensive experiments and comparisons, we demonstrate the effectiveness of DiffusionGPT, showcasing its potential for pushing the boundaries of image synthesis in diverse domains.

Diffusion-based text-to-image generative models, e.g., Stable Diffusion, have revolutionized the field of content generation, enabling significant advancements in areas like image editing and video synthesis. Despite their formidable capabilities, these models are not without their limitations. It is still challenging to synthesize an image that aligns well with the input text, and multiple runs with carefully crafted prompts are required to achieve satisfactory results. To mitigate these limitations, numerous studies have endeavored to fine-tune the pre-trained diffusion models, i.e., UNet, utilizing various technologies. Yet, amidst these efforts, a pivotal question of text-to-image diffusion model training has remained largely unexplored: Is it possible and feasible to fine-tune the text encoder to improve the performance of text-to-image diffusion models? Our findings reveal that, instead of replacing the CLIP text encoder used in Stable Diffusion with other large language models, we can enhance it through our proposed fine-tuning approach, TextCraftor, leading to substantial improvements in quantitative benchmarks and human assessments. Interestingly, our technique also empowers controllable image generation through the interpolation of different text encoders fine-tuned with various rewards. We also demonstrate that TextCraftor is orthogonal to UNet finetuning, and can be combined to further improve generative quality.

Recent advancements in large language models (LLMs) reveal a perplexing phenomenon in continual learning: despite extensive training, models experience significant performance declines, raising questions about task alignment and underlying knowledge retention. This study first explores the concept of "spurious forgetting", proposing that such performance drops often reflect a decline in task alignment rather than true knowledge loss. Through controlled experiments with a synthesized dataset, we investigate the dynamics of model performance during the initial training phases of new tasks, discovering that early optimization steps can disrupt previously established task alignments. Our theoretical analysis connects these shifts to orthogonal updates in model weights, providing a robust framework for understanding this behavior. Ultimately, we introduce a Freezing strategy that fix the bottom layers of the model, leading to substantial improvements in four continual learning scenarios. Our findings underscore the critical distinction between task alignment and knowledge retention, paving the way for more effective strategies in continual learning.

This study focuses on the topic of offline preference-based reinforcement learning (PbRL), a variant of conventional reinforcement learning that dispenses with the need for online interaction or specification of reward functions. Instead, the agent is provided with fixed offline trajectories and human preferences between pairs of trajectories to extract the dynamics and task information, respectively. Since the dynamics and task information are orthogonal, a naive approach would involve using preference-based reward learning followed by an off-the-shelf offline RL algorithm. However, this requires the separate learning of a scalar reward function, which is assumed to be an information bottleneck of the learning process. To address this issue, we propose the offline preference-guided policy optimization (OPPO) paradigm, which models offline trajectories and preferences in a one-step process, eliminating the need for separately learning a reward function. OPPO achieves this by introducing an offline hindsight information matching objective for optimizing a contextual policy and a preference modeling objective for finding the optimal context. OPPO further integrates a well-performing decision policy by optimizing the two objectives iteratively. Our empirical results demonstrate that OPPO effectively models offline preferences and outperforms prior competing baselines, including offline RL algorithms performed over either true or pseudo reward function specifications. Our code is available on the project website: https://sites.google.com/view/oppo-icml-2023 .

Source-Free Video Unsupervised Domain Adaptation (SFVUDA) methods consists in the task of adapting an action recognition model, trained on a labelled source dataset, to an unlabelled target dataset, without accessing the actual source data. Previous approaches have attempted to address SFVUDA by leveraging self-supervision (e.g., enforcing temporal consistency) derived from the target data itself. In this work we take an orthogonal approach by exploiting "web-supervision" from Large Language-Vision Models (LLVMs), driven by the rationale that LLVMs contain rich world prior, which is surprisingly robust to domain-shift. We showcase the unreasonable effectiveness of integrating LLVMs for SFVUDA by devising an intuitive and parameter efficient method, which we name as Domain Adaptation with Large Language-Vision models (DALL-V), that distills the world prior and complementary source model information into a student network tailored for the target. Despite the simplicity, DALL-V achieves significant improvement over state-of-the-art SFVUDA methods.

An effective way to realize non-orthogonal multiple access (NOMA) assisted grant-free transmission is to first create multiple receive signal-to-noise ratio (SNR) levels and then serve multiple grant-free users by employing these SNR levels as bandwidth resources. These SNR levels need to be pre-configured prior to the grant-free transmission and have great impact on the performance of grant-free networks. The aim of this letter is to illustrate different designs for configuring the SNR levels and investigate their impact on the performance of grant-free transmission, where age-of-information is used as the performance metric. The presented analytical and simulation results demonstrate the performance gain achieved by NOMA over orthogonal multiple access, and also reveal the relative merits of the considered designs for pre-configured SNR levels.

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi^4 model and weak lensing convergence maps with higher resolution than in previous works.

This paper presents a new, provably-convergent algorithm for computing the flag-mean and flag-median of a set of points on a flag manifold under the chordal metric. The flag manifold is a mathematical space consisting of flags, which are sequences of nested subspaces of a vector space that increase in dimension. The flag manifold is a superset of a wide range of known matrix spaces, including Stiefel and Grassmanians, making it a general object that is useful in a wide variety computer vision problems. To tackle the challenge of computing first order flag statistics, we first transform the problem into one that involves auxiliary variables constrained to the Stiefel manifold. The Stiefel manifold is a space of orthogonal frames, and leveraging the numerical stability and efficiency of Stiefel-manifold optimization enables us to compute the flag-mean effectively. Through a series of experiments, we show the competence of our method in Grassmann and rotation averaging, as well as principal component analysis. We release our source code under https://github.com/nmank/FlagAveraging.

Medical vision-and-language pre-training (Med-VLP) has shown promising improvements on many downstream medical tasks owing to its applicability to extracting generic representations from medical images and texts. Practically, there exist two typical types, i.e., the fusion-encoder type and the dual-encoder type, depending on whether a heavy fusion module is used. The former is superior at multi-modal tasks owing to the sufficient interaction between modalities; the latter is good at uni-modal and cross-modal tasks due to the single-modality encoding ability. To take advantage of these two types, we propose an effective yet straightforward scheme named PTUnifier to unify the two types. We first unify the input format by introducing visual and textual prompts, which serve as a feature bank that stores the most representative images/texts. By doing so, a single model could serve as a foundation model that processes various tasks adopting different input formats (i.e., image-only, text-only, and image-text-pair). Furthermore, we construct a prompt pool (instead of static ones) to improve diversity and scalability. Experimental results show that our approach achieves state-of-the-art results on a broad range of tasks, spanning uni-modal tasks (i.e., image/text classification and text summarization), cross-modal tasks (i.e., image-to-text generation and image-text/text-image retrieval), and multi-modal tasks (i.e., visual question answering), demonstrating the effectiveness of our approach. Note that the adoption of prompts is orthogonal to most existing Med-VLP approaches and could be a beneficial and complementary extension to these approaches.

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.

Research on Automatic Story Generation (ASG) relies heavily on human and automatic evaluation. However, there is no consensus on which human evaluation criteria to use, and no analysis of how well automatic criteria correlate with them. In this paper, we propose to re-evaluate ASG evaluation. We introduce a set of 6 orthogonal and comprehensive human criteria, carefully motivated by the social sciences literature. We also present HANNA, an annotated dataset of 1,056 stories produced by 10 different ASG systems. HANNA allows us to quantitatively evaluate the correlations of 72 automatic metrics with human criteria. Our analysis highlights the weaknesses of current metrics for ASG and allows us to formulate practical recommendations for ASG evaluation.

In this work, we introduce Dual Attention Vision Transformers (DaViT), a simple yet effective vision transformer architecture that is able to capture global context while maintaining computational efficiency. We propose approaching the problem from an orthogonal angle: exploiting self-attention mechanisms with both "spatial tokens" and "channel tokens". With spatial tokens, the spatial dimension defines the token scope, and the channel dimension defines the token feature dimension. With channel tokens, we have the inverse: the channel dimension defines the token scope, and the spatial dimension defines the token feature dimension. We further group tokens along the sequence direction for both spatial and channel tokens to maintain the linear complexity of the entire model. We show that these two self-attentions complement each other: (i) since each channel token contains an abstract representation of the entire image, the channel attention naturally captures global interactions and representations by taking all spatial positions into account when computing attention scores between channels; (ii) the spatial attention refines the local representations by performing fine-grained interactions across spatial locations, which in turn helps the global information modeling in channel attention. Extensive experiments show our DaViT achieves state-of-the-art performance on four different tasks with efficient computations. Without extra data, DaViT-Tiny, DaViT-Small, and DaViT-Base achieve 82.8%, 84.2%, and 84.6% top-1 accuracy on ImageNet-1K with 28.3M, 49.7M, and 87.9M parameters, respectively. When we further scale up DaViT with 1.5B weakly supervised image and text pairs, DaViT-Gaint reaches 90.4% top-1 accuracy on ImageNet-1K. Code is available at https://github.com/dingmyu/davit.

The task of few-shot style transfer for voice cloning in text-to-speech (TTS) synthesis aims at transferring speaking styles of an arbitrary source speaker to a target speaker's voice using very limited amount of neutral data. This is a very challenging task since the learning algorithm needs to deal with few-shot voice cloning and speaker-prosody disentanglement at the same time. Accelerating the adaptation process for a new target speaker is of importance in real-world applications, but even more challenging. In this paper, we approach to the hard fast few-shot style transfer for voice cloning task using meta learning. We investigate the model-agnostic meta-learning (MAML) algorithm and meta-transfer a pre-trained multi-speaker and multi-prosody base TTS model to be highly sensitive for adaptation with few samples. Domain adversarial training mechanism and orthogonal constraint are adopted to disentangle speaker and prosody representations for effective cross-speaker style transfer. Experimental results show that the proposed approach is able to conduct fast voice cloning using only 5 samples (around 12 second speech data) from a target speaker, with only 100 adaptation steps. Audio samples are available online.

Learning visual knowledge from massive weakly-labeled web videos has attracted growing research interests thanks to the large corpus of easily accessible video data on the Internet. However, for video action recognition, the action of interest might only exist in arbitrary clips of untrimmed web videos, resulting in high label noises in the temporal space. To address this issue, we introduce a new method for pre-training video action recognition models using queried web videos. Instead of trying to filter out, we propose to convert the potential noises in these queried videos to useful supervision signals by defining the concept of Sub-Pseudo Label (SPL). Specifically, SPL spans out a new set of meaningful "middle ground" label space constructed by extrapolating the original weak labels during video querying and the prior knowledge distilled from a teacher model. Consequently, SPL provides enriched supervision for video models to learn better representations. SPL is fairly simple and orthogonal to popular teacher-student self-training frameworks without extra training cost. We validate the effectiveness of our method on four video action recognition datasets and a weakly-labeled image dataset to study the generalization ability. Experiments show that SPL outperforms several existing pre-training strategies using pseudo-labels and the learned representations lead to competitive results when fine-tuning on HMDB-51 and UCF-101 compared with recent pre-training methods.

The capability of the self-attention mechanism to model the long-range dependencies has catapulted its deployment in vision models. Unlike convolution operators, self-attention offers infinite receptive field and enables compute-efficient modeling of global dependencies. However, the existing state-of-the-art attention mechanisms incur high compute and/or parameter overheads, and hence unfit for compact convolutional neural networks (CNNs). In this work, we propose a simple yet effective "Ultra-Lightweight Subspace Attention Mechanism" (ULSAM), which infers different attention maps for each feature map subspace. We argue that leaning separate attention maps for each feature subspace enables multi-scale and multi-frequency feature representation, which is more desirable for fine-grained image classification. Our method of subspace attention is orthogonal and complementary to the existing state-of-the-arts attention mechanisms used in vision models. ULSAM is end-to-end trainable and can be deployed as a plug-and-play module in the pre-existing compact CNNs. Notably, our work is the first attempt that uses a subspace attention mechanism to increase the efficiency of compact CNNs. To show the efficacy of ULSAM, we perform experiments with MobileNet-V1 and MobileNet-V2 as backbone architectures on ImageNet-1K and three fine-grained image classification datasets. We achieve approx13% and approx25% reduction in both the FLOPs and parameter counts of MobileNet-V2 with a 0.27% and more than 1% improvement in top-1 accuracy on the ImageNet-1K and fine-grained image classification datasets (respectively). Code and trained models are available at https://github.com/Nandan91/ULSAM.

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

As Large Language Models (LLMs) continue to advance in performance, their size has escalated significantly, with current LLMs containing billions or even trillions of parameters. However, in this study, we discovered that many layers of LLMs exhibit high similarity, and some layers play a negligible role in network functionality. Based on this observation, we define a metric called Block Influence (BI) to gauge the significance of each layer in LLMs. We then propose a straightforward pruning approach: layer removal, in which we directly delete the redundant layers in LLMs based on their BI scores. Experiments demonstrate that our method, which we call ShortGPT, significantly outperforms previous state-of-the-art (SOTA) methods in model pruning. Moreover, ShortGPT is orthogonal to quantization-like methods, enabling further reduction in parameters and computation. The ability to achieve better results through simple layer removal, as opposed to more complex pruning techniques, suggests a high degree of redundancy in the model architecture.

We find that, simply via a sampling-and-voting method, the performance of large language models (LLMs) scales with the number of agents instantiated. Also, this method is orthogonal to existing complicated methods to further enhance LLMs, while the degree of enhancement is correlated to the task difficulty. We conduct comprehensive experiments on a wide range of LLM benchmarks to verify the presence of our finding, and to study the properties that can facilitate its occurrence. Our code is publicly available at: https://anonymous.4open.science/r/more_agent_is_all_you_need.

Classifier-free guidance (CFG) is crucial for improving both generation quality and alignment between the input condition and final output in diffusion models. While a high guidance scale is generally required to enhance these aspects, it also causes oversaturation and unrealistic artifacts. In this paper, we revisit the CFG update rule and introduce modifications to address this issue. We first decompose the update term in CFG into parallel and orthogonal components with respect to the conditional model prediction and observe that the parallel component primarily causes oversaturation, while the orthogonal component enhances image quality. Accordingly, we propose down-weighting the parallel component to achieve high-quality generations without oversaturation. Additionally, we draw a connection between CFG and gradient ascent and introduce a new rescaling and momentum method for the CFG update rule based on this insight. Our approach, termed adaptive projected guidance (APG), retains the quality-boosting advantages of CFG while enabling the use of higher guidance scales without oversaturation. APG is easy to implement and introduces practically no additional computational overhead to the sampling process. Through extensive experiments, we demonstrate that APG is compatible with various conditional diffusion models and samplers, leading to improved FID, recall, and saturation scores while maintaining precision comparable to CFG, making our method a superior plug-and-play alternative to standard classifier-free guidance.

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

This paper investigates the performance of network non-orthogonal multiple access (N-NOMA) in a downlink coordinated multi-point (CoMP) system. In the considered N-NOMA scheme, multiple base stations (BSs) cooperatively serve a CoMP user, meanwhile, each BS serves additional NOMA users by occupying the same resource block allocated to the CoMP user. The locations of the BSs and users are modeled by stochastic geometric models and the interference from the whole network is considered. Through rigorous derivations, the outage probabilities achieved by the CoMP and NOMA users are obtained, respectively. Numerical results are provided to verify the accuracy of the analytical results and also demonstrate the superior performance of N-NOMA compared to orthogonal multiple access (OMA) based CoMP scheme.

Large language models (LLMs) have revolutionized the field of AI, demonstrating unprecedented capacity across various tasks. However, the inference process for LLMs comes with significant computational costs. In this paper, we propose an efficient LLM inference pipeline that harnesses the power of LLMs. Our approach begins by tapping into the potential of LLMs to accurately perceive and predict the response length with minimal overhead. By leveraging this information, we introduce an efficient sequence scheduling technique that groups queries with similar response lengths into micro-batches. We evaluate our approach on real-world instruction datasets using the LLaMA-based model, and our results demonstrate an impressive 86% improvement in inference throughput without compromising effectiveness. Notably, our method is orthogonal to other inference acceleration techniques, making it a valuable addition to many existing toolkits (e.g., FlashAttention, Quantization) for LLM inference.

Scaling long-context ability is essential for Large Language Models (LLMs). To amortize the memory consumption across multiple devices in long-context training, inter-data partitioning (a.k.a. Data Parallelism) and intra-data partitioning (a.k.a. Context Parallelism) are commonly used. Current training frameworks predominantly treat the two techniques as orthogonal, and establish static communication groups to organize the devices as a static mesh (e.g., a 2D mesh). However, the sequences for LLM training typically vary in lengths, no matter for texts, multi-modalities or reinforcement learning. The mismatch between data heterogeneity and static mesh causes redundant communication and imbalanced computation, degrading the training efficiency. In this work, we introduce ByteScale, an efficient, flexible, and scalable LLM training framework for large-scale mixed training of long and short sequences. The core of ByteScale is a novel parallelism strategy, namely Hybrid Data Parallelism (HDP), which unifies the inter- and intra-data partitioning with a dynamic mesh design. In particular, we build a communication optimizer, which eliminates the redundant communication for short sequences by data-aware sharding and dynamic communication, and further compresses the communication cost for long sequences by selective offloading. Besides, we also develop a balance scheduler to mitigate the imbalanced computation by parallelism-aware data assignment. We evaluate ByteScale with the model sizes ranging from 7B to 141B, context lengths from 256K to 2048K, on a production cluster with more than 12,000 GPUs. Experiment results show that ByteScale outperforms the state-of-the-art training system by up to 7.89x.

Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their specialized capabilities across different tasks and domains. Current model merging techniques focus on merging all available models simultaneously, with weight interpolation-based methods being the predominant approaches. However, these conventional approaches are not well-suited for scenarios where models become available sequentially, and they often suffer from high memory requirements and potential interference between tasks. In this study, we propose a training-free projection-based continual merging method that processes models sequentially through orthogonal projections of weight matrices and adaptive scaling mechanisms. Our method operates by projecting new parameter updates onto subspaces orthogonal to existing merged parameter updates while using an adaptive scaling mechanism to maintain stable parameter distances, enabling efficient sequential integration of task-specific knowledge. Our approach maintains constant memory complexity to the number of models, minimizes interference between tasks through orthogonal projections, and retains the performance of previously merged models through adaptive task vector scaling. Extensive experiments on CLIP-ViT models demonstrate that our method achieves a 5-8% average accuracy improvement while maintaining robust performance in different task orderings.

Evaluating the capability of Large Language Models (LLMs) in following instructions has heavily relied on a powerful LLM as the judge, introducing unresolved biases that deviate the judgments from human judges. In this work, we reevaluate various choices for automatic evaluation on a wide range of instruction-following tasks. We experiment with methods that leverage human-written responses and observe that they enhance the reliability of automatic evaluations across a wide range of tasks, resulting in up to a 3.2% improvement in agreement with human judges. We also discovered that human-written responses offer an orthogonal perspective to model-generated responses in following instructions and should be used as an additional context when comparing model responses. Based on these observations, we develop a new evaluation benchmark, Human Response-Guided Evaluation of Instruction Following (HREF), comprising 4,258 samples across 11 task categories with a composite evaluation setup, employing a composite evaluation setup that selects the most reliable method for each category. In addition to providing reliable evaluation, HREF emphasizes individual task performance and is free from contamination. Finally, we study the impact of key design choices in HREF, including the size of the evaluation set, the judge model, the baseline model, and the prompt template. We host a live leaderboard that evaluates LLMs on the private evaluation set of HREF.

The development of vision-language and generative models has significantly advanced text-guided image editing, which seeks preservation of core elements in the source image while implementing modifications based on the target text. However, in the absence of evaluation metrics specifically tailored for text-guided image editing, existing metrics are limited in balancing the consideration of preservation and modification. Especially, our analysis reveals that CLIPScore, the most commonly used metric, tends to favor modification and ignore core attributes to be preserved, resulting in inaccurate evaluations. To address this problem, we propose AugCLIP, which balances preservation and modification by estimating the representation of an ideal edited image that aligns with the target text with minimum alteration on the source image. We augment detailed textual descriptions on the source image and the target text using a multi-modal large language model, to model a hyperplane that separates CLIP space into source or target. The representation of the ideal edited image is an orthogonal projection of the source image into the hyperplane, which encapsulates the relative importance of each attribute considering the interdependent relationships. Our extensive experiments on five benchmark datasets, encompassing a diverse range of editing scenarios, demonstrate that AugCLIP aligns remarkably well with human evaluation standards compared to existing metrics. The code for evaluation will be open-sourced to contribute to the community.

In recent years roboticists have achieved remarkable progress in solving increasingly general tasks on dexterous robotic hardware by leveraging high capacity Transformer network architectures and generative diffusion models. Unfortunately, combining these two orthogonal improvements has proven surprisingly difficult, since there is no clear and well-understood process for making important design choices. In this paper, we identify, study and improve key architectural design decisions for high-capacity diffusion transformer policies. The resulting models can efficiently solve diverse tasks on multiple robot embodiments, without the excruciating pain of per-setup hyper-parameter tuning. By combining the results of our investigation with our improved model components, we are able to present a novel architecture, named \method, that significantly outperforms the state of the art in solving long-horizon (1500+ time-steps) dexterous tasks on a bi-manual ALOHA robot. In addition, we find that our policies show improved scaling performance when trained on 10 hours of highly multi-modal, language annotated ALOHA demonstration data. We hope this work will open the door for future robot learning techniques that leverage the efficiency of generative diffusion modeling with the scalability of large scale transformer architectures. Code, robot dataset, and videos are available at: https://dit-policy.github.io

This letter investigates a short-packet downlink transmission system using non-orthogonal multiple access (NOMA) enhanced via movable antenna (MA). We focuses on maximizing the effective throughput for a core user while ensuring reliable communication for an edge user by optimizing the MAs' coordinates and the power and rate allocations from the access point (AP). The optimization challenge is approached by decomposing it into two subproblems, utilizing successive convex approximation (SCA) to handle the highly non-concave nature of channel gains. Numerical results confirm that the proposed solution offers substantial improvements in effective throughput compared to NOMA short-packet communication with fixed position antennas (FPAs).

The inference phase of Large Language Models (LLMs) is very expensive. An ideal inference stage of LLMs could utilize fewer computational resources while still maintaining its capabilities (e.g., generalization and in-context learning ability). In this paper, we try to answer the question, "During LLM inference, can we use shallow layers for easy instances; and deep layers for hard ones?" To answer this question, we first indicate that Not all Layers are Necessary during Inference by statistically analyzing the activated layers across tasks. Then, we propose a simple algorithm named AdaInfer to determine the inference termination moment based on the input instance adaptively. More importantly, AdaInfer does not alter LLM parameters and maintains generalizability across tasks. Experiments on well-known LLMs (i.e., Llama2 series and OPT) show that AdaInfer saves an average of 14.8% of computational resources, even up to 50% on sentiment tasks, while maintaining comparable performance. Additionally, this method is orthogonal to other model acceleration techniques, potentially boosting inference efficiency further.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Recent years have witnessed the prevailing progress of Generative Adversarial Networks (GANs) in image-to-image translation. However, the success of these GAN models hinges on ponderous computational costs and labor-expensive training data. Current efficient GAN learning techniques often fall into two orthogonal aspects: i) model slimming via reduced calculation costs; ii)data/label-efficient learning with fewer training data/labels. To combine the best of both worlds, we propose a new learning paradigm, Unified GAN Compression (UGC), with a unified optimization objective to seamlessly prompt the synergy of model-efficient and label-efficient learning. UGC sets up semi-supervised-driven network architecture search and adaptive online semi-supervised distillation stages sequentially, which formulates a heterogeneous mutual learning scheme to obtain an architecture-flexible, label-efficient, and performance-excellent model.

Imbalanced distributions are ubiquitous in real-world data. They create constraints on Deep Neural Networks to represent the minority labels and avoid bias towards majority labels. The extensive body of imbalanced approaches address categorical label spaces but fail to effectively extend to regression problems where the label space is continuous. Local and global correlations among continuous labels provide valuable insights towards effectively modelling relationships in feature space. In this work, we propose ConR, a contrastive regularizer that models global and local label similarities in feature space and prevents the features of minority samples from being collapsed into their majority neighbours. ConR discerns the disagreements between the label space and feature space and imposes a penalty on these disagreements. ConR addresses the continuous nature of label space with two main strategies in a contrastive manner: incorrect proximities are penalized proportionate to the label similarities and the correct ones are encouraged to model local similarities. ConR consolidates essential considerations into a generic, easy-to-integrate, and efficient method that effectively addresses deep imbalanced regression. Moreover, ConR is orthogonal to existing approaches and smoothly extends to uni- and multi-dimensional label spaces. Our comprehensive experiments show that ConR significantly boosts the performance of all the state-of-the-art methods on four large-scale deep imbalanced regression benchmarks. Our code is publicly available in https://github.com/BorealisAI/ConR.

The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this paper, we propose two new algorithms, AOGD-ALD and NONS-ALD, which can keep nearly optimal regret bounds at a sublinear computational complexity, and give sufficient conditions under which our algorithms work. Both algorithms dynamically maintain a group of nearly orthogonal basis used to approximate the kernel mapping, and keep nearly optimal regret bounds by controlling the approximate error. The number of basis depends on the approximate error and the decay rate of eigenvalues of the kernel matrix. If the eigenvalues decay exponentially, then AOGD-ALD and NONS-ALD separately achieves a regret of O(L(f)) and O(d_{eff}(mu)T) at a computational complexity in O(ln^2{T}). If the eigenvalues decay polynomially with degree pgeq 1, then our algorithms keep the same regret bounds at a computational complexity in o(T) in the case of p>4 and pgeq 10, respectively. L(f) is the cumulative losses of f and d_{eff}(mu) is the effective dimension of the problem. The two regret bounds are nearly optimal and are not comparable.

Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs 7x7 depthwise convolution. Although such depthwise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves 60% throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation. It is still unclear how to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e. small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely IncepitonNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves 1.6x higher training throughputs than ConvNeX-T, as well as attains 0.2% top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint. Code is available at https://github.com/sail-sg/inceptionnext.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

The scaling of large language models (LLMs) has revolutionized their capabilities in various tasks, yet this growth must be matched with efficient computational strategies. The Mixture-of-Experts (MoE) architecture stands out for its ability to scale model size without significantly increasing training costs. Despite their advantages, current MoE models often display parameter inefficiency. For instance, a pre-trained MoE-based LLM with 52 billion parameters might perform comparably to a standard model with 6.7 billion parameters. Being a crucial part of MoE, current routers in different layers independently assign tokens without leveraging historical routing information, potentially leading to suboptimal token-expert combinations and the parameter inefficiency problem. To alleviate this issue, we introduce the Layerwise Recurrent Router for Mixture-of-Experts (RMoE). RMoE leverages a Gated Recurrent Unit (GRU) to establish dependencies between routing decisions across consecutive layers. Such layerwise recurrence can be efficiently parallelly computed for input tokens and introduces negotiable costs. Our extensive empirical evaluations demonstrate that RMoE-based language models consistently outperform a spectrum of baseline models. Furthermore, RMoE integrates a novel computation stage orthogonal to existing methods, allowing seamless compatibility with other MoE architectures. Our analyses attribute RMoE's gains to its effective cross-layer information sharing, which also improves expert selection and diversity. Our code is at https://github.com/qiuzh20/RMoE

Huge memory consumption has been a major bottleneck for deploying high-throughput large language models in real-world applications. In addition to the large number of parameters, the key-value (KV) cache for the attention mechanism in the transformer architecture consumes a significant amount of memory, especially when the number of layers is large for deep language models. In this paper, we propose a novel method that only computes and caches the KVs of a small number of layers, thus significantly saving memory consumption and improving inference throughput. Our experiments on large language models show that our method achieves up to 26times higher throughput than standard transformers and competitive performance in language modeling and downstream tasks. In addition, our method is orthogonal to existing transformer memory-saving techniques, so it is straightforward to integrate them with our model, achieving further improvement in inference efficiency. Our code is available at https://github.com/whyNLP/LCKV.

Reconstructing detailed 3D objects from single-view images remains a challenging task due to the limited information available. In this paper, we introduce FDGaussian, a novel two-stage framework for single-image 3D reconstruction. Recent methods typically utilize pre-trained 2D diffusion models to generate plausible novel views from the input image, yet they encounter issues with either multi-view inconsistency or lack of geometric fidelity. To overcome these challenges, we propose an orthogonal plane decomposition mechanism to extract 3D geometric features from the 2D input, enabling the generation of consistent multi-view images. Moreover, we further accelerate the state-of-the-art Gaussian Splatting incorporating epipolar attention to fuse images from different viewpoints. We demonstrate that FDGaussian generates images with high consistency across different views and reconstructs high-quality 3D objects, both qualitatively and quantitatively. More examples can be found at our website https://qjfeng.net/FDGaussian/.

Human visual perception can easily generalize to out-of-distributed visual data, which is far beyond the capability of modern machine learning models. Domain generalization (DG) aims to close this gap, with existing DG methods mainly focusing on the loss function design. In this paper, we propose to explore an orthogonal direction, i.e., the design of the backbone architecture. It is motivated by an empirical finding that transformer-based models trained with empirical risk minimization (ERM) outperform CNN-based models employing state-of-the-art (SOTA) DG algorithms on multiple DG datasets. We develop a formal framework to characterize a network's robustness to distribution shifts by studying its architecture's alignment with the correlations in the dataset. This analysis guides us to propose a novel DG model built upon vision transformers, namely Generalizable Mixture-of-Experts (GMoE). Extensive experiments on DomainBed demonstrate that GMoE trained with ERM outperforms SOTA DG baselines by a large margin. Moreover, GMoE is complementary to existing DG methods and its performance is substantially improved when trained with DG algorithms.

The COVID-19 pandemic has underscored the need for low-cost, scalable approaches to measuring contactless vital signs, either during initial triage at a healthcare facility or virtual telemedicine visits. Remote photoplethysmography (rPPG) can accurately estimate heart rate (HR) when applied to close-up videos of healthy volunteers in well-lit laboratory settings. However, results from such highly optimized laboratory studies may not be readily translated to healthcare settings. One significant barrier to the practical application of rPPG in health care is the accurate localization of the region of interest (ROI). Clinical or telemedicine visits may involve sub-optimal lighting, movement artifacts, variable camera angle, and subject distance. This paper presents an rPPG ROI selection method based on 3D facial landmarks and patient head yaw angle. We then demonstrate the robustness of this ROI selection method when coupled to the Plane-Orthogonal-to-Skin (POS) rPPG method when applied to videos of patients presenting to an Emergency Department for respiratory complaints. Our results demonstrate the effectiveness of our proposed approach in improving the accuracy and robustness of rPPG in a challenging clinical environment.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Neural networks often suffer from catastrophic interference (CI): performance on previously learned tasks drops off significantly when learning a new task. This contrasts strongly with humans, who can sequentially learn new tasks without appreciably forgetting previous tasks. Prior work has explored various techniques for mitigating CI such as regularization, rehearsal, generative replay, and distillation methods. The current work takes a different approach, one guided by cognitive science research showing that in naturalistic environments, the probability of encountering a task decreases as a power-law of the time since it was last performed. We argue that a realistic evaluation of techniques for the mitigation of CI should be performed in simulated naturalistic learning environments. Thus, we evaluate the extent of mitigation of CI when training simple rehearsal-based methods in power-law environments similar to the ones humans face. Our work explores this novel rehearsal-based approach for a domain-incremental task: learning permutations in the MNIST task. We compare our rehearsal environment with other baselines to show its efficacy in promoting continual learning. Additionally, we investigate whether this environment shows forward facilitation, i.e., faster learning of later tasks. Next, we explore the robustness of our learning environment to the number of tasks, model size, and amount of data rehearsed after each task. Notably, our results show that the performance is comparable or superior to that of models trained using popular regularization methods and also to rehearsals in non-power-law environments. The benefits of this training paradigm include simplicity and the lack of a need for extra neural circuitry. In addition, because our method is orthogonal to other methods, future research can combine training in power-law environments with other continual learning mechanisms.

Transformers have been recently explored for 3D point cloud understanding with impressive progress achieved. A large number of points, over 0.1 million, make the global self-attention infeasible for point cloud data. Thus, most methods propose to apply the transformer in a local region, e.g., spherical or cubic window. However, it still contains a large number of Query-Key pairs, which requires high computational costs. In addition, previous methods usually learn the query, key, and value using a linear projection without modeling the local 3D geometric structure. In this paper, we attempt to reduce the costs and model the local geometry prior by developing a new transformer block, named ConDaFormer. Technically, ConDaFormer disassembles the cubic window into three orthogonal 2D planes, leading to fewer points when modeling the attention in a similar range. The disassembling operation is beneficial to enlarging the range of attention without increasing the computational complexity, but ignores some contexts. To provide a remedy, we develop a local structure enhancement strategy that introduces a depth-wise convolution before and after the attention. This scheme can also capture the local geometric information. Taking advantage of these designs, ConDaFormer captures both long-range contextual information and local priors. The effectiveness is demonstrated by experimental results on several 3D point cloud understanding benchmarks. Code is available at https://github.com/LHDuan/ConDaFormer .

Despite the tremendous progress in neural radiance fields (NeRF), we still face a dilemma of the trade-off between quality and efficiency, e.g., MipNeRF presents fine-detailed and anti-aliased renderings but takes days for training, while Instant-ngp can accomplish the reconstruction in a few minutes but suffers from blurring or aliasing when rendering at various distances or resolutions due to ignoring the sampling area. To this end, we propose a novel Tri-Mip encoding that enables both instant reconstruction and anti-aliased high-fidelity rendering for neural radiance fields. The key is to factorize the pre-filtered 3D feature spaces in three orthogonal mipmaps. In this way, we can efficiently perform 3D area sampling by taking advantage of 2D pre-filtered feature maps, which significantly elevates the rendering quality without sacrificing efficiency. To cope with the novel Tri-Mip representation, we propose a cone-casting rendering technique to efficiently sample anti-aliased 3D features with the Tri-Mip encoding considering both pixel imaging and observing distance. Extensive experiments on both synthetic and real-world datasets demonstrate our method achieves state-of-the-art rendering quality and reconstruction speed while maintaining a compact representation that reduces 25% model size compared against Instant-ngp.

Large pre-trained vision-language models have shown great prominence in transferring pre-acquired knowledge to various domains and downstream tasks with appropriate prompting or tuning. Existing prevalent tuning methods can be generally categorized into three genres: 1) prompt engineering by creating suitable prompt texts, which is time-consuming and requires domain expertise; 2) or simply fine-tuning the whole model, which is extremely inefficient; 3) prompt tuning through parameterized prompt embeddings with the text encoder. Nevertheless, all methods rely on the text encoder for bridging the modality gap between vision and language. In this work, we question the necessity of the cumbersome text encoder for a more lightweight and efficient tuning paradigm as well as more representative prompt embeddings closer to the image representations. To achieve this, we propose a Concept Embedding Search (ConES) approach by optimizing prompt embeddings -- without the need of the text encoder -- to capture the 'concept' of the image modality through a variety of task objectives. By dropping the text encoder, we are able to significantly speed up the learning process, \eg, from about an hour to just ten minutes in our experiments for personalized text-to-image generation without impairing the generation quality. Moreover, our proposed approach is orthogonal to current existing tuning methods since the searched concept embeddings can be further utilized in the next stage of fine-tuning the pre-trained large models for boosting performance. Extensive experiments show that our approach can beat the prompt tuning and textual inversion methods in a variety of downstream tasks including objection detection, instance segmentation, and image generation. Our approach also shows better generalization capability for unseen concepts in specialized domains, such as the medical domain.

Due to the modality gap between visible and infrared images with high visual ambiguity, learning diverse modality-shared semantic concepts for visible-infrared person re-identification (VI-ReID) remains a challenging problem. Body shape is one of the significant modality-shared cues for VI-ReID. To dig more diverse modality-shared cues, we expect that erasing body-shape-related semantic concepts in the learned features can force the ReID model to extract more and other modality-shared features for identification. To this end, we propose shape-erased feature learning paradigm that decorrelates modality-shared features in two orthogonal subspaces. Jointly learning shape-related feature in one subspace and shape-erased features in the orthogonal complement achieves a conditional mutual information maximization between shape-erased feature and identity discarding body shape information, thus enhancing the diversity of the learned representation explicitly. Extensive experiments on SYSU-MM01, RegDB, and HITSZ-VCM datasets demonstrate the effectiveness of our method.

Prompt tuning, a recently emerging paradigm, enables the powerful vision-language pre-training models to adapt to downstream tasks in a parameter -- and data -- efficient way, by learning the ``soft prompts'' to condition frozen pre-training models. Though effective, it is particularly problematic in the few-shot scenario, where prompt tuning performance is sensitive to the initialization and requires a time-consuming process to find a good initialization, thus restricting the fast adaptation ability of the pre-training models. In addition, prompt tuning could undermine the generalizability of the pre-training models, because the learnable prompt tokens are easy to overfit to the limited training samples. To address these issues, we introduce a novel Gradient-RegulAted Meta-prompt learning (GRAM) framework that jointly meta-learns an efficient soft prompt initialization for better adaptation and a lightweight gradient regulating function for strong cross-domain generalizability in a meta-learning paradigm using only the unlabeled image-text pre-training data. Rather than designing a specific prompt tuning method, our GRAM can be easily incorporated into various prompt tuning methods in a model-agnostic way, and comprehensive experiments show that GRAM brings about consistent improvement for them in several settings (i.e., few-shot learning, cross-domain generalization, cross-dataset generalization, etc.) over 11 datasets. Further, experiments show that GRAM enables the orthogonal methods of textual and visual prompt tuning to work in a mutually-enhanced way, offering better generalizability beyond the uni-modal prompt tuning methods.

Generating factual-consistent summaries is a challenging task for abstractive summarization. Previous works mainly encode factual information or perform post-correct/rank after decoding. In this paper, we provide a factual-consistent solution from the perspective of contrastive learning, which is a natural extension of previous works. We propose CO2Sum (Contrastive for Consistency), a contrastive learning scheme that can be easily applied on sequence-to-sequence models for factual-consistent abstractive summarization, proving that the model can be fact-aware without modifying the architecture. CO2Sum applies contrastive learning on the encoder, which can help the model be aware of the factual information contained in the input article, or performs contrastive learning on the decoder, which makes the model to generate factual-correct output summary. What's more, these two schemes are orthogonal and can be combined to further improve faithfulness. Comprehensive experiments on public benchmarks demonstrate that CO2Sum improves the faithfulness on large pre-trained language models and reaches competitive results compared to other strong factual-consistent summarization baselines.

Unsupervised domain adaptation (UDA) aims to transfer knowledge learned from a labeled source domain to an unlabeled and unseen target domain, which is usually trained on data from both domains. Access to the source domain data at the adaptation stage, however, is often limited, due to data storage or privacy issues. To alleviate this, in this work, we target source free UDA for segmentation, and propose to adapt an ``off-the-shelf" segmentation model pre-trained in the source domain to the target domain, with an adaptive batch-wise normalization statistics adaptation framework. Specifically, the domain-specific low-order batch statistics, i.e., mean and variance, are gradually adapted with an exponential momentum decay scheme, while the consistency of domain shareable high-order batch statistics, i.e., scaling and shifting parameters, is explicitly enforced by our optimization objective. The transferability of each channel is adaptively measured first from which to balance the contribution of each channel. Moreover, the proposed source free UDA framework is orthogonal to unsupervised learning methods, e.g., self-entropy minimization, which can thus be simply added on top of our framework. Extensive experiments on the BraTS 2018 database show that our source free UDA framework outperformed existing source-relaxed UDA methods for the cross-subtype UDA segmentation task and yielded comparable results for the cross-modality UDA segmentation task, compared with a supervised UDA methods with the source data.

The creation of manipulated multimedia content involving human characters has reached in the last years unprecedented realism, calling for automated techniques to expose synthetically generated faces in images and videos. This work explores the analysis of spatio-temporal texture dynamics of the video signal, with the goal of characterizing and distinguishing real and fake sequences. We propose to build a binary decision on the joint analysis of multiple temporal segments and, in contrast to previous approaches, to exploit the textural dynamics of both the spatial and temporal dimensions. This is achieved through the use of Local Derivative Patterns on Three Orthogonal Planes (LDP-TOP), a compact feature representation known to be an important asset for the detection of face spoofing attacks. Experimental analyses on state-of-the-art datasets of manipulated videos show the discriminative power of such descriptors in separating real and fake sequences, and also identifying the creation method used. Linear Support Vector Machines (SVMs) are used which, despite the lower complexity, yield comparable performance to previously proposed deep models for fake content detection.

We introduce a self-supervised speech pre-training method called TERA, which stands for Transformer Encoder Representations from Alteration. Recent approaches often learn by using a single auxiliary task like contrastive prediction, autoregressive prediction, or masked reconstruction. Unlike previous methods, we use alteration along three orthogonal axes to pre-train Transformer Encoders on a large amount of unlabeled speech. The model learns through the reconstruction of acoustic frames from their altered counterpart, where we use a stochastic policy to alter along various dimensions: time, frequency, and magnitude. TERA can be used for speech representations extraction or fine-tuning with downstream models. We evaluate TERA on several downstream tasks, including phoneme classification, keyword spotting, speaker recognition, and speech recognition. We present a large-scale comparison of various self-supervised models. TERA achieves strong performance in the comparison by improving upon surface features and outperforming previous models. In our experiments, we study the effect of applying different alteration techniques, pre-training on more data, and pre-training on various features. We analyze different model sizes and find that smaller models are strong representation learners than larger models, while larger models are more effective for downstream fine-tuning than smaller models. Furthermore, we show the proposed method is transferable to downstream datasets not used in pre-training.

Sequential models achieve state-of-the-art results in audio, visual and textual domains with respect to both estimating the data distribution and generating high-quality samples. Efficient sampling for this class of models has however remained an elusive problem. With a focus on text-to-speech synthesis, we describe a set of general techniques for reducing sampling time while maintaining high output quality. We first describe a single-layer recurrent neural network, the WaveRNN, with a dual softmax layer that matches the quality of the state-of-the-art WaveNet model. The compact form of the network makes it possible to generate 24kHz 16-bit audio 4x faster than real time on a GPU. Second, we apply a weight pruning technique to reduce the number of weights in the WaveRNN. We find that, for a constant number of parameters, large sparse networks perform better than small dense networks and this relationship holds for sparsity levels beyond 96%. The small number of weights in a Sparse WaveRNN makes it possible to sample high-fidelity audio on a mobile CPU in real time. Finally, we propose a new generation scheme based on subscaling that folds a long sequence into a batch of shorter sequences and allows one to generate multiple samples at once. The Subscale WaveRNN produces 16 samples per step without loss of quality and offers an orthogonal method for increasing sampling efficiency.

We explore a key architectural aspect of deep convolutional neural networks: the pattern of internal skip connections used to aggregate outputs of earlier layers for consumption by deeper layers. Such aggregation is critical to facilitate training of very deep networks in an end-to-end manner. This is a primary reason for the widespread adoption of residual networks, which aggregate outputs via cumulative summation. While subsequent works investigate alternative aggregation operations (e.g. concatenation), we focus on an orthogonal question: which outputs to aggregate at a particular point in the network. We propose a new internal connection structure which aggregates only a sparse set of previous outputs at any given depth. Our experiments demonstrate this simple design change offers superior performance with fewer parameters and lower computational requirements. Moreover, we show that sparse aggregation allows networks to scale more robustly to 1000+ layers, thereby opening future avenues for training long-running visual processes.

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

Understanding human preferences is crucial for improving foundation models and building personalized AI systems. However, preferences are inherently diverse and complex, making it difficult for traditional reward models to capture their full range. While fine-grained preference data can help, collecting it is expensive and hard to scale. In this paper, we introduce Decomposed Reward Models (DRMs), a novel approach that extracts diverse human preferences from binary comparisons without requiring fine-grained annotations. Our key insight is to represent human preferences as vectors and analyze them using Principal Component Analysis (PCA). By constructing a dataset of embedding differences between preferred and rejected responses, DRMs identify orthogonal basis vectors that capture distinct aspects of preference. These decomposed rewards can be flexibly combined to align with different user needs, offering an interpretable and scalable alternative to traditional reward models. We demonstrate that DRMs effectively extract meaningful preference dimensions (e.g., helpfulness, safety, humor) and adapt to new users without additional training. Our results highlight DRMs as a powerful framework for personalized and interpretable LLM alignment.

Recent work in language modeling demonstrates that training large transformer models advances the state of the art in Natural Language Processing applications. However, very large models can be quite difficult to train due to memory constraints. In this work, we present our techniques for training very large transformer models and implement a simple, efficient intra-layer model parallel approach that enables training transformer models with billions of parameters. Our approach does not require a new compiler or library changes, is orthogonal and complimentary to pipeline model parallelism, and can be fully implemented with the insertion of a few communication operations in native PyTorch. We illustrate this approach by converging transformer based models up to 8.3 billion parameters using 512 GPUs. We sustain 15.1 PetaFLOPs across the entire application with 76% scaling efficiency when compared to a strong single GPU baseline that sustains 39 TeraFLOPs, which is 30% of peak FLOPs. To demonstrate that large language models can further advance the state of the art (SOTA), we train an 8.3 billion parameter transformer language model similar to GPT-2 and a 3.9 billion parameter model similar to BERT. We show that careful attention to the placement of layer normalization in BERT-like models is critical to achieving increased performance as the model size grows. Using the GPT-2 model we achieve SOTA results on the WikiText103 (10.8 compared to SOTA perplexity of 15.8) and LAMBADA (66.5% compared to SOTA accuracy of 63.2%) datasets. Our BERT model achieves SOTA results on the RACE dataset (90.9% compared to SOTA accuracy of 89.4%).

Recent advancements in large language models (LLMs) have shown promise in multi-step reasoning tasks, yet their reliance on extensive manual labeling to provide procedural feedback remains a significant impediment. To address this challenge, in this paper, we propose a novel self-supervised framework AutoPRM that efficiently enhances the fine-tuning of LLMs for intricate reasoning challenges. Specifically, AutoPRM first decomposes complex problems into more manageable subquestions with a controllable granularity switch, then sequentially apply reinforcement learning to iteratively improve the subquestion solver. Additionally, we propose context-guided-decoding to avoid reward tampering and guide the subquestion solver towards the solution of the holistic problem. Extensive experiments show that AutoPRM significantly improves performance on mathematical and commonsense reasoning tasks over SOTA. More encouragingly, AutoPRM can be easily integrated with other orthogonal reasoning pipelines.

While generative AI is now widespread and useful in society, there are potential risks of misuse, e.g., unconsciously influencing cognitive processes or decision-making. Although this causes a security problem in the cognitive domain, there has been no research about neural and computational mechanisms counteracting the impact of malicious generative AI in humans. We propose DecNefGAN, a novel framework that combines a generative adversarial system and a neural reinforcement model. More specifically, DecNefGAN bridges human and generative AI in a closed-loop system, with the AI creating stimuli that induce specific mental states, thus exerting external control over neural activity. The objective of the human is the opposite, to compete and reach an orthogonal mental state. This framework can contribute to elucidating how the human brain responds to and counteracts the potential influence of generative AI.

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

A deep hashing model typically has two main learning objectives: to make the learned binary hash codes discriminative and to minimize a quantization error. With further constraints such as bit balance and code orthogonality, it is not uncommon for existing models to employ a large number (>4) of losses. This leads to difficulties in model training and subsequently impedes their effectiveness. In this work, we propose a novel deep hashing model with only a single learning objective. Specifically, we show that maximizing the cosine similarity between the continuous codes and their corresponding binary orthogonal codes can ensure both hash code discriminativeness and quantization error minimization. Further, with this learning objective, code balancing can be achieved by simply using a Batch Normalization (BN) layer and multi-label classification is also straightforward with label smoothing. The result is an one-loss deep hashing model that removes all the hassles of tuning the weights of various losses. Importantly, extensive experiments show that our model is highly effective, outperforming the state-of-the-art multi-loss hashing models on three large-scale instance retrieval benchmarks, often by significant margins. Code is available at https://github.com/kamwoh/orthohash

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

Recent space-borne and ground-based observations provide photometric measurements as time series. The effect of interstellar dust extinction in the near-infrared range is only 10% of that measured in the V band. However, the sensitivity of the light curve shape to the physical parameters in the near-infrared is much lower. So, interpreting these types of data sets requires new approaches like the different large-scale surveys, which create similar problems with big data. Using a selected data set, we provide a method for applying routines implemented in R to extract most information of measurements to determine physical parameters, which can also be used in automatic classification schemes and pipeline processing. We made a multivariate classification of 131 Cepheid light curves (LC) in J, H, and K colors, where all the LCs were represented in 20D parameter space in these colors separately. Performing a Principal Component Analysis (PCA), we got an orthogonal coordinate system and squared Euclidean distances between LCs, with 6 significant eigenvalues, reducing the 20-dimension to 6. We also estimated the optimal number of partitions of similar objects and found it to be equal to 7 in each color; their dependence on the period, absolute magnitude, amplitude, and metallicity are also discussed. We computed the Spearman rank correlations, showing that periods and absolute magnitudes correlate with the first three PCs significantly. The first two PC are also found to have a relationship with the amplitude, but the metallicity effects are only marginal. The method shown can be generalized and implemented in unsupervised classification schemes and analysis of mixed and biased samples. The analysis of our Classical Cepheid near-infrared LC sample showed that the J, H, K curves are insufficient for determination of stellar metallicity, with mass being the key factor shaping them.

The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has investigated various speculative decoding techniques for multi-token generation, these efforts have primarily focused on improving processing speed such as throughput. Crucially, they often neglect other metrics essential for real-life deployments, such as memory consumption and training cost. To overcome these limitations, we propose a novel parallel prompt decoding that requires only 0.0002% trainable parameters, enabling efficient training on a single A100-40GB GPU in just 16 hours. Inspired by the human natural language generation process, PPD approximates outputs generated at future timesteps in parallel by using multiple prompt tokens. This approach partially recovers the missing conditional dependency information necessary for multi-token generation, resulting in up to a 28% higher acceptance rate for long-range predictions. Furthermore, we present a hardware-aware dynamic sparse tree technique that adaptively optimizes this decoding scheme to fully leverage the computational capacities on different GPUs. Through extensive experiments across LLMs ranging from MobileLlama to Vicuna-13B on a wide range of benchmarks, our approach demonstrates up to 2.49times speedup and maintains a minimal runtime memory overhead of just 0.0004%. More importantly, our parallel prompt decoding can serve as an orthogonal optimization for synergistic integration with existing speculative decoding, showing up to 1.22times further speed improvement. Our code is available at https://github.com/hmarkc/parallel-prompt-decoding.

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capabilities. In this study, we examine the matching mechanism employed by Transformer for multi-step reasoning on a constructed dataset. We investigate factors that influence the model's matching mechanism and discover that small initialization and post-LayerNorm can facilitate the formation of the matching mechanism, thereby enhancing the model's reasoning ability. Moreover, we propose a method to improve the model's reasoning capability by adding orthogonal noise. Finally, we investigate the parallel reasoning mechanism of Transformers and propose a conjecture on the upper bound of the model's reasoning ability based on this phenomenon. These insights contribute to a deeper understanding of the reasoning processes in large language models and guide designing more effective reasoning architectures and training strategies.

Recent developments in Parameter-Efficient Fine-Tuning (PEFT) methods for pretrained deep neural networks have captured widespread interest. In this work, we study the enhancement of current PEFT methods by incorporating the spectral information of pretrained weight matrices into the fine-tuning procedure. We investigate two spectral adaptation mechanisms, namely additive tuning and orthogonal rotation of the top singular vectors, both are done via first carrying out Singular Value Decomposition (SVD) of pretrained weights and then fine-tuning the top spectral space. We provide a theoretical analysis of spectral fine-tuning and show that our approach improves the rank capacity of low-rank adapters given a fixed trainable parameter budget. We show through extensive experiments that the proposed fine-tuning model enables better parameter efficiency and tuning performance as well as benefits multi-adapter fusion. The code will be open-sourced for reproducibility.

Neural Radiance Field (NeRF) has achieved superior performance for novel view synthesis by modeling the scene with a Multi-Layer Perception (MLP) and a volume rendering procedure, however, when fewer known views are given (i.e., few-shot view synthesis), the model is prone to overfit the given views. To handle this issue, previous efforts have been made towards leveraging learned priors or introducing additional regularizations. In contrast, in this paper, we for the first time provide an orthogonal method from the perspective of network structure. Given the observation that trivially reducing the number of model parameters alleviates the overfitting issue, but at the cost of missing details, we propose the multi-input MLP (mi-MLP) that incorporates the inputs (i.e., location and viewing direction) of the vanilla MLP into each layer to prevent the overfitting issue without harming detailed synthesis. To further reduce the artifacts, we propose to model colors and volume density separately and present two regularization terms. Extensive experiments on multiple datasets demonstrate that: 1) although the proposed mi-MLP is easy to implement, it is surprisingly effective as it boosts the PSNR of the baseline from 14.73 to 24.23. 2) the overall framework achieves state-of-the-art results on a wide range of benchmarks. We will release the code upon publication.

This study presents an innovative approach for predicting cryptocurrency time series, specifically focusing on Bitcoin, Ethereum, and Litecoin. The methodology integrates the use of technical indicators, a Performer neural network, and BiLSTM (Bidirectional Long Short-Term Memory) to capture temporal dynamics and extract significant features from raw cryptocurrency data. The application of technical indicators, such facilitates the extraction of intricate patterns, momentum, volatility, and trends. The Performer neural network, employing Fast Attention Via positive Orthogonal Random features (FAVOR+), has demonstrated superior computational efficiency and scalability compared to the traditional Multi-head attention mechanism in Transformer models. Additionally, the integration of BiLSTM in the feedforward network enhances the model's capacity to capture temporal dynamics in the data, processing it in both forward and backward directions. This is particularly advantageous for time series data where past and future data points can influence the current state. The proposed method has been applied to the hourly and daily timeframes of the major cryptocurrencies and its performance has been benchmarked against other methods documented in the literature. The results underscore the potential of the proposed method to outperform existing models, marking a significant progression in the field of cryptocurrency price prediction.

The hull of a linear code C is the intersection of C with its dual code. We present and analyze the number of linear q-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension k and length nge 2k the number of all [n,k]_q linear codes with hull dimension l decreases as l increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length n and dimension k, comparing the obtained numbers with the number of all linear codes for the given n and k.

Despite the remarkable success of deep neural networks in a myriad of settings, several works have demonstrated their overwhelming sensitivity to near-imperceptible perturbations, known as adversarial attacks. On the other hand, prior works have also observed that deep networks can be under-sensitive, wherein large-magnitude perturbations in input space do not induce appreciable changes to network activations. In this work, we study in detail the phenomenon of under-sensitivity in vision models such as CNNs and Transformers, and present techniques to study the geometry and extent of "equi-confidence" level sets of such networks. We propose a Level Set Traversal algorithm that iteratively explores regions of high confidence with respect to the input space using orthogonal components of the local gradients. Given a source image, we use this algorithm to identify inputs that lie in the same equi-confidence level set as the source image despite being perceptually similar to arbitrary images from other classes. We further observe that the source image is linearly connected by a high-confidence path to these inputs, uncovering a star-like structure for level sets of deep networks. Furthermore, we attempt to identify and estimate the extent of these connected higher-dimensional regions over which the model maintains a high degree of confidence. The code for this project is publicly available at https://github.com/SriramB-98/blindspots-neurips-sub

Large Language Models (LLMs) have demonstrated great capabilities in solving a wide range of tasks in a resource-efficient manner through prompting, which does not require task-specific training, but suffers from performance fluctuation when there are multiple prompt candidates. Previous works have introduced gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but fail to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common NLP tasks. We find that all existing methods can be unified into some variant of the method that maximizes the mutual information between the input and the corresponding model output (denoted as MI). Using the finding, we develop several variants of MI and increases the effectiveness of the best prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to existing methods and helps increase the prompt selection effectiveness of the best method by 99.44%. The code and datasets used in our work will be released at https://github.com/soheeyang/unified-prompt-selection.

Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by efficiently incorporating second-order information during the optimization process. In each iteration, FOSI implicitly splits the function into two quadratic functions defined on orthogonal subspaces, then uses a second-order method to minimize the first, and the base optimizer to minimize the other. We formally analyze FOSI's convergence and the conditions under which it improves a base optimizer. Our empirical evaluation demonstrates that FOSI improves the convergence rate and optimization time of first-order methods such as Heavy-Ball and Adam, and outperforms second-order methods (K-FAC and L-BFGS).

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on ell_1 regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest.

Even though 3D face reconstruction has achieved impressive progress, most orthogonal projection-based face reconstruction methods can not achieve accurate and consistent reconstruction results when the face is very close to the camera due to the distortion under the perspective projection. In this paper, we propose to simultaneously reconstruct 3D face mesh in the world space and predict 2D face landmarks on the image plane to address the problem of perspective 3D face reconstruction. Based on the predicted 3D vertices and 2D landmarks, the 6DoF (6 Degrees of Freedom) face pose can be easily estimated by the PnP solver to represent perspective projection. Our approach achieves 1st place on the leader-board of the ECCV 2022 WCPA challenge and our model is visually robust under different identities, expressions and poses. The training code and models are released to facilitate future research.

In the real world, the degradation of images taken under haze can be quite complex, where the spatial distribution of haze is varied from image to image. Recent methods adopt deep neural networks to recover clean scenes from hazy images directly. However, due to the paradox caused by the variation of real captured haze and the fixed degradation parameters of the current networks, the generalization ability of recent dehazing methods on real-world hazy images is not ideal.To address the problem of modeling real-world haze degradation, we propose to solve this problem by perceiving and modeling density for uneven haze distribution. We propose a novel Separable Hybrid Attention (SHA) module to encode haze density by capturing features in the orthogonal directions to achieve this goal. Moreover, a density map is proposed to model the uneven distribution of the haze explicitly. The density map generates positional encoding in a semi-supervised way. Such a haze density perceiving and modeling capture the unevenly distributed degeneration at the feature level effectively. Through a suitable combination of SHA and density map, we design a novel dehazing network architecture, which achieves a good complexity-performance trade-off. The extensive experiments on two large-scale datasets demonstrate that our method surpasses all state-of-the-art approaches by a large margin both quantitatively and qualitatively, boosting the best published PSNR metric from 28.53 dB to 33.49 dB on the Haze4k test dataset and from 37.17 dB to 38.41 dB on the SOTS indoor test dataset.

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2^nd-order optimizers for deep learning in low precision settings. Code: https://github.com/yorkerlin/StructuredNGD-DL

We introduce CroissantLLM, a 1.3B language model pretrained on a set of 3T English and French tokens, to bring to the research and industrial community a high-performance, fully open-sourced bilingual model that runs swiftly on consumer-grade local hardware. To that end, we pioneer the approach of training an intrinsically bilingual model with a 1:1 English-to-French pretraining data ratio, a custom tokenizer, and bilingual finetuning datasets. We release the training dataset, notably containing a French split with manually curated, high-quality, and varied data sources. To assess performance outside of English, we craft a novel benchmark, FrenchBench, consisting of an array of classification and generation tasks, covering various orthogonal aspects of model performance in the French Language. Additionally, rooted in transparency and to foster further Large Language Model research, we release codebases, and dozens of checkpoints across various model sizes, training data distributions, and training steps, as well as fine-tuned Chat models, and strong translation models. We evaluate our model through the FMTI framework, and validate 81 % of the transparency criteria, far beyond the scores of even most open initiatives. This work enriches the NLP landscape, breaking away from previous English-centric work in order to strengthen our understanding of multilinguality in language models.

The quality of finetuning data is crucial for aligning large language models (LLMs) with human values. Current methods to improve data quality are either labor-intensive or prone to factual errors caused by LLM hallucinations. This paper explores elevating the quality of existing instruction data to better align with human values, introducing a simple and effective approach named ReAlign, which reformats the responses of instruction data into a format that better aligns with pre-established criteria and the collated evidence. This approach minimizes human annotation, hallucination, and the difficulty in scaling, remaining orthogonal to existing alignment techniques. Experimentally, ReAlign significantly boosts the general alignment ability, math reasoning, factuality, and readability of the LLMs. Encouragingly, without introducing any additional data or advanced training techniques, and merely by reformatting the response, LLaMA-2-13B's mathematical reasoning ability on GSM8K can be improved from 46.77% to 56.63% in accuracy. Additionally, a mere 5% of ReAlign data yields a 67% boost in general alignment ability measured by the Alpaca dataset. This work highlights the need for further research into the science and mechanistic interpretability of LLMs. We have made the associated code and data publicly accessible to support future studies at https://github.com/GAIR-NLP/ReAlign.

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present variational score distillation (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i.e., 7.5). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed ProlificDreamer, can generate high rendering resolution (i.e., 512times512) and high-fidelity NeRF with rich structure and complex effects (e.g., smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic. Project page: https://ml.cs.tsinghua.edu.cn/prolificdreamer/

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Layer-wise quantization is a key technique for efficiently compressing large models without expensive retraining. Previous methods typically quantize the weights of each layer by "uniformly" optimizing the layer reconstruction loss across all output tokens. However, in this paper, we demonstrate that better-quantized models can be obtained by prioritizing learning from important tokens (e.g. which have large attention scores). Building on this finding, we propose RSQ (Rotate, Scale, then Quantize), which (1) applies rotations (orthogonal transformation) to the model to mitigate outliers (those with exceptionally large magnitude), (2) scales the token feature based on its importance, and (3) quantizes the model using the GPTQ framework with the second-order statistics computed by scaled tokens. To compute token importance, we explore both heuristic and dynamic strategies. Based on a thorough analysis of all approaches, we adopt attention concentration, which uses attention scores of each token as its importance, as the best approach. We demonstrate that RSQ consistently outperforms baseline methods across multiple downstream tasks and three model families: LLaMA3, Mistral, and Qwen2.5. Additionally, models quantized with RSQ achieve superior performance on long-context tasks, further highlighting its effectiveness. Lastly, RSQ demonstrates generalizability across various setups, including different model sizes, calibration datasets, bit precisions, and quantization methods.

The rapid growth of large models has raised concerns about their environmental impact and equity in accessibility due to significant computational costs. Low-Rank Adapters (LoRA) offer a lightweight solution for finetuning large models, resulting in an abundance of publicly available adapters tailored to diverse domains. We ask: Can these pretrained adapters be leveraged to further streamline adaptation to new tasks while addressing these challenges? We introduce EigenLoRAx, a parameter-efficient finetuning method that recycles existing adapters to create a principal subspace aligned with their shared domain knowledge which can be further augmented with orthogonal basis vectors in low-resource scenarios. This enables rapid adaptation to new tasks by learning only lightweight coefficients on the principal components of the subspace - eliminating the need to finetune entire adapters. EigenLoRAx requires significantly fewer parameters and memory, improving efficiency for both training and inference. Our method demonstrates strong performance across diverse domains and tasks, offering a scalable for edge-based applications, personalization, and equitable deployment of large models in resource-constrained environments.

The widespread application of Large Language Models (LLMs) across various tasks and fields has necessitated the alignment of these models with human values and preferences. Given various approaches of human value alignment, ranging from Reinforcement Learning with Human Feedback (RLHF), to constitutional learning, etc. there is an urgent need to understand the scope and nature of human values injected into these models before their release. There is also a need for model alignment without a costly large scale human annotation effort. We propose UniVaR, a high-dimensional representation of human value distributions in LLMs, orthogonal to model architecture and training data. Trained from the value-relevant output of eight multilingual LLMs and tested on the output from four multilingual LLMs, namely LlaMA2, ChatGPT, JAIS and Yi, we show that UniVaR is a powerful tool to compare the distribution of human values embedded in different LLMs with different langauge sources. Through UniVaR, we explore how different LLMs prioritize various values in different languages and cultures, shedding light on the complex interplay between human values and language modeling.

Through pretraining on a corpus with various sources, Large Language Models (LLMs) have gained impressive performance. However, the impact of each component of the pretraining corpus remains opaque. As a result, the organization of the pretraining corpus is still empirical and may deviate from the optimal. To address this issue, we systematically analyze the impact of 48 datasets from 5 major categories of pretraining data of LLMs and measure their impacts on LLMs using benchmarks about nine major categories of model capabilities. Our analyses provide empirical results about the contribution of multiple corpora on the performances of LLMs, along with their joint impact patterns, including complementary, orthogonal, and correlational relationships. We also identify a set of ``high-impact data'' such as Books that is significantly related to a set of model capabilities. These findings provide insights into the organization of data to support more efficient pretraining of LLMs.

We introduce Aligner, a novel Parameter-Efficient Fine-Tuning (PEFT) method for aligning multi-billion-parameter-sized Large Language Models (LLMs). Aligner employs a unique design that constructs a globally shared set of tunable tokens that modify the attention of every layer. Remarkably with this method, even when using one token accounting for a mere 5,000 parameters, Aligner can still perform comparably well to state-of-the-art LLM adaptation methods like LoRA that require millions of parameters. This capacity is substantiated in both instruction following and value alignment tasks. Besides the multiple order-of-magnitude improvement in parameter efficiency, the insight Aligner provides into the internal mechanisms of LLMs is also valuable. The architectural features and efficacy of our method, in addition to our experiments demonstrate that an LLM separates its internal handling of "form" and "knowledge" in a somewhat orthogonal manner. This finding promises to motivate new research into LLM mechanism understanding and value alignment.

Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated how to design an Innately Forgetting-Free Network (IF2Net) for continual learning context. This study proposed a straightforward yet effective learning paradigm by ingeniously keeping the weights relative to each seen task untouched before and after learning a new task. We first presented the novel representation-level learning on task sequences with random weights. This technique refers to tweaking the drifted representations caused by randomization back to their separate task-optimal working states, but the involved weights are frozen and reused (opposite to well-known layer-wise updates of weights). Then, sequential decision-making without forgetting can be achieved by projecting the output weight updates into the parsimonious orthogonal space, making the adaptations not disturb old knowledge while maintaining model plasticity. IF2Net allows a single network to inherently learn unlimited mapping rules without telling task identities at test time by integrating the respective strengths of randomization and orthogonalization. We validated the effectiveness of our approach in the extensive theoretical analysis and empirical study.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 16s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

Large language models (LLMs) power many state-of-the-art systems in natural language processing. However, these models are extremely computationally expensive, even at inference time, raising the natural question: when is the extra cost of deploying a larger model worth the anticipated boost in capabilities? Better understanding this tradeoff fundamentally could benefit from an inference efficiency metric that is both (i) easily comparable across models from different providers, and (ii) representative of the true cost of running queries in an isolated performance environment. Unfortunately, access to LLMs today is largely restricted to black-box text generation APIs and raw runtimes measured through this interface do not satisfy these desiderata: model providers can apply various software and hardware optimizations orthogonal to the model, and models served on shared infrastructure are susceptible to performance contention. To circumvent these problems, we propose a new metric for comparing inference efficiency across models. This metric puts models on equal footing as though they were served (i) on uniform hardware and software, and (ii) without performance contention. We call this metric the idealized runtime, and we propose a methodology to efficiently estimate this metric for autoregressive Transformer models. We also propose cost-aware variants that incorporate the number of accelerators needed to serve the model. Using these metrics, we compare ten state-of-the-art LLMs to provide the first analysis of inference efficiency-capability tradeoffs; we make several observations from this analysis, including the fact that the superior inference runtime performance of certain APIs is often a byproduct of optimizations within the API rather than the underlying model. Our methodology also facilitates the efficient comparison of different software and hardware stacks.

Despite their many desirable properties, Gaussian processes (GPs) are often compared unfavorably to deep neural networks (NNs) for lacking the ability to learn representations. Recent efforts to bridge the gap between GPs and deep NNs have yielded a new class of inter-domain variational GPs in which the inducing variables correspond to hidden units of a feedforward NN. In this work, we examine some practical issues associated with this approach and propose an extension that leverages the orthogonal decomposition of GPs to mitigate these limitations. In particular, we introduce spherical inter-domain features to construct more flexible data-dependent basis functions for both the principal and orthogonal components of the GP approximation and show that incorporating NN activation features under this framework not only alleviates these shortcomings but is more scalable than alternative strategies. Experiments on multiple benchmark datasets demonstrate the effectiveness of our approach.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

In this work, we develop a specialized dataset aimed at enhancing the evaluation and fine-tuning of large language models (LLMs) specifically for wireless communication applications. The dataset includes a diverse set of multi-hop questions, including true/false and multiple-choice types, spanning varying difficulty levels from easy to hard. By utilizing advanced language models for entity extraction and question generation, rigorous data curation processes are employed to maintain high quality and relevance. Additionally, we introduce a Pointwise V-Information (PVI) based fine-tuning method, providing a detailed theoretical analysis and justification for its use in quantifying the information content of training data with 2.24\% and 1.31\% performance boost for different models compared to baselines, respectively. To demonstrate the effectiveness of the fine-tuned models with the proposed methodologies on practical tasks, we also consider different tasks, including summarizing optimization problems from technical papers and solving the mathematical problems related to non-orthogonal multiple access (NOMA), which are generated by using the proposed multi-agent framework. Simulation results show significant performance gain in summarization tasks with 20.9\% in the ROUGE-L metrics. We also study the scaling laws of fine-tuning LLMs and the challenges LLMs face in the field of wireless communications, offering insights into their adaptation to wireless communication tasks. This dataset and fine-tuning methodology aim to enhance the training and evaluation of LLMs, contributing to advancements in LLMs for wireless communication research and applications.

Text-to-image (T2I) models can effectively capture the content or style of reference images to perform high-quality customization. A representative technique for this is fine-tuning using low-rank adaptations (LoRA), which enables efficient model customization with reference images. However, fine-tuning with a limited number of reference images often leads to overfitting, resulting in issues such as prompt misalignment or content leakage. These issues prevent the model from accurately following the input prompt or generating undesired objects during inference. To address this problem, we examine the text embeddings that guide the diffusion model during inference. This study decomposes the text embedding matrix and conducts a component analysis to understand the embedding space geometry and identify the cause of overfitting. Based on this, we propose DECOR, which projects text embeddings onto a vector space orthogonal to undesired token vectors, thereby reducing the influence of unwanted semantics in the text embeddings. Experimental results demonstrate that DECOR outperforms state-of-the-art customization models and achieves Pareto frontier performance across text and visual alignment evaluation metrics. Furthermore, it generates images more faithful to the input prompts, showcasing its effectiveness in addressing overfitting and enhancing text-to-image customization.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Attention mechanisms that confer selective focus on a strict subset of input elements are nearly ubiquitous in language models today. We posit there to be downside to the use of attention: most information present in the input is necessarily lost. In support of this idea we observe poor input representation accuracy in transformers, but find more accurate representation in what we term masked mixers which replace self-attention with masked convolutions. Applied to TinyStories the masked mixer learns causal language tasks more efficiently than early transformer implementations and somewhat less efficiently than optimized, current implementations. The most efficient learning algorithm observed for this dataset is a transformer-masked mixer hybrid, suggesting that these models learn in an orthogonal manner. We hypothesized that the information loss exhibited by transformers would be much more detrimental to retrieval than generation, and to test this we introduce an efficient training approach for retrieval models based on existing generative model embeddings. With this method, embeddings from masked mixers are found to result in far better summary-to-story retrieval compared to embeddings from transformers.

Large Language Models (LLMs) exhibit high inference latency due to their autoregressive decoding nature. While the draft head in speculative decoding mitigates this issue, its full potential remains unexplored. In this paper, we introduce KOALA (K-layer Optimized Adversarial Learning Architecture), an orthogonal approach to the draft head. By transforming the conventional single-layer draft head into a multi-layer architecture and incorporating adversarial learning into the traditional supervised training, KOALA significantly improves the accuracy of the draft head in predicting subsequent tokens, thus more closely mirroring the functionality of LLMs. Although this improvement comes at the cost of slightly increased drafting overhead, KOALA substantially unlocks the draft head's potential, greatly enhancing speculative decoding. We conducted comprehensive evaluations of KOALA, including both autoregressive and non-autoregressive draft heads across various tasks, demonstrating a latency speedup ratio improvement of 0.24x-0.41x, which is 10.57%-14.09% faster than the original draft heads.

Large language models (LLMs) have shown substantial progress in natural language understanding and generation, proving valuable especially in the medical field. Despite advancements, challenges persist due to the complexity and diversity inherent in medical tasks, which can be categorized as knowledge-intensive tasks and alignment-required tasks. Previous approaches either ignore the latter task or focus on a minority of tasks and hence lose generalization. To address these drawbacks, we propose a progressive fine-tuning pipeline. This pipeline employs a Knowledge Aggregator and a Noise aggregator to encode diverse knowledge in the first stage and filter out detrimental information. In the second stage, we drop the Noise Aggregator to avoid the interference of suboptimal representation and leverage an additional alignment module optimized towards an orthogonal direction to the knowledge space to mitigate knowledge forgetting. Based on this two-stage paradigm, we proposed a Medical LLM through decoupling Clinical Alignment and Knowledge Aggregation (MedCare), which is designed to achieve state-of-the-art (SOTA) performance on over 20 medical tasks, as well as SOTA results on specific medical alignment tasks. Various model sizes of MedCare (1.8B, 7B, 14B) all demonstrate significant improvements over existing models with similar model sizes.

Task planning in language agents is emerging as an important research topic alongside the development of large language models (LLMs). It aims to break down complex user requests in natural language into solvable sub-tasks, thereby fulfilling the original requests. In this context, the sub-tasks can be naturally viewed as a graph, where the nodes represent the sub-tasks, and the edges denote the dependencies among them. Consequently, task planning is a decision-making problem that involves selecting a connected path or subgraph within the corresponding graph and invoking it. In this paper, we explore graph learning-based methods for task planning, a direction that is orthogonal to the prevalent focus on prompt design. Our interest in graph learning stems from a theoretical discovery: the biases of attention and auto-regressive loss impede LLMs' ability to effectively navigate decision-making on graphs, which is adeptly addressed by graph neural networks (GNNs). This theoretical insight led us to integrate GNNs with LLMs to enhance overall performance. Extensive experiments demonstrate that GNN-based methods surpass existing solutions even without training, and minimal training can further enhance their performance. The performance gain increases with a larger task graph size.

3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without considering spatial consistency. As a result, these approaches exhibit limited versatility in 3D data representation and shape generation, hindering their ability to generate highly diverse 3D shapes that comply with the specified constraints. In this paper, we introduce a novel spatial-aware 3D shape generation framework that leverages 2D plane representations for enhanced 3D shape modeling. To ensure spatial coherence and reduce memory usage, we incorporate a hybrid shape representation technique that directly learns a continuous signed distance field representation of the 3D shape using orthogonal 2D planes. Additionally, we meticulously enforce spatial correspondences across distinct planes using a transformer-based autoencoder structure, promoting the preservation of spatial relationships in the generated 3D shapes. This yields an algorithm that consistently outperforms state-of-the-art 3D shape generation methods on various tasks, including unconditional shape generation, multi-modal shape completion, single-view reconstruction, and text-to-shape synthesis.

Factual inconsistencies pose a significant hurdle for the faithful summarization by generative models. While a major direction to enhance inconsistency detection is to derive stronger Natural Language Inference (NLI) models, we propose an orthogonal aspect that underscores the importance of incorporating task-specific taxonomy into the inference. To this end, we consolidate key error types of inconsistent facts in summaries, and incorporate them to facilitate both the zero-shot and supervised paradigms of LLMs. Extensive experiments on ten datasets of five distinct domains suggest that, zero-shot LLM inference could benefit from the explicit solution space depicted by the error type taxonomy, and achieves state-of-the-art performance overall, surpassing specialized non-LLM baselines, as well as recent LLM baselines. We further distill models that fuse the taxonomy into parameters through our designed prompt completions and supervised training strategies, efficiently substituting state-of-the-art zero-shot inference with much larger LLMs.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e.g. performance on another dataset, robustness, agreement with a prior). Although the simplest approach to incorporating an auxiliary loss is to sum it with the training loss as a regularizer, recent works have shown that one can improve performance by blending the gradients beyond a simple sum; this is known as gradient surgery. We cast the problem as a constrained minimization problem where the auxiliary objective is minimized among the set of minimizers of the training loss. To solve this bilevel problem, we follow a parameter update direction that combines the training loss gradient and the orthogonal projection of the auxiliary gradient to the training gradient. In a setting where gradients come from mini-batches, we explain how, using a moving average of the training loss gradients, we can carefully maintain this critical orthogonality property. We demonstrate that our method, Bloop, can lead to much better performances on NLP and vision experiments than other gradient surgery methods without EMA.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

The infinitely wide neural network has been proven a useful and manageable mathematical model that enables the understanding of many phenomena appearing in deep learning. One example is the convergence of random deep networks to Gaussian processes that allows a rigorous analysis of the way the choice of activation function and network weights impacts the training dynamics. In this paper, we extend the seminal proof of Matthews et al. (2018) to a larger class of initial weight distributions (which we call PSEUDO-IID), including the established cases of IID and orthogonal weights, as well as the emerging low-rank and structured sparse settings celebrated for their computational speed-up benefits. We show that fully-connected and convolutional networks initialized with PSEUDO-IID distributions are all effectively equivalent up to their variance. Using our results, one can identify the Edge-of-Chaos for a broader class of neural networks and tune them at criticality in order to enhance their training. Moreover, they enable the posterior distribution of Bayesian Neural Networks to be tractable across these various initialization schemes.

The brain has computational capabilities that surpass those of modern systems, being able to solve complex problems efficiently in a simple way. Neuromorphic engineering aims to mimic biology in order to develop new systems capable of incorporating such capabilities. Bio-inspired learning systems continue to be a challenge that must be solved, and much work needs to be done in this regard. Among all brain regions, the hippocampus stands out as an autoassociative short-term memory with the capacity to learn and recall memories from any fragment of them. These characteristics make the hippocampus an ideal candidate for developing bio-inspired learning systems that, in addition, resemble content-addressable memories. Therefore, in this work we propose a bio-inspired spiking content-addressable memory model based on the CA3 region of the hippocampus with the ability to learn, forget and recall memories, both orthogonal and non-orthogonal, from any fragment of them. The model was implemented on the SpiNNaker hardware platform using Spiking Neural Networks. A set of experiments based on functional, stress and applicability tests were performed to demonstrate its correct functioning. This work presents the first hardware implementation of a fully-functional bio-inspired spiking hippocampal content-addressable memory model, paving the way for the development of future more complex neuromorphic systems.

We present the requirements, design and evaluation of the cryogenic continuously rotating half-wave plate (CHWP) for the Simons Observatory (SO). SO is a cosmic microwave background (CMB) polarization experiment at Parque Astron\'{o}mico Atacama in northern Chile that covers a wide range of angular scales using both small (0.42 m) and large (6 m) aperture telescopes. In particular, the small aperture telescopes (SATs) focus on large angular scales for primordial B-mode polarization. To this end, the SATs employ a CHWP to modulate the polarization of the incident light at 8 Hz, suppressing atmospheric 1/f noise and mitigating systematic uncertainties that would otherwise arise due to the differential response of detectors sensitive to orthogonal polarizations. The CHWP consists of a 505 mm diameter achromatic sapphire HWP and a cryogenic rotation mechanism, both of which are cooled down to sim50 K to reduce detector thermal loading. Under normal operation the HWP is suspended by a superconducting magnetic bearing and rotates with a constant 2 Hz frequency, controlled by an electromagnetic synchronous motor. We find that the number of superconductors and magnets that make up the superconducting magnetic bearing are important design parameters, especially for the rotation mechanism's vibration performance. The rotation angle is detected through an angular encoder with a noise level of 0.07 muradmathrm{s}. During a cooldown, the rotor is held in place by a grip-and-release mechanism that serves as both an alignment device and a thermal path. In this paper we provide an overview of the SO SAT CHWP: its requirements, hardware design, and laboratory performance.

Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced data, this symmetry breaks under class imbalances. This paper presents an intriguing discovery: the introduction of a ReLU activation at the final layer effectively restores the symmetry in SCL-learned representations. We arrive at this finding analytically, by establishing that the global minimizers of an unconstrained features model with SCL loss and entry-wise non-negativity constraints form an orthogonal frame. Extensive experiments conducted across various datasets, architectures, and imbalance scenarios corroborate our finding. Importantly, our experiments reveal that the inclusion of the ReLU activation restores symmetry without compromising test accuracy. This constitutes the first geometry characterization of SCL under imbalances. Additionally, our analysis and experiments underscore the pivotal role of batch selection strategies in representation geometry. By proving necessary and sufficient conditions for mini-batch choices that ensure invariant symmetric representations, we introduce batch-binding as an efficient strategy that guarantees these conditions hold.

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple modifications to DDIM using insights from our theoretical results. In as few as 5-10 function evaluations, our sampler achieves state-of-the-art FID scores on pretrained CIFAR-10 and CelebA models and can generate high quality samples on latent diffusion models.

In a multi-task learning (MTL) setting, a single model is trained to tackle a diverse set of tasks jointly. Despite rapid progress in the field, MTL remains challenging due to optimization issues such as conflicting and dominating gradients. In this work, we propose using a condition number of a linear system of gradients as a stability criterion of an MTL optimization. We theoretically demonstrate that a condition number reflects the aforementioned optimization issues. Accordingly, we present Aligned-MTL, a novel MTL optimization approach based on the proposed criterion, that eliminates instability in the training process by aligning the orthogonal components of the linear system of gradients. While many recent MTL approaches guarantee convergence to a minimum, task trade-offs cannot be specified in advance. In contrast, Aligned-MTL provably converges to an optimal point with pre-defined task-specific weights, which provides more control over the optimization result. Through experiments, we show that the proposed approach consistently improves performance on a diverse set of MTL benchmarks, including semantic and instance segmentation, depth estimation, surface normal estimation, and reinforcement learning. The source code is publicly available at https://github.com/SamsungLabs/MTL .

Layer Normalization (LayerNorm) is an inherent component in all Transformer-based models. In this paper, we show that LayerNorm is crucial to the expressivity of the multi-head attention layer that follows it. This is in contrast to the common belief that LayerNorm's only role is to normalize the activations during the forward pass, and their gradients during the backward pass. We consider a geometric interpretation of LayerNorm and show that it consists of two components: (a) projection of the input vectors to a d-1 space that is orthogonal to the left[1,1,...,1right] vector, and (b) scaling of all vectors to the same norm of d. We show that each of these components is important for the attention layer that follows it in Transformers: (a) projection allows the attention mechanism to create an attention query that attends to all keys equally, offloading the need to learn this operation by the attention; and (b) scaling allows each key to potentially receive the highest attention, and prevents keys from being "un-select-able". We show empirically that Transformers do indeed benefit from these properties of LayeNorm in general language modeling and even in computing simple functions such as "majority". Our code is available at https://github.com/tech-srl/layer_norm_expressivity_role .

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.

Test-time task adaptation in few-shot learning aims to adapt a pre-trained task-agnostic model for capturing taskspecific knowledge of the test task, rely only on few-labeled support samples. Previous approaches generally focus on developing advanced algorithms to achieve the goal, while neglecting the inherent problems of the given support samples. In fact, with only a handful of samples available, the adverse effect of either the image noise (a.k.a. X-noise) or the label noise (a.k.a. Y-noise) from support samples can be severely amplified. To address this challenge, in this work we propose DEnoised Task Adaptation (DETA), a first, unified image- and label-denoising framework orthogonal to existing task adaptation approaches. Without extra supervision, DETA filters out task-irrelevant, noisy representations by taking advantage of both global visual information and local region details of support samples. On the challenging Meta-Dataset, DETA consistently improves the performance of a broad spectrum of baseline methods applied on various pre-trained models. Notably, by tackling the overlooked image noise in Meta-Dataset, DETA establishes new state-of-the-art results. Code is released at https://github.com/nobody-1617/DETA.

Complex vector modes, entangled in spin and orbital angular momentum, are opening burgeoning opportunities for a wide variety of applications. Importantly, the flexible manipulation the various properties of such beams will pave the way to novel applications. As such, in this manuscript, we demonstrate a longitudinal spin-orbit separation of complex vector modes propagating in free space. To achieve this we employed the recently demonstrated circular Airy Gaussian vortex vector (CAGVV) modes, which feature a self-focusing property. More precisely, by properly manipulating the intrinsic parameters of CAGVV modes, the strong coupling between the two constituting orthogonal components of CAGVV mode undergo a spin-orbit separation along the propagation direction namely, while one polarisation component, focuses at a specific plane, the other focuses at a different plane. Such spin-orbit separation, which we demonstrated by numerical simulations and corroborated experimentally, can be adjusted on-demand by simply changing the initial parameters of CAGVV modes. Our findings will be of great relevance, for example in optical tweezers, to manipulate micro- or nano-particles at two different parallel planes.

The Lunar Surface Electromagnetics Explorer 'LuSEE Night' is a low frequency radio astronomy experiment that will be delivered to the farside of the Moon by the NASA Commercial Lunar Payload Services (CLPS) program in late 2025 or early 2026. The payload system is being developed jointly by NASA and the US Department of Energy (DOE) and consists of a 4 channel, 50 MHz Nyquist baseband receiver system and 2 orthogonal sim6m tip-to-tip electric dipole antennas. LuSEE Night will enjoy standalone operations through the lunar night, without the electromagnetic interference (EMI) of an operating lander system and antipodal to our noisy home planet.

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of a valley to the other causing loss stabilization, and (ii) this stabilization induces a hidden stochastic dynamics orthogonal to the bouncing directions that biases it implicitly toward sparse predictors. Furthermore, we show empirically that the longer large step sizes keep SGD high in the loss landscape valleys, the better the implicit regularization can operate and find sparse representations. Notably, no explicit regularization is used so that the regularization effect comes solely from the SGD training dynamics influenced by the step size schedule. Therefore, these observations unveil how, through the step size schedules, both gradient and noise drive together the SGD dynamics through the loss landscape of neural networks. We justify these findings theoretically through the study of simple neural network models as well as qualitative arguments inspired from stochastic processes. Finally, this analysis allows us to shed a new light on some common practice and observed phenomena when training neural networks. The code of our experiments is available at https://github.com/tml-epfl/sgd-sparse-features.

Face animation, one of the hottest topics in computer vision, has achieved a promising performance with the help of generative models. However, it remains a critical challenge to generate identity preserving and photo-realistic images due to the sophisticated motion deformation and complex facial detail modeling. To address these problems, we propose a Face Neural Volume Rendering (FNeVR) network to fully explore the potential of 2D motion warping and 3D volume rendering in a unified framework. In FNeVR, we design a 3D Face Volume Rendering (FVR) module to enhance the facial details for image rendering. Specifically, we first extract 3D information with a well-designed architecture, and then introduce an orthogonal adaptive ray-sampling module for efficient rendering. We also design a lightweight pose editor, enabling FNeVR to edit the facial pose in a simple yet effective way. Extensive experiments show that our FNeVR obtains the best overall quality and performance on widely used talking-head benchmarks.

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.

Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common defense mechanism is regularization through adversarial training which injects worst-case perturbations back into training to strengthen the decision boundaries, and to reduce overfitting. In this context, we perform an investigation of 3x3 convolution filters that form in adversarially-trained models. Filters are extracted from 71 public models of the linf-RobustBench CIFAR-10/100 and ImageNet1k leaderboard and compared to filters extracted from models built on the same architectures but trained without robust regularization. We observe that adversarially-robust models appear to form more diverse, less sparse, and more orthogonal convolution filters than their normal counterparts. The largest differences between robust and normal models are found in the deepest layers, and the very first convolution layer, which consistently and predominantly forms filters that can partially eliminate perturbations, irrespective of the architecture. Data & Project website: https://github.com/paulgavrikov/cvpr22w_RobustnessThroughTheLens

The alignment problem in the context of large language models must consider the plurality of human values in our world. Whilst there are many resonant and overlapping values amongst the world's cultures, there are also many conflicting, yet equally valid, values. It is important to observe which cultural values a model exhibits, particularly when there is a value conflict between input prompts and generated outputs. We discuss how the co-creation of language and cultural value impacts large language models (LLMs). We explore the constitution of the training data for GPT-3 and compare that to the world's language and internet access demographics, as well as to reported statistical profiles of dominant values in some Nation-states. We stress tested GPT-3 with a range of value-rich texts representing several languages and nations; including some with values orthogonal to dominant US public opinion as reported by the World Values Survey. We observed when values embedded in the input text were mutated in the generated outputs and noted when these conflicting values were more aligned with reported dominant US values. Our discussion of these results uses a moral value pluralism (MVP) lens to better understand these value mutations. Finally, we provide recommendations for how our work may contribute to other current work in the field.

Recent advances in semi-supervised object detection (SSOD) are largely driven by consistency-based pseudo-labeling methods for image classification tasks, producing pseudo labels as supervisory signals. However, when using pseudo labels, there is a lack of consideration in localization precision and amplified class imbalance, both of which are critical for detection tasks. In this paper, we introduce certainty-aware pseudo labels tailored for object detection, which can effectively estimate the classification and localization quality of derived pseudo labels. This is achieved by converting conventional localization as a classification task followed by refinement. Conditioned on classification and localization quality scores, we dynamically adjust the thresholds used to generate pseudo labels and reweight loss functions for each category to alleviate the class imbalance problem. Extensive experiments demonstrate that our method improves state-of-the-art SSOD performance by 1-2% AP on COCO and PASCAL VOC while being orthogonal and complementary to most existing methods. In the limited-annotation regime, our approach improves supervised baselines by up to 10% AP using only 1-10% labeled data from COCO.

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of fast weights generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank.

The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes {the classical unenriched proper orthogonal decomposition method} fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the {error indicator} becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

Popular parameter-efficient fine-tuning (PEFT) methods, such as LoRA and its variants, freeze pre-trained model weights \(W\) and inject learnable matrices \(\Delta W\). These \(\Delta W\) matrices are structured for efficient parameterization, often using techniques like low-rank approximations or scaling vectors. However, these methods typically show a performance gap compared to full fine-tuning. Although recent PEFT methods have narrowed this gap, they do so at the cost of additional learnable parameters. We propose SVFT, a simple approach that fundamentally differs from existing methods: the structure imposed on \(\Delta W\) depends on the specific weight matrix \(W\). Specifically, SVFT updates \(W\) as a sparse combination of outer products of its singular vectors, training only the coefficients (scales) of these sparse combinations. This approach allows fine-grained control over expressivity through the number of coefficients. Extensive experiments on language and vision benchmarks show that SVFT recovers up to 96% of full fine-tuning performance while training only 0.006 to 0.25% of parameters, outperforming existing methods that only recover up to 85% performance using 0.03 to 0.8% of the trainable parameter budget.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.

We demonstrate a compact, cost-effective snapshot spectral imaging system named Aperture Diffraction Imaging Spectrometer (ADIS), which consists only of an imaging lens with an ultra-thin orthogonal aperture mask and a mosaic filter sensor, requiring no additional physical footprint compared to common RGB cameras. Then we introduce a new optical design that each point in the object space is multiplexed to discrete encoding locations on the mosaic filter sensor by diffraction-based spatial-spectral projection engineering generated from the orthogonal mask. The orthogonal projection is uniformly accepted to obtain a weakly calibration-dependent data form to enhance modulation robustness. Meanwhile, the Cascade Shift-Shuffle Spectral Transformer (CSST) with strong perception of the diffraction degeneration is designed to solve a sparsity-constrained inverse problem, realizing the volume reconstruction from 2D measurements with Large amount of aliasing. Our system is evaluated by elaborating the imaging optical theory and reconstruction algorithm with demonstrating the experimental imaging under a single exposure. Ultimately, we achieve the sub-super-pixel spatial resolution and high spectral resolution imaging. The code will be available at: https://github.com/Krito-ex/CSST.

Let F be a field, and n geq r>0 be integers, with r even. Denote by A_n(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible dimension for an affine subspace of A_n(F) in which every matrix has rank equal to r (or rank at least r). Recently Rubei has solved this problem over the field of real numbers. We extend her result to all fields with large enough cardinality. Provided that n geq r+3 and |F|geq minbigl(r-1,r{2}+2bigr), we also determine the affine subspaces of rank r matrices in A_n(F) that have the greatest possible dimension, and we point to difficulties for the corresponding problem in the case nleq r+2.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

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.

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of Obigl(NKD^3bigr) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to Obigl(NKD^2bigr) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.

We begin the study of list-decodable linear regression using batches. In this setting only an alpha in (0,1] fraction of the batches are genuine. Each genuine batch contains ge n i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any nge tilde Omega(1/alpha) returns a list of size mathcal O(1/alpha^2) such that one of the items in the list is close to the true regression parameter. The algorithm requires only mathcal{O}(d/alpha^2) genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound diakonikolas2021statistical for the non-batch setting.