Daily Papers

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: https://github.com/shivram1987/ActivationFunctions.

Activation functions are core components of all deep learning architectures. Currently, the most popular activation functions are smooth ReLU variants like GELU and SiLU. These are self-gated activation functions where the range of the gating function is between zero and one. In this paper, we explore the viability of using arctan as a gating mechanism. A self-gated activation function that uses arctan as its gating function has a monotonically increasing first derivative. To make this activation function competitive, it is necessary to introduce a trainable parameter for every MLP block to expand the range of the gating function beyond zero and one. We find that this technique also improves existing self-gated activation functions. We conduct an empirical evaluation of Expanded ArcTan Linear Unit (xATLU), Expanded GELU (xGELU), and Expanded SiLU (xSiLU) and show that they outperform existing activation functions within a transformer architecture. Additionally, expanded gating ranges show promising results in improving first-order Gated Linear Units (GLU).

Sparse Neural Networks (SNNs) can potentially demonstrate similar performance to their dense counterparts while saving significant energy and memory at inference. However, the accuracy drop incurred by SNNs, especially at high pruning ratios, can be an issue in critical deployment conditions. While recent works mitigate this issue through sophisticated pruning techniques, we shift our focus to an overlooked factor: hyperparameters and activation functions. Our analyses have shown that the accuracy drop can additionally be attributed to (i) Using ReLU as the default choice for activation functions unanimously, and (ii) Fine-tuning SNNs with the same hyperparameters as dense counterparts. Thus, we focus on learning a novel way to tune activation functions for sparse networks and combining these with a separate hyperparameter optimization (HPO) regime for sparse networks. By conducting experiments on popular DNN models (LeNet-5, VGG-16, ResNet-18, and EfficientNet-B0) trained on MNIST, CIFAR-10, and ImageNet-16 datasets, we show that the novel combination of these two approaches, dubbed Sparse Activation Function Search, short: SAFS, results in up to 15.53%, 8.88%, and 6.33% absolute improvement in the accuracy for LeNet-5, VGG-16, and ResNet-18 over the default training protocols, especially at high pruning ratios. Our code can be found at https://github.com/automl/SAFS

Sparse computation offers a compelling solution for the inference of Large Language Models (LLMs) in low-resource scenarios by dynamically skipping the computation of inactive neurons. While traditional approaches focus on ReLU-based LLMs, leveraging zeros in activation values, we broaden the scope of sparse LLMs beyond zero activation values. We introduce a general method that defines neuron activation through neuron output magnitudes and a tailored magnitude threshold, demonstrating that non-ReLU LLMs also exhibit sparse activation. To find the most efficient activation function for sparse computation, we propose a systematic framework to examine the sparsity of LLMs from three aspects: the trade-off between sparsity and performance, the predictivity of sparsity, and the hardware affinity. We conduct thorough experiments on LLMs utilizing different activation functions, including ReLU, SwiGLU, ReGLU, and ReLU^2. The results indicate that models employing ReLU^2 excel across all three evaluation aspects, highlighting its potential as an efficient activation function for sparse LLMs. We will release the code to facilitate future research.

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x cdot sigmoid(beta x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9\% for Mobile NASNet-A and 0.6\% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal's spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or Sirens, are ideally suited for representing complex natural signals and their derivatives. We analyze Siren activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how Sirens can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine Sirens with hypernetworks to learn priors over the space of Siren functions.

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance. Moreover, PAUs pave the way to approximations with provable robustness. https://github.com/ml-research/pau

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.

Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.

We propose Mish, a novel self-regularized non-monotonic activation function which can be mathematically defined as: f(x)=xtanh(softplus(x)). As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks against the best combinations of architectures and activation functions. We also observe that data augmentation techniques have a favorable effect on benchmarks like ImageNet-1k and MS-COCO across multiple architectures. For example, Mish outperformed Leaky ReLU on YOLOv4 with a CSP-DarkNet-53 backbone on average precision (AP_{50}^{val}) by 2.1% in MS-COCO object detection and ReLU on ResNet-50 on ImageNet-1k in Top-1 accuracy by approx1% while keeping all other network parameters and hyperparameters constant. Furthermore, we explore the mathematical formulation of Mish in relation with the Swish family of functions and propose an intuitive understanding on how the first derivative behavior may be acting as a regularizer helping the optimization of deep neural networks. Code is publicly available at https://github.com/digantamisra98/Mish.

The widely used ReLU is favored for its hardware efficiency, {as the implementation at inference is a one bit sign case,} yet suffers from issues such as the ``dying ReLU'' problem, where during training, neurons fail to activate and constantly remain at zero, as highlighted by Lu et al. Traditional approaches to mitigate this issue often introduce more complex and less hardware-friendly activation functions. In this work, we propose a Hysteresis Rectified Linear Unit (HeLU), an efficient activation function designed to address the ``dying ReLU'' problem with minimal complexity. Unlike traditional activation functions with fixed thresholds for training and inference, HeLU employs a variable threshold that refines the backpropagation. This refined mechanism allows simpler activation functions to achieve competitive performance comparable to their more complex counterparts without introducing unnecessary complexity or requiring inductive biases. Empirical evaluations demonstrate that HeLU enhances model generalization across diverse datasets, offering a promising solution for efficient and effective inference suitable for a wide range of neural network architectures.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.12% improvement with ShuffleNet V2 (2.0x) model on CIFAR100 dataset.

Large Language Models (LLMs) with billions of parameters have drastically transformed AI applications. However, their demanding computation during inference has raised significant challenges for deployment on resource-constrained devices. Despite recent trends favoring alternative activation functions such as GELU or SiLU, known for increased computation, this study strongly advocates for reinstating ReLU activation in LLMs. We demonstrate that using the ReLU activation function has a negligible impact on convergence and performance while significantly reducing computation and weight transfer. This reduction is particularly valuable during the memory-bound inference step, where efficiency is paramount. Exploring sparsity patterns in ReLU-based LLMs, we unveil the reutilization of activated neurons for generating new tokens and leveraging these insights, we propose practical strategies to substantially reduce LLM inference computation up to three times, using ReLU activations with minimal performance trade-offs.

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear Unit (GELU) activation function has emerged as a dominant method, surpassing traditional functions such as the Rectified Linear Unit (ReLU) in various applications. This study presents a rigorous mathematical investigation of the GELU activation function, exploring its differentiability, boundedness, stationarity, and smoothness properties in detail. Additionally, we conduct an extensive experimental comparison of the GELU function against a broad range of alternative activation functions, utilizing a residual convolutional network trained on the CIFAR-10, CIFAR-100, and STL-10 datasets as the empirical testbed. Our results demonstrate the superior performance of GELU compared to other activation functions, establishing its suitability for a wide range of deep learning applications. This comprehensive study contributes to a more profound understanding of the underlying mathematical properties of GELU and provides valuable insights for practitioners aiming to select activation functions that optimally align with their specific objectives and constraints in deep learning.

Activation sparsity denotes the existence of substantial weakly-contributed elements within activation outputs that can be eliminated, benefiting many important applications concerned with large language models (LLMs). Although promoting greater activation sparsity within LLMs deserves deep studies, existing works lack comprehensive and quantitative research on the correlation between activation sparsity and potentially influential factors. In this paper, we present a comprehensive study on the quantitative scaling properties and influential factors of the activation sparsity within decoder-only Transformer-based LLMs. Specifically, we propose PPL-p% sparsity, a precise and performance-aware activation sparsity metric that is applicable to any activation function. Through extensive experiments, we find several important phenomena. Firstly, different activation functions exhibit comparable performance but opposite training-time sparsity trends. The activation ratio (i.e., 1-sparsity ratio) evolves as a convergent increasing power-law and decreasing logspace power-law with the amount of training data for SiLU-activated and ReLU-activated LLMs, respectively. These demonstrate that ReLU is more efficient as the activation function than SiLU and can leverage more training data to improve activation sparsity. Secondly, the activation ratio linearly increases with the width-depth ratio below a certain bottleneck point, indicating the potential advantage of a deeper architecture at a fixed parameter scale. Finally, at similar width-depth ratios, we surprisingly find that the limit value of activation sparsity varies weakly with the parameter scale, i.e., the activation patterns within LLMs are insensitive to the parameter scale. These empirical laws towards LLMs with greater activation sparsity have important implications for making LLMs more efficient and interpretable.

Activation sparsity refers to the existence of considerable weakly-contributed elements among activation outputs. As a prevalent property of the models using the ReLU activation function, it has been proven a promising paradigm to boost model inference efficiency. Nevertheless, most large language models (LLMs) adopt activation functions without intrinsic activation sparsity (e.g., GELU and Swish). Some recent efforts have explored introducing ReLU or its variants as the substitutive activation function to help LLMs achieve activation sparsity and inference acceleration, but few can simultaneously obtain high sparsity and comparable model performance. This paper introduces an effective sparsification method named "ProSparse" to push LLMs for higher activation sparsity without decreasing model performance. Specifically, after substituting the activation function of LLMs with ReLU, ProSparse adopts progressive sparsity regularization with a factor smoothly increasing along sine curves in multiple stages. This can enhance activation sparsity and alleviate performance degradation by avoiding radical shifts in activation distribution. With ProSparse, we obtain high sparsity of 89.32% and 88.80% for LLaMA2-7B and LLaMA2-13B, respectively, achieving comparable performance to their original Swish-activated versions. Our inference acceleration experiments further demonstrate the practical acceleration brought by higher activation sparsity.

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the optimal approximation rate, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.

LayerNorm is a critical component in modern large language models (LLMs) for stabilizing training and ensuring smooth optimization. However, it introduces significant challenges in mechanistic interpretability, outlier feature suppression, faithful signal propagation, and computational and communication complexity of private inference. This work explores desirable activation functions in normalization-free decoder-only LLMs. Contrary to the conventional preference for the GELU in transformer-based models, our empirical findings demonstrate an {\em opposite trend} -- ReLU significantly outperforms GELU in LayerNorm-free models, leading to an {\bf 8.2\%} perplexity improvement. We discover a key issue with GELU, where early layers experience entropic overload, leading to the under-utilization of the representational capacity of attention heads. This highlights that smoother activations like GELU are {\em ill-suited} for LayerNorm-free architectures, whereas ReLU's geometrical properties -- specialization in input space and intra-class selectivity -- lead to improved learning dynamics and better information retention in the absence of LayerNorm. This study offers key insights for optimizing transformer architectures where LayerNorm introduces significant challenges.

Layer-sequential unit-variance (LSUV) initialization - a simple method for weight initialization for deep net learning - is proposed. The method consists of the two steps. First, pre-initialize weights of each convolution or inner-product layer with orthonormal matrices. Second, proceed from the first to the final layer, normalizing the variance of the output of each layer to be equal to one. Experiment with different activation functions (maxout, ReLU-family, tanh) show that the proposed initialization leads to learning of very deep nets that (i) produces networks with test accuracy better or equal to standard methods and (ii) is at least as fast as the complex schemes proposed specifically for very deep nets such as FitNets (Romero et al. (2015)) and Highway (Srivastava et al. (2015)). Performance is evaluated on GoogLeNet, CaffeNet, FitNets and Residual nets and the state-of-the-art, or very close to it, is achieved on the MNIST, CIFAR-10/100 and ImageNet datasets.

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Implicit neural representations (INRs) use neural networks to provide continuous and resolution-independent representations of complex signals with a small number of parameters. However, existing INR models often fail to capture important frequency components specific to each task. To address this issue, in this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The proposed FKAN utilizes learnable activation functions modeled as Fourier series in the first layer to effectively control and learn the task-specific frequency components. In addition, the activation functions with learnable Fourier coefficients improve the ability of the network to capture complex patterns and details, which is beneficial for high-resolution and high-dimensional data. Experimental results show that our proposed FKAN model outperforms three state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) for the image representation task and intersection over union (IoU) for the 3D occupancy volume representation task, respectively.

In this paper, we introduce the Convolutional Kolmogorov-Arnold Networks (Convolutional KANs), an innovative alternative to the standard Convolutional Neural Networks (CNNs) that have revolutionized the field of computer vision. We integrate the non-linear activation functions presented in Kolmogorov-Arnold Networks (KANs) into convolutions to build a new layer. Throughout the paper, we empirically validate the performance of Convolutional KANs against traditional architectures across MNIST and Fashion-MNIST benchmarks, illustrating that this new approach maintains a similar level of accuracy while using half the amount of parameters. This significant reduction of parameters opens up a new approach to advance the optimization of neural network architectures.

Catastrophic forgetting remains a significant challenge to continual learning for decades. While recent works have proposed effective methods to mitigate this problem, they mainly focus on the algorithmic side. Meanwhile, we do not fully understand what architectural properties of neural networks lead to catastrophic forgetting. This study aims to fill this gap by studying the role of activation functions in the training dynamics of neural networks and their impact on catastrophic forgetting. Our study reveals that, besides sparse representations, the gradient sparsity of activation functions also plays an important role in reducing forgetting. Based on this insight, we propose a new class of activation functions, elephant activation functions, that can generate both sparse representations and sparse gradients. We show that by simply replacing classical activation functions with elephant activation functions, we can significantly improve the resilience of neural networks to catastrophic forgetting. Our method has broad applicability and benefits for continual learning in regression, class incremental learning, and reinforcement learning tasks. Specifically, we achieves excellent performance on Split MNIST dataset in just one single pass, without using replay buffer, task boundary information, or pre-training.

Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and different kinds of penalties. To investigate the effectiveness of sparsity by itself, we propose the k-sparse autoencoder, which is an autoencoder with linear activation function, where in hidden layers only the k highest activities are kept. When applied to the MNIST and NORB datasets, we find that this method achieves better classification results than denoising autoencoders, networks trained with dropout, and RBMs. k-sparse autoencoders are simple to train and the encoding stage is very fast, making them well-suited to large problem sizes, where conventional sparse coding algorithms cannot be applied.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

We show that both an LSTM and a unitary-evolution recurrent neural network (URN) can achieve encouraging accuracy on two types of syntactic patterns: context-free long distance agreement, and mildly context-sensitive cross serial dependencies. This work extends recent experiments on deeply nested context-free long distance dependencies, with similar results. URNs differ from LSTMs in that they avoid non-linear activation functions, and they apply matrix multiplication to word embeddings encoded as unitary matrices. This permits them to retain all information in the processing of an input string over arbitrary distances. It also causes them to satisfy strict compositionality. URNs constitute a significant advance in the search for explainable models in deep learning applied to NLP.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions and to impose additional constraints on them. Monotonicity constraint is one of the most requested properties in real-world scenarios and is the focus of this paper. One of the oldest ways to construct a monotonic fully connected neural network is to constrain signs on its weights. Unfortunately, this construction does not work with popular non-saturated activation functions as it can only approximate convex functions. We show this shortcoming can be fixed by constructing two additional activation functions from a typical unsaturated monotonic activation function and employing each of them on the part of neurons. Our experiments show this approach of building monotonic neural networks has better accuracy when compared to other state-of-the-art methods, while being the simplest one in the sense of having the least number of parameters, and not requiring any modifications to the learning procedure or post-learning steps. Finally, we prove it can approximate any continuous monotone function on a compact subset of R^n.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Deep learning models have become increasingly useful in many different industries. On the domain of image classification, convolutional neural networks proved the ability to learn robust features for the closed set problem, as shown in many different datasets, such as MNIST FASHIONMNIST, CIFAR10, CIFAR100, and IMAGENET. These approaches use deep neural networks with dense layers with softmax activation functions in order to learn features that can separate classes in a latent space. However, this traditional approach is not useful for identifying classes unseen on the training set, known as the open set problem. A similar problem occurs in scenarios involving learning on small data. To tackle both problems, few-shot learning has been proposed. In particular, metric learning learns features that obey constraints of a metric distance in the latent space in order to perform classification. However, while this approach proves to be useful for the open set problem, current implementation requires pair-wise training, where both positive and negative examples of similar images are presented during the training phase, which limits the applicability of these approaches in large data or large class scenarios given the combinatorial nature of the possible inputs.In this paper, we present a constraint-based approach applied to the representations in the latent space under the normalized softmax loss, proposed by[18]. We experimentally validate the proposed approach for the classification of unseen classes on different datasets using both metric learning and the normalized softmax loss, on disjoint and joint scenarios. Our results show that not only our proposed strategy can be efficiently trained on larger set of classes, as it does not require pairwise learning, but also present better classification results than the metric learning strategies surpassing its accuracy by a significant margin.

Because learning sometimes involves sensitive data, machine learning algorithms have been extended to offer privacy for training data. In practice, this has been mostly an afterthought, with privacy-preserving models obtained by re-running training with a different optimizer, but using the model architectures that already performed well in a non-privacy-preserving setting. This approach leads to less than ideal privacy/utility tradeoffs, as we show here. Instead, we propose that model architectures are chosen ab initio explicitly for privacy-preserving training. To provide guarantees under the gold standard of differential privacy, one must bound as strictly as possible how individual training points can possibly affect model updates. In this paper, we are the first to observe that the choice of activation function is central to bounding the sensitivity of privacy-preserving deep learning. We demonstrate analytically and experimentally how a general family of bounded activation functions, the tempered sigmoids, consistently outperform unbounded activation functions like ReLU. Using this paradigm, we achieve new state-of-the-art accuracy on MNIST, FashionMNIST, and CIFAR10 without any modification of the learning procedure fundamentals or differential privacy analysis.

Recently, semidefinite programming (SDP) techniques have shown great promise in providing accurate Lipschitz bounds for neural networks. Specifically, the LipSDP approach (Fazlyab et al., 2019) has received much attention and provides the least conservative Lipschitz upper bounds that can be computed with polynomial time guarantees. However, one main restriction of LipSDP is that its formulation requires the activation functions to be slope-restricted on [0,1], preventing its further use for more general activation functions such as GroupSort, MaxMin, and Householder. One can rewrite MaxMin activations for example as residual ReLU networks. However, a direct application of LipSDP to the resultant residual ReLU networks is conservative and even fails in recovering the well-known fact that the MaxMin activation is 1-Lipschitz. Our paper bridges this gap and extends LipSDP beyond slope-restricted activation functions. To this end, we provide novel quadratic constraints for GroupSort, MaxMin, and Householder activations via leveraging their underlying properties such as sum preservation. Our proposed analysis is general and provides a unified approach for estimating ell_2 and ell_infty Lipschitz bounds for a rich class of neural network architectures, including non-residual and residual neural networks and implicit models, with GroupSort, MaxMin, and Householder activations. Finally, we illustrate the utility of our approach with a variety of experiments and show that our proposed SDPs generate less conservative Lipschitz bounds in comparison to existing approaches.

Exploiting activation sparsity is a promising approach to significantly accelerating the inference process of large language models (LLMs) without compromising performance. However, activation sparsity is determined by activation functions, and commonly used ones like SwiGLU and GeGLU exhibit limited sparsity. Simply replacing these functions with ReLU fails to achieve sufficient sparsity. Moreover, inadequate training data can further increase the risk of performance degradation. To address these challenges, we propose a novel dReLU function, which is designed to improve LLM activation sparsity, along with a high-quality training data mixture ratio to facilitate effective sparsification. Additionally, we leverage sparse activation patterns within the Feed-Forward Network (FFN) experts of Mixture-of-Experts (MoE) models to further boost efficiency. By applying our neuron sparsification method to the Mistral and Mixtral models, only 2.5 billion and 4.3 billion parameters are activated per inference iteration, respectively, while achieving even more powerful model performance. Evaluation results demonstrate that this sparsity achieves a 2-5x decoding speedup. Remarkably, on mobile phones, our TurboSparse-Mixtral-47B achieves an inference speed of 11 tokens per second. Our models are available at https://huggingface.co/PowerInfer

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer (KAT), a novel architecture that replaces MLP layers with Kolmogorov-Arnold Network (KAN) layers to enhance the expressiveness and performance of the model. Integrating KANs into transformers, however, is no easy feat, especially when scaled up. Specifically, we identify three key challenges: (C1) Base function. The standard B-spline function used in KANs is not optimized for parallel computing on modern hardware, resulting in slower inference speeds. (C2) Parameter and Computation Inefficiency. KAN requires a unique function for each input-output pair, making the computation extremely large. (C3) Weight initialization. The initialization of weights in KANs is particularly challenging due to their learnable activation functions, which are critical for achieving convergence in deep neural networks. To overcome the aforementioned challenges, we propose three key solutions: (S1) Rational basis. We replace B-spline functions with rational functions to improve compatibility with modern GPUs. By implementing this in CUDA, we achieve faster computations. (S2) Group KAN. We share the activation weights through a group of neurons, to reduce the computational load without sacrificing performance. (S3) Variance-preserving initialization. We carefully initialize the activation weights to make sure that the activation variance is maintained across layers. With these designs, KAT scales effectively and readily outperforms traditional MLP-based transformers.

Soft prompt tuning is a widely studied parameter-efficient fine-tuning method. However, it has a clear drawback: many soft tokens must be inserted into the input sequences to guarantee downstream performance. As a result, soft prompt tuning is less considered than Low-rank adaptation (LoRA) in the large language modeling (LLM) era. In this work, we propose a novel prompt tuning method, Instruction-Aware Prompt Tuning (IAPT), that requires only four soft tokens. First, we install a parameter-efficient soft prompt generator at each Transformer layer to generate idiosyncratic soft prompts for each input instruction. The generated soft prompts can be seen as a semantic summary of the input instructions and can effectively guide the output generation. Second, the soft prompt generators are modules with a bottleneck architecture consisting of a self-attention pooling operation, two linear projections, and an activation function. Pilot experiments show that prompt generators at different Transformer layers require different activation functions. Thus, we propose to learn the idiosyncratic activation functions for prompt generators automatically with the help of rational functions. We have conducted experiments on various tasks, and the experimental results demonstrate that (a) our IAPT method can outperform the recent baselines with comparable tunable parameters. (b) Our IAPT method is more efficient than LoRA under the single-backbone multi-tenant setting.

We introduce a new analytical framework to quantify the changes in a machine learning algorithm's output distribution following the inclusion of a few data points in its training set, a notion we define as leave-one-out distinguishability (LOOD). This problem is key to measuring data **memorization** and **information leakage** in machine learning, and the **influence** of training data points on model predictions. We illustrate how our method broadens and refines existing empirical measures of memorization and privacy risks associated with training data. We use Gaussian processes to model the randomness of machine learning algorithms, and validate LOOD with extensive empirical analysis of information leakage using membership inference attacks. Our theoretical framework enables us to investigate the causes of information leakage and where the leakage is high. For example, we analyze the influence of activation functions, on data memorization. Additionally, our method allows us to optimize queries that disclose the most significant information about the training data in the leave-one-out setting. We illustrate how optimal queries can be used for accurate **reconstruction** of training data.

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory.

The Transformer architecture consists of self-attention and feed-forward networks (FFNs) which can be viewed as key-value memories according to previous works. However, FFN and traditional memory utilize different activation functions (i.e., ReLU and Softmax respectively), which makes them not equivalent. In this paper, we first rebuild the connections between FFN and key-value memory by conducting extensive studies on ReLU and Softmax, and find they are equivalent when adding an additional layer normalization module on Softmax. In addition, ReLU outperforms Softmax on both FFN and key-value memory when the number of value slots is large. We analyze the reasons and then explore this good property of ReLU on the self-attention network where the original Softmax activation performs poorly on long input sequences. We then propose a full ReLU architecture named ReLUFormer which performs better than the baseline Transformer on long sequence tasks such as document translation. This paper sheds light on the following points: 1) Softmax and ReLU use different normalization methods over elements which lead to different variances of results, and ReLU is good at dealing with a large number of key-value slots; 2) FFN and key-value memory are equivalent, and thus the Transformer can be viewed as a memory network where FFNs and self-attention networks are both key-value memories.

Privacy concerns in client-server machine learning have given rise to private inference (PI), where neural inference occurs directly on encrypted inputs. PI protects clients' personal data and the server's intellectual property. A common practice in PI is to use garbled circuits to compute nonlinear functions privately, namely ReLUs. However, garbled circuits suffer from high storage, bandwidth, and latency costs. To mitigate these issues, PI-friendly polynomial activation functions have been employed to replace ReLU. In this work, we ask: Is it feasible to substitute all ReLUs with low-degree polynomial activation functions for building deep, privacy-friendly neural networks? We explore this question by analyzing the challenges of substituting ReLUs with polynomials, starting with simple drop-and-replace solutions to novel, more involved replace-and-retrain strategies. We examine the limitations of each method and provide commentary on the use of polynomial activation functions for PI. We find all evaluated solutions suffer from the escaping activation problem: forward activation values inevitably begin to expand at an exponential rate away from stable regions of the polynomials, which leads to exploding values (NaNs) or poor approximations.

Virtual try-on has garnered interest as a neural rendering benchmark task to evaluate complex object transfer and scene composition. Recent works in virtual clothing try-on feature a plethora of possible architectural and data representation choices. However, they present little clarity on quantifying the isolated visual effect of each choice, nor do they specify the hyperparameter details that are key to experimental reproduction. Our work, ShineOn, approaches the try-on task from a bottom-up approach and aims to shine light on the visual and quantitative effects of each experiment. We build a series of scientific experiments to isolate effective design choices in video synthesis for virtual clothing try-on. Specifically, we investigate the effect of different pose annotations, self-attention layer placement, and activation functions on the quantitative and qualitative performance of video virtual try-on. We find that DensePose annotations not only enhance face details but also decrease memory usage and training time. Next, we find that attention layers improve face and neck quality. Finally, we show that GELU and ReLU activation functions are the most effective in our experiments despite the appeal of newer activations such as Swish and Sine. We will release a well-organized code base, hyperparameters, and model checkpoints to support the reproducibility of our results. We expect our extensive experiments and code to greatly inform future design choices in video virtual try-on. Our code may be accessed at https://github.com/andrewjong/ShineOn-Virtual-Tryon.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds.

It has been shown that deep neural networks of a large enough width are universal approximators but they are not if the width is too small. There were several attempts to characterize the minimum width w_{min} enabling the universal approximation property; however, only a few of them found the exact values. In this work, we show that the minimum width for L^p approximation of L^p functions from [0,1]^{d_x} to mathbb R^{d_y} is exactly max{d_x,d_y,2} if an activation function is ReLU-Like (e.g., ReLU, GELU, Softplus). Compared to the known result for ReLU networks, w_{min}=max{d_x+1,d_y} when the domain is mathbb R^{d_x}, our result first shows that approximation on a compact domain requires smaller width than on mathbb R^{d_x}. We next prove a lower bound on w_{min} for uniform approximation using general activation functions including ReLU: w_{min}ge d_y+1 if d_x<d_yle2d_x. Together with our first result, this shows a dichotomy between L^p and uniform approximations for general activation functions and input/output dimensions.

Extending the context length of Language Models (LMs) by improving Rotary Position Embedding (RoPE) has become a trend. While existing works mainly address RoPE's limitations within attention mechanism, this paper provides an analysis across nearly all parts of LMs, uncovering their adverse effects on length generalization for RoPE-based attention. Using Discrete Signal Processing theory, we show that RoPE enables periodic attention by implicitly achieving Non-Uniform Discrete Fourier Transform. However, this periodicity is undermined by the spectral damage caused by: 1) linear layers and activation functions outside of attention; 2) insufficiently trained frequency components brought by time-domain truncation. Building on our observations, we propose Fourier Position Embedding (FoPE), which enhances attention's frequency-domain properties to improve both its periodic extension and length generalization. FoPE constructs Fourier Series and zero-outs the destructive frequency components, increasing model robustness against the spectrum damage. Experiments across various model scales show that, within varying context windows, FoPE can maintain a more stable perplexity and a more consistent accuracy in a needle-in-haystack task compared to RoPE and ALiBi. Several analyses and ablations bring further support to our method and theoretical modeling.

Batch Normalization is a key component in almost all state-of-the-art image classifiers, but it also introduces practical challenges: it breaks the independence between training examples within a batch, can incur compute and memory overhead, and often results in unexpected bugs. Building on recent theoretical analyses of deep ResNets at initialization, we propose a simple set of analysis tools to characterize signal propagation on the forward pass, and leverage these tools to design highly performant ResNets without activation normalization layers. Crucial to our success is an adapted version of the recently proposed Weight Standardization. Our analysis tools show how this technique preserves the signal in networks with ReLU or Swish activation functions by ensuring that the per-channel activation means do not grow with depth. Across a range of FLOP budgets, our networks attain performance competitive with the state-of-the-art EfficientNets on ImageNet.

While the activations of neurons in deep neural networks usually do not have a simple human-understandable interpretation, sparse autoencoders (SAEs) can be used to transform these activations into a higher-dimensional latent space which may be more easily interpretable. However, these SAEs can have millions of distinct latent features, making it infeasible for humans to manually interpret each one. In this work, we build an open-source automated pipeline to generate and evaluate natural language explanations for SAE features using LLMs. We test our framework on SAEs of varying sizes, activation functions, and losses, trained on two different open-weight LLMs. We introduce five new techniques to score the quality of explanations that are cheaper to run than the previous state of the art. One of these techniques, intervention scoring, evaluates the interpretability of the effects of intervening on a feature, which we find explains features that are not recalled by existing methods. We propose guidelines for generating better explanations that remain valid for a broader set of activating contexts, and discuss pitfalls with existing scoring techniques. We use our explanations to measure the semantic similarity of independently trained SAEs, and find that SAEs trained on nearby layers of the residual stream are highly similar. Our large-scale analysis confirms that SAE latents are indeed much more interpretable than neurons, even when neurons are sparsified using top-k postprocessing. Our code is available at https://github.com/EleutherAI/sae-auto-interp, and our explanations are available at https://huggingface.co/datasets/EleutherAI/auto_interp_explanations.

Considering the hardware-friendly characteristics and broad applicability, structured pruning has emerged as an efficient solution to reduce the resource demands of large language models (LLMs) on resource-constrained devices. Traditional structured pruning methods often need fine-tuning to recover performance loss, which incurs high memory overhead and substantial data requirements, rendering them unsuitable for on-device applications. Additionally, post-training structured pruning techniques typically necessitate specific activation functions or architectural modifications, thereby limiting their scope of applications. Herein, we introduce COMP, a lightweight post-training structured pruning method that employs a hybrid-granularity pruning strategy. COMP initially prunes selected model layers based on their importance at a coarse granularity, followed by fine-grained neuron pruning within the dense layers of each remaining model layer. To more accurately evaluate neuron importance, COMP introduces a new matrix condition-based metric. Subsequently, COMP utilizes mask tuning to recover accuracy without the need for fine-tuning, significantly reducing memory consumption. Experimental results demonstrate that COMP improves performance by 6.13\% on the LLaMA-2-7B model with a 20\% pruning ratio compared to LLM-Pruner, while simultaneously reducing memory overhead by 80\%.

In recent years, many neural network (NN) verifiers have been developed to formally verify certain properties of neural networks such as robustness. Although many benchmarks have been constructed to evaluate the performance of NN verifiers, they typically lack a ground-truth for hard instances where no current verifier can verify and no counterexample can be found, which makes it difficult to check the soundness of a new verifier if it claims to verify hard instances which no other verifier can do. We propose to develop a soundness benchmark for NN verification. Our benchmark contains instances with deliberately inserted counterexamples while we also try to hide the counterexamples from regular adversarial attacks which can be used for finding counterexamples. We design a training method to produce neural networks with such hidden counterexamples. Our benchmark aims to be used for testing the soundness of NN verifiers and identifying falsely claimed verifiability when it is known that hidden counterexamples exist. We systematically construct our benchmark and generate instances across diverse model architectures, activation functions, input sizes, and perturbation radii. We demonstrate that our benchmark successfully identifies bugs in state-of-the-art NN verifiers, as well as synthetic bugs, providing a crucial step toward enhancing the reliability of testing NN verifiers. Our code is available at https://github.com/MVP-Harry/SoundnessBench and our benchmark is available at https://huggingface.co/datasets/SoundnessBench/SoundnessBench.

Fine-tuning pretrained large models to downstream tasks is an important problem, which however suffers from huge memory overhead due to large-scale parameters. This work strives to reduce memory overhead in fine-tuning from perspectives of activation function and layer normalization. To this end, we propose the Approximate Backpropagation (Approx-BP) theory, which provides the theoretical feasibility of decoupling the forward and backward passes. We apply our Approx-BP theory to backpropagation training and derive memory-efficient alternatives of GELU and SiLU activation functions, which use derivative functions of ReLUs in the backward pass while keeping their forward pass unchanged. In addition, we introduce a Memory-Sharing Backpropagation strategy, which enables the activation memory to be shared by two adjacent layers, thereby removing activation memory usage redundancy. Our method neither induces extra computation nor reduces training efficiency. We conduct extensive experiments with pretrained vision and language models, and the results demonstrate that our proposal can reduce up to sim30% of the peak memory usage. Our code is released at https://github.com/yyyyychen/LowMemoryBP.

Despite the remarkable capabilities of deep neural networks in image recognition, the dependence on activation functions remains a largely unexplored area and has yet to be eliminated. On the other hand, Polynomial Networks is a class of models that does not require activation functions, but have yet to perform on par with modern architectures. In this work, we aim close this gap and propose MONet, which relies solely on multilinear operators. The core layer of MONet, called Mu-Layer, captures multiplicative interactions of the elements of the input token. MONet captures high-degree interactions of the input elements and we demonstrate the efficacy of our approach on a series of image recognition and scientific computing benchmarks. The proposed model outperforms prior polynomial networks and performs on par with modern architectures. We believe that MONet can inspire further research on models that use entirely multilinear operations.

At the heart of foundation models is the philosophy of "more is different", exemplified by the astonishing success in computer vision and natural language processing. However, the challenges of optimization and inherent complexity of transformer models call for a paradigm shift towards simplicity. In this study, we introduce VanillaNet, a neural network architecture that embraces elegance in design. By avoiding high depth, shortcuts, and intricate operations like self-attention, VanillaNet is refreshingly concise yet remarkably powerful. Each layer is carefully crafted to be compact and straightforward, with nonlinear activation functions pruned after training to restore the original architecture. VanillaNet overcomes the challenges of inherent complexity, making it ideal for resource-constrained environments. Its easy-to-understand and highly simplified architecture opens new possibilities for efficient deployment. Extensive experimentation demonstrates that VanillaNet delivers performance on par with renowned deep neural networks and vision transformers, showcasing the power of minimalism in deep learning. This visionary journey of VanillaNet has significant potential to redefine the landscape and challenge the status quo of foundation model, setting a new path for elegant and effective model design. Pre-trained models and codes are available at https://github.com/huawei-noah/VanillaNet and https://gitee.com/mindspore/models/tree/master/research/cv/vanillanet.

We consider the neural contextual bandit problem. In contrast to the existing work which primarily focuses on ReLU neural nets, we consider a general set of smooth activation functions. Under this more general setting, (i) we derive non-asymptotic error bounds on the difference between an overparameterized neural net and its corresponding neural tangent kernel, (ii) we propose an algorithm with a provably sublinear regret bound that is also efficient in the finite regime as demonstrated by empirical studies. The non-asymptotic error bounds may be of broader interest as a tool to establish the relation between the smoothness of the activation functions in neural contextual bandits and the smoothness of the kernels in kernel bandits.

Although there have been significant advances in the field of image restoration recently, the system complexity of the state-of-the-art (SOTA) methods is increasing as well, which may hinder the convenient analysis and comparison of methods. In this paper, we propose a simple baseline that exceeds the SOTA methods and is computationally efficient. To further simplify the baseline, we reveal that the nonlinear activation functions, e.g. Sigmoid, ReLU, GELU, Softmax, etc. are not necessary: they could be replaced by multiplication or removed. Thus, we derive a Nonlinear Activation Free Network, namely NAFNet, from the baseline. SOTA results are achieved on various challenging benchmarks, e.g. 33.69 dB PSNR on GoPro (for image deblurring), exceeding the previous SOTA 0.38 dB with only 8.4% of its computational costs; 40.30 dB PSNR on SIDD (for image denoising), exceeding the previous SOTA 0.28 dB with less than half of its computational costs. The code and the pre-trained models are released at https://github.com/megvii-research/NAFNet.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

We introduce a data-free quantization method for deep neural networks that does not require fine-tuning or hyperparameter selection. It achieves near-original model performance on common computer vision architectures and tasks. 8-bit fixed-point quantization is essential for efficient inference on modern deep learning hardware. However, quantizing models to run in 8-bit is a non-trivial task, frequently leading to either significant performance reduction or engineering time spent on training a network to be amenable to quantization. Our approach relies on equalizing the weight ranges in the network by making use of a scale-equivariance property of activation functions. In addition the method corrects biases in the error that are introduced during quantization. This improves quantization accuracy performance, and can be applied to many common computer vision architectures with a straight forward API call. For common architectures, such as the MobileNet family, we achieve state-of-the-art quantized model performance. We further show that the method also extends to other computer vision architectures and tasks such as semantic segmentation and object detection.

Deep learning expresses a category of machine learning algorithms that have the capability to combine raw inputs into intermediate features layers. These deep learning algorithms have demonstrated great results in different fields. Deep learning has particularly witnessed for a great achievement of human level performance across a number of domains in computer vision and pattern recognition. For the achievement of state-of-the-art performances in diverse domains, the deep learning used different architectures and these architectures used activation functions to perform various computations between hidden and output layers of any architecture. This paper presents a survey on the existing studies of deep learning in handwriting recognition field. Even though the recent progress indicates that the deep learning methods has provided valuable means for speeding up or proving accurate results in handwriting recognition, but following from the extensive literature survey, the present study finds that the deep learning has yet to revolutionize more and has to resolve many of the most pressing challenges in this field, but promising advances have been made on the prior state of the art. Additionally, an inadequate availability of labelled data to train presents problems in this domain. Nevertheless, the present handwriting recognition survey foresees deep learning enabling changes at both bench and bedside with the potential to transform several domains as image processing, speech recognition, computer vision, machine translation, robotics and control, medical imaging, medical information processing, bio-informatics, natural language processing, cyber security, and many others.

Modern deep-learning systems are specialized to problem settings in which training occurs once and then never again, as opposed to continual-learning settings in which training occurs continually. If deep-learning systems are applied in a continual learning setting, then it is well known that they may fail to remember earlier examples. More fundamental, but less well known, is that they may also lose their ability to learn on new examples, a phenomenon called loss of plasticity. We provide direct demonstrations of loss of plasticity using the MNIST and ImageNet datasets repurposed for continual learning as sequences of tasks. In ImageNet, binary classification performance dropped from 89\% accuracy on an early task down to 77\%, about the level of a linear network, on the 2000th task. Loss of plasticity occurred with a wide range of deep network architectures, optimizers, activation functions, batch normalization, dropout, but was substantially eased by L^2-regularization, particularly when combined with weight perturbation. Further, we introduce a new algorithm -- continual backpropagation -- which slightly modifies conventional backpropagation to reinitialize a small fraction of less-used units after each example and appears to maintain plasticity indefinitely.

Branch-and-bound (BaB) is among the most effective techniques for neural network (NN) verification. However, existing works on BaB for NN verification have mostly focused on NNs with piecewise linear activations, especially ReLU networks. In this paper, we develop a general framework, named GenBaB, to conduct BaB on general nonlinearities to verify NNs with general architectures, based on linear bound propagation for NN verification. To decide which neuron to branch, we design a new branching heuristic which leverages linear bounds as shortcuts to efficiently estimate the potential improvement after branching. To decide nontrivial branching points for general nonlinear functions, we propose to pre-optimize branching points, which can be efficiently leveraged during verification with a lookup table. We demonstrate the effectiveness of our GenBaB on verifying a wide range of NNs, including NNs with activation functions such as Sigmoid, Tanh, Sine and GeLU, as well as NNs involving multi-dimensional nonlinear operations such as multiplications in LSTMs and Vision Transformers. Our framework also allows the verification of general nonlinear computation graphs and enables verification applications beyond simple NNs, particularly for AC Optimal Power Flow (ACOPF). GenBaB is part of the latest alpha,!beta-CROWN, the winner of the 4th and the 5th International Verification of Neural Networks Competition (VNN-COMP 2023 and 2024).

The initial state of neural networks plays a central role in conditioning the subsequent training dynamics. In the context of classification problems, we provide a theoretical analysis demonstrating that the structure of a neural network can condition the model to assign all predictions to the same class, even before the beginning of training, and in the absence of explicit biases. We show that the presence of this phenomenon, which we call "Initial Guessing Bias" (IGB), depends on architectural choices such as activation functions, max-pooling layers, and network depth. Our analysis of IGB has practical consequences, in that it guides architecture selection and initialization. We also highlight theoretical consequences, such as the breakdown of node-permutation symmetry, the violation of self-averaging, the validity of some mean-field approximations, and the non-trivial differences arising with depth.

Recent work has shown that forward- and reverse- mode automatic differentiation (AD) over the reals is almost always correct in a mathematically precise sense. However, actual programs work with machine-representable numbers (e.g., floating-point numbers), not reals. In this paper, we study the correctness of AD when the parameter space of a neural network consists solely of machine-representable numbers. In particular, we analyze two sets of parameters on which AD can be incorrect: the incorrect set on which the network is differentiable but AD does not compute its derivative, and the non-differentiable set on which the network is non-differentiable. For a neural network with bias parameters, we first prove that the incorrect set is always empty. We then prove a tight bound on the size of the non-differentiable set, which is linear in the number of non-differentiabilities in activation functions, and give a simple necessary and sufficient condition for a parameter to be in this set. We further prove that AD always computes a Clarke subderivative even on the non-differentiable set. We also extend these results to neural networks possibly without bias parameters.

Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm-restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJU-DHD datasets indicate that the proposed method achieves competitive results in diverse scenes.

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack of robustness, unveiled by the striking effectiveness of adversarial attacks. Current attack methods are able to manipulate the network's prediction by adding specific but small amounts of noise to the input. In turn, adversarial training (AT) aims to achieve robustness against such attacks and ideally a better model generalization ability by including adversarial samples in the trainingset. However, an in-depth analysis of the resulting robust models beyond adversarial robustness is still pending. In this paper, we empirically analyze a variety of adversarially trained models that achieve high robust accuracies when facing state-of-the-art attacks and we show that AT has an interesting side-effect: it leads to models that are significantly less overconfident with their decisions, even on clean data than non-robust models. Further, our analysis of robust models shows that not only AT but also the model's building blocks (like activation functions and pooling) have a strong influence on the models' prediction confidences. Data & Project website: https://github.com/GeJulia/robustness_confidences_evaluation

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

Accurate and fast scene understanding is one of the challenging task for autonomous driving, which requires to take full advantage of LiDAR point clouds for semantic segmentation. In this paper, we present a concise and efficient image-based semantic segmentation network, named CENet. In order to improve the descriptive power of learned features and reduce the computational as well as time complexity, our CENet integrates the convolution with larger kernel size instead of MLP, carefully-selected activation functions, and multiple auxiliary segmentation heads with corresponding loss functions into architecture. Quantitative and qualitative experiments conducted on publicly available benchmarks, SemanticKITTI and SemanticPOSS, demonstrate that our pipeline achieves much better mIoU and inference performance compared with state-of-the-art models. The code will be available at https://github.com/huixiancheng/CENet.

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.

A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that such techniques are not able to reliably identify OOD samples in a classification setting, since their level of confidence is generalized to unseen areas of the feature space. This result stems from the interplay between the representation of ReLU networks as piece-wise affine transformations, the saturating nature of activation functions like softmax, and the most widely-used uncertainty metrics.

This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection of reachability algorithms that make use of a variety of set representations, such as polyhedra, star sets, zonotopes, and abstract-domain representations. NNV supports both exact (sound and complete) and over-approximate (sound) reachability algorithms for verifying safety and robustness properties of feed-forward neural networks (FFNNs) with various activation functions. For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers with piecewise-linear activation functions, such as ReLUs. For similar neural network control systems (NNCS) that instead have nonlinear plant models, NNV supports over-approximate analysis by combining the star set analysis used for FFNN controllers with zonotope-based analysis for nonlinear plant dynamics building on CORA. We evaluate NNV using two real-world case studies: the first is safety verification of ACAS Xu networks and the second deals with the safety verification of a deep learning-based adaptive cruise control system.

We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under different number of layers, neurons per layer, and various different activation functions in order to find which combinations work better empirically. For training, we consider various different loss functions and optimization routines. We demonstrate that deep neural networks exponentially expedite option pricing compared to commonly used option pricing methods which consequently make calibration and parameter estimation super fast.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

Gastrointestinal (GI) diseases represent a significant global health concern, with Capsule Endoscopy (CE) offering a non-invasive method for diagnosis by capturing a large number of GI tract images. However, the sheer volume of video frames necessitates automated analysis to reduce the workload on doctors and increase the diagnostic accuracy. In this paper, we present CapsuleNet, a deep learning model developed for the Capsule Vision 2024 Challenge, aimed at classifying 10 distinct GI abnormalities. Using a highly imbalanced dataset, we implemented various data augmentation strategies, reducing the data imbalance to a manageable level. Our model leverages a pretrained EfficientNet-b7 backbone, tuned with additional layers for classification and optimized with PReLU activation functions. The model demonstrated superior performance on validation data, achieving a micro accuracy of 84.5% and outperforming the VGG16 baseline across most classes. Despite these advances, challenges remain in classifying certain abnormalities, such as Erythema. Our findings suggest that CNN-based models like CapsuleNet can provide an efficient solution for GI tract disease classification, particularly when inference time is a critical factor.

Graph transformers (GTs) have emerged as a promising architecture that is theoretically more expressive than message-passing graph neural networks (GNNs). However, typical GT models have at least quadratic complexity and thus cannot scale to large graphs. While there are several linear GTs recently proposed, they still lag behind GNN counterparts on several popular graph datasets, which poses a critical concern on their practical expressivity. To balance the trade-off between expressivity and scalability of GTs, we propose Polynormer, a polynomial-expressive GT model with linear complexity. Polynormer is built upon a novel base model that learns a high-degree polynomial on input features. To enable the base model permutation equivariant, we integrate it with graph topology and node features separately, resulting in local and global equivariant attention models. Consequently, Polynormer adopts a linear local-to-global attention scheme to learn high-degree equivariant polynomials whose coefficients are controlled by attention scores. Polynormer has been evaluated on 13 homophilic and heterophilic datasets, including large graphs with millions of nodes. Our extensive experiment results show that Polynormer outperforms state-of-the-art GNN and GT baselines on most datasets, even without the use of nonlinear activation functions.

We define the bicategory of Graph Convolutional Neural Networks GCNN_n for an arbitrary graph with n nodes. We show it can be factored through the already existing categorical constructions for deep learning called Para and Lens with the base category set to the CoKleisli category of the product comonad. We prove that there exists an injective-on-objects, faithful 2-functor GCNN_n to Para(CoKl(R^{n times n} times -)). We show that this construction allows us to treat the adjacency matrix of a GCNN as a global parameter instead of a a local, layer-wise one. This gives us a high-level categorical characterisation of a particular kind of inductive bias GCNNs possess. Lastly, we hypothesize about possible generalisations of GCNNs to general message-passing graph neural networks, connections to equivariant learning, and the (lack of) functoriality of activation functions.

Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for interpreting neural networks by analysing their weights and neuron structures. However, classic works adapt CNT metrics that only permit a topological analysis as they do not account for the effect of the input data. In addition, CNT metrics have been applied to a limited range of architectures, mainly including Fully Connected neural networks. In this work, we extend the existing CNT metrics with measures that sample from the DNNs' training distribution, shifting from a purely topological analysis to one that connects with the interpretability of deep learning. For the novel metrics, in addition to the existing ones, we provide a mathematical formalisation for Fully Connected, AutoEncoder, Convolutional and Recurrent neural networks, of which we vary the activation functions and the number of hidden layers. We show that these metrics differentiate DNNs based on the architecture, the number of hidden layers, and the activation function. Our contribution provides a method rooted in physics for interpreting DNNs that offers insights beyond the traditional input-output relationship and the CNT topological analysis.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

The Conformer has become the most popular encoder model for automatic speech recognition (ASR). It adds convolution modules to a transformer to learn both local and global dependencies. In this work we describe a faster, more memory-efficient, and better-performing transformer, called Zipformer. Modeling changes include: 1) a U-Net-like encoder structure where middle stacks operate at lower frame rates; 2) reorganized block structure with more modules, within which we re-use attention weights for efficiency; 3) a modified form of LayerNorm called BiasNorm allows us to retain some length information; 4) new activation functions SwooshR and SwooshL work better than Swish. We also propose a new optimizer, called ScaledAdam, which scales the update by each tensor's current scale to keep the relative change about the same, and also explictly learns the parameter scale. It achieves faster convergence and better performance than Adam. Extensive experiments on LibriSpeech, Aishell-1, and WenetSpeech datasets demonstrate the effectiveness of our proposed Zipformer over other state-of-the-art ASR models. Our code is publicly available at https://github.com/k2-fsa/icefall.

Transformers are central to recent successes in natural language processing and computer vision. Transformers have a mostly uniform backbone where layers alternate between feed-forward and self-attention in order to build a deep network. Here we investigate this design choice and find that more complex blocks that have different permutations of layer primitives can be more efficient. Using this insight, we develop a complex block, named Brainformer, that consists of a diverse sets of layers such as sparsely gated feed-forward layers, dense feed-forward layers, attention layers, and various forms of layer normalization and activation functions. Brainformer consistently outperforms the state-of-the-art dense and sparse Transformers, in terms of both quality and efficiency. A Brainformer model with 8 billion activated parameters per token demonstrates 2x faster training convergence and 5x faster step time compared to its GLaM counterpart. In downstream task evaluation, Brainformer also demonstrates a 3% higher SuperGLUE score with fine-tuning compared to GLaM with a similar number of activated parameters. Finally, Brainformer largely outperforms a Primer dense model derived with NAS with similar computation per token on fewshot evaluations.

Out-of-distribution (OOD) detection is critical to building reliable machine learning systems in the open world. Researchers have proposed various strategies to reduce model overconfidence on OOD data. Among them, ReAct is a typical and effective technique to deal with model overconfidence, which truncates high activations to increase the gap between in-distribution and OOD. Despite its promising results, is this technique the best choice for widening the gap? To answer this question, we leverage the variational method to find the optimal operation and verify the necessity of suppressing abnormally low and high activations and amplifying intermediate activations in OOD detection, rather than focusing only on high activations like ReAct. This motivates us to propose a novel technique called ``Variational Rectified Activation (VRA)'', which simulates these suppression and amplification operations using piecewise functions. Experimental results on multiple benchmark datasets demonstrate that our method outperforms existing post-hoc strategies. Meanwhile, VRA is compatible with different scoring functions and network architectures. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.

Transformer architecture currently represents the main driver behind many successes in a variety of tasks addressed by deep learning, especially the recent advances in natural language processing (NLP) culminating with large language models (LLM). In addition, transformer architecture has found a wide spread of interest from computer vision (CV) researchers and practitioners, allowing for many advancements in vision-related tasks and opening the door for multi-task and multi-modal deep learning architectures that share the same principle of operation. One drawback to these architectures is their reliance on the scaled dot product attention mechanism with the softmax activation function, which is computationally expensive and requires large compute capabilities both for training and inference. This paper investigates substituting the attention mechanism usually adopted for transformer architecture with an architecture incorporating gated linear unit (GLU) activation within a multi-layer perceptron (MLP) structure in conjunction with the default MLP incorporated in the traditional transformer design. Another step forward taken by this paper is to eliminate the second non-gated MLP to further reduce the computational cost. Experimental assessments conducted by this research show that both proposed modifications and reductions offer competitive performance in relation to baseline architectures, in support of the aims of this work in establishing a more efficient yet capable alternative to the traditional attention mechanism as the core component in designing transformer architectures.

SWIN transformer is a prominent vision transformer model that has state-of-the-art accuracy in image classification tasks. Despite this success, its unique architecture causes slower inference compared with similar deep neural networks. Integer quantization of the model is one of the methods used to improve its inference latency. However, state-of-the-art has not been able to fully quantize the model. In this work, we improve upon the inference latency of the state-of-the-art methods by removing the floating-point operations, which are associated with the GELU activation in Swin Transformer. While previous work proposed to replace the non-integer operations with linear approximation functions, we propose to replace GELU with ReLU activation. The advantage of ReLU over previous methods is its low memory and computation complexity. We use iterative knowledge distillation to compensate for the lost accuracy due to replacing GELU with ReLU. We quantize our GELU-less SWIN transformer and show that on an RTX 4090 NVIDIA GPU we can improve the inference latency of the quantized SWIN transformer by at least 11% while maintaining an accuracy drop of under 0.5% on the ImageNet evaluation dataset.

Previous literature offers limited clues on how to learn a periodic function using modern neural networks. We start with a study of the extrapolation properties of neural networks; we prove and demonstrate experimentally that the standard activations functions, such as ReLU, tanh, sigmoid, along with their variants, all fail to learn to extrapolate simple periodic functions. We hypothesize that this is due to their lack of a "periodic" inductive bias. As a fix of this problem, we propose a new activation, namely, x + sin^2(x), which achieves the desired periodic inductive bias to learn a periodic function while maintaining a favorable optimization property of the ReLU-based activations. Experimentally, we apply the proposed method to temperature and financial data prediction.

Printed Electronics (PE) feature distinct and remarkable characteristics that make them a prominent technology for achieving true ubiquitous computing. This is particularly relevant in application domains that require conformal and ultra-low cost solutions, which have experienced limited penetration of computing until now. Unlike silicon-based technologies, PE offer unparalleled features such as non-recurring engineering costs, ultra-low manufacturing cost, and on-demand fabrication of conformal, flexible, non-toxic, and stretchable hardware. However, PE face certain limitations due to their large feature sizes, that impede the realization of complex circuits, such as machine learning classifiers. In this work, we address these limitations by leveraging the principles of Approximate Computing and Bespoke (fully-customized) design. We propose an automated framework for designing ultra-low power Multilayer Perceptron (MLP) classifiers which employs, for the first time, a holistic approach to approximate all functions of the MLP's neurons: multiplication, accumulation, and activation. Through comprehensive evaluation across various MLPs of varying size, our framework demonstrates the ability to enable battery-powered operation of even the most intricate MLP architecture examined, significantly surpassing the current state of the art.

Recent works on neural network pruning advocate that reducing the depth of the network is more effective in reducing run-time memory usage and accelerating inference latency than reducing the width of the network through channel pruning. In this regard, some recent works propose depth compression algorithms that merge convolution layers. However, the existing algorithms have a constricted search space and rely on human-engineered heuristics. In this paper, we propose a novel depth compression algorithm which targets general convolution operations. We propose a subset selection problem that replaces inefficient activation layers with identity functions and optimally merges consecutive convolution operations into shallow equivalent convolution operations for efficient end-to-end inference latency. Since the proposed subset selection problem is NP-hard, we formulate a surrogate optimization problem that can be solved exactly via two-stage dynamic programming within a few seconds. We evaluate our methods and baselines by TensorRT for a fair inference latency comparison. Our method outperforms the baseline method with higher accuracy and faster inference speed in MobileNetV2 on the ImageNet dataset. Specifically, we achieve 1.41times speed-up with 0.11\%p accuracy gain in MobileNetV2-1.0 on the ImageNet.

In this paper, we propose a post-training quantization framework of large vision-language models (LVLMs) for efficient multi-modal inference. Conventional quantization methods sequentially search the layer-wise rounding functions by minimizing activation discretization errors, which fails to acquire optimal quantization strategy without considering cross-layer dependency. On the contrary, we mine the cross-layer dependency that significantly influences discretization errors of the entire vision-language model, and embed this dependency into optimal quantization strategy searching with low search cost. Specifically, we observe the strong correlation between the activation entropy and the cross-layer dependency concerning output discretization errors. Therefore, we employ the entropy as the proxy to partition blocks optimally, which aims to achieve satisfying trade-offs between discretization errors and the search cost. Moreover, we optimize the visual encoder to disentangle the cross-layer dependency for fine-grained decomposition of search space, so that the search cost is further reduced without harming the quantization accuracy. Experimental results demonstrate that our method compresses the memory by 2.78x and increase generate speed by 1.44x about 13B LLaVA model without performance degradation on diverse multi-modal reasoning tasks. Code is available at https://github.com/ChangyuanWang17/QVLM.

In this work, we present a novel physics-based data-driven framework for reduced-order modeling of laser ignition in a model rocket combustor based on parameterized neural ordinary differential equations (PNODE). Deep neural networks are embedded as functions of high-dimensional parameters of laser ignition to predict various terms in a 0D flow model including the heat source function, pre-exponential factors, and activation energy. Using the governing equations of a 0D flow model, our PNODE needs only a limited number of training samples and predicts trajectories of various quantities such as temperature, pressure, and mass fractions of species while satisfying physical constraints. We validate our physics-based PNODE on solution snapshots of high-fidelity Computational Fluid Dynamics (CFD) simulations of laser-induced ignition in a prototype rocket combustor. We compare the performance of our physics-based PNODE with that of kernel ridge regression and fully connected neural networks. Our results show that our physics-based PNODE provides solutions with lower mean absolute errors of average temperature over time, thus improving the prediction of successful laser ignition with high-dimensional parameters.

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 have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This innovation has led to the creation of a new class of neural networks, which we call (Comple)XNet, or simply XNet. We will demonstrate that XNet is particularly effective for high-dimensional challenges such as image classification and solving Partial Differential Equations (PDEs). Our evaluations show that XNet significantly outperforms established benchmarks like MNIST and CIFAR-10 in computer vision, and offers substantial advantages over Physics-Informed Neural Networks (PINNs) in both low-dimensional and high-dimensional PDE scenarios.

The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward propagation and the exponential vanishing/exploding of gradients during back-propagation. Understanding the theoretical properties of untrained random networks is key to identifying which deep networks may be trained successfully as recently demonstrated by Samuel et al (2017) who showed that for deep feedforward neural networks only a specific choice of hyperparameters known as the `Edge of Chaos' can lead to good performance. While the work by Samuel et al (2017) discuss trainability issues, we focus here on training acceleration and overall performance. We give a comprehensive theoretical analysis of the Edge of Chaos and show that we can indeed tune the initialization parameters and the activation function in order to accelerate the training and improve the performance.

For many segmentation tasks, especially for the biomedical image, the topological prior is vital information which is useful to exploit. The containment/nesting is a typical inter-class geometric relationship. In the MICCAI Brain tumor segmentation challenge, with its three hierarchically nested classes 'whole tumor', 'tumor core', 'active tumor', the nested classes relationship is introduced into the 3D-residual-Unet architecture. The network comprises a context aggregation pathway and a localization pathway, which encodes increasingly abstract representation of the input as going deeper into the network, and then recombines these representations with shallower features to precisely localize the interest domain via a localization path. The nested-class-prior is combined by proposing the multi-class activation function and its corresponding loss function. The model is trained on the training dataset of Brats2018, and 20% of the dataset is regarded as the validation dataset to determine parameters. When the parameters are fixed, we retrain the model on the whole training dataset. The performance achieved on the validation leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing tumor and tumor core classes without relying on ensembles or complicated post-processing steps. Based on the same start-of-the-art network architecture, the accuracy of nested-class (enhancing tumor) is reasonably improved from 69% to 72% compared with the traditional Softmax-based method which blind to topological prior.

In practice, deeper networks tend to be more powerful than shallow ones, but this has not been understood theoretically. In this paper, we find the analytical solution of a three-layer network with a matrix exponential activation function, i.e., $ f(X)=W_3exp(W_2exp(W_1X)), Xin C^{dtimes d} have analytical solutions for the equations Y_1=f(X_1),Y_2=f(X_2) for X_1,X_2,Y_1,Y_2 with only invertible assumptions. Our proof shows the power of depth and the use of a non-linear activation function, since one layer network can only solve one equation,i.e.,Y=WX$.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network pruning, we find that the sparsity introduced by ReLU, which we quantify by a term called dynamic dead neuron rate (DNR), is not beneficial for the pruned network. Interestingly, the more the network is pruned, the smaller the dynamic DNR becomes during optimization. This motivates us to propose a method to explicitly reduce the dynamic DNR for the pruned network, i.e., de-sparsify the network. We refer to our method as Activating-while-Pruning (AP). We note that AP does not function as a stand-alone method, as it does not evaluate the importance of weights. Instead, it works in tandem with existing pruning methods and aims to improve their performance by selective activation of nodes to reduce the dynamic DNR. We conduct extensive experiments using popular networks (e.g., ResNet, VGG) via two classical and three state-of-the-art pruning methods. The experimental results on public datasets (e.g., CIFAR-10/100) suggest that AP works well with existing pruning methods and improves the performance by 3% - 4%. For larger scale datasets (e.g., ImageNet) and state-of-the-art networks (e.g., vision transformer), we observe an improvement of 2% - 3% with AP as opposed to without. Lastly, we conduct an ablation study to examine the effectiveness of the components comprising AP.

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

Implicit Neural Representation (INR), leveraging a neural network to transform coordinate input into corresponding attributes, has recently driven significant advances in several vision-related domains. However, the performance of INR is heavily influenced by the choice of the nonlinear activation function used in its multilayer perceptron (MLP) architecture. Multiple nonlinearities have been investigated; yet, current INRs face limitations in capturing high-frequency components, diverse signal types, and handling inverse problems. We have identified that these problems can be greatly alleviated by introducing a paradigm shift in INRs. We find that an architecture with learnable activations in initial layers can represent fine details in the underlying signals. Specifically, we propose SL^{2}A-INR, a hybrid network for INR with a single-layer learnable activation function, prompting the effectiveness of traditional ReLU-based MLPs. Our method performs superior across diverse tasks, including image representation, 3D shape reconstructions, inpainting, single image super-resolution, CT reconstruction, and novel view synthesis. Through comprehensive experiments, SL^{2}A-INR sets new benchmarks in accuracy, quality, and convergence rates for INR.

The recent trend of large language models (LLMs) is to increase the scale of both model size (\aka the number of parameters) and dataset to achieve better generative ability, which is definitely proved by a lot of work such as the famous GPT and Llama. However, large models often involve massive computational costs, and practical applications cannot afford such high prices. However, the method of constructing a strong model architecture for LLMs is rarely discussed. We first analyze the state-of-the-art language model architectures and observe the feature collapse problem. Based on the theoretical analysis, we propose that the nonlinearity is also very important for language models, which is usually studied in convolutional neural networks for vision tasks. The series informed activation function is then introduced with tiny calculations that can be ignored, and an augmented shortcut is further used to enhance the model nonlinearity. We then demonstrate that the proposed approach is significantly effective for enhancing the model nonlinearity through carefully designed ablations; thus, we present a new efficient model architecture for establishing modern, namely, PanGu-pi. Experiments are then conducted using the same dataset and training strategy to compare PanGu-pi with state-of-the-art LLMs. The results show that PanGu-pi-7B can achieve a comparable performance to that of benchmarks with about 10\% inference speed-up, and PanGu-pi-1B can achieve state-of-the-art performance in terms of accuracy and efficiency. In addition, we have deployed PanGu-pi-7B in the high-value domains of finance and law, developing an LLM named YunShan for practical application. The results show that YunShan can surpass other models with similar scales on benchmarks.

Despite recent progress in generative adversarial network (GAN)-based vocoders, where the model generates raw waveform conditioned on acoustic features, it is challenging to synthesize high-fidelity audio for numerous speakers across various recording environments. In this work, we present BigVGAN, a universal vocoder that generalizes well for various out-of-distribution scenarios without fine-tuning. We introduce periodic activation function and anti-aliased representation into the GAN generator, which brings the desired inductive bias for audio synthesis and significantly improves audio quality. In addition, we train our GAN vocoder at the largest scale up to 112M parameters, which is unprecedented in the literature. We identify and address the failure modes in large-scale GAN training for audio, while maintaining high-fidelity output without over-regularization. Our BigVGAN, trained only on clean speech (LibriTTS), achieves the state-of-the-art performance for various zero-shot (out-of-distribution) conditions, including unseen speakers, languages, recording environments, singing voices, music, and instrumental audio. We release our code and model at: https://github.com/NVIDIA/BigVGAN

We propose the Gaussian Error Linear Unit (GELU), a high-performing neural network activation function. The GELU activation function is xPhi(x), where Phi(x) the standard Gaussian cumulative distribution function. The GELU nonlinearity weights inputs by their value, rather than gates inputs by their sign as in ReLUs (x1_{x>0}). We perform an empirical evaluation of the GELU nonlinearity against the ReLU and ELU activations and find performance improvements across all considered computer vision, natural language processing, and speech tasks.

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as O(1/log(n)), where n denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates.

Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.

Despite achieving state-of-the-art results in nearly all Natural Language Processing applications, fine-tuning Transformer-based language models still requires a significant amount of labeled data to work. A well known technique to reduce the amount of human effort in acquiring a labeled dataset is Active Learning (AL): an iterative process in which only the minimal amount of samples is labeled. AL strategies require access to a quantified confidence measure of the model predictions. A common choice is the softmax activation function for the final layer. As the softmax function provides misleading probabilities, this paper compares eight alternatives on seven datasets. Our almost paradoxical finding is that most of the methods are too good at identifying the true most uncertain samples (outliers), and that labeling therefore exclusively outliers results in worse performance. As a heuristic we propose to systematically ignore samples, which results in improvements of various methods compared to the softmax function.

We propose a general method for measuring complex variables on a continuous, interval spectrum by combining supervised deep learning with the Constructing Measures approach to faceted Rasch item response theory (IRT). We decompose the target construct, hate speech in our case, into multiple constituent components that are labeled as ordinal survey items. Those survey responses are transformed via IRT into a debiased, continuous outcome measure. Our method estimates the survey interpretation bias of the human labelers and eliminates that influence on the generated continuous measure. We further estimate the response quality of each labeler using faceted IRT, allowing responses from low-quality labelers to be removed. Our faceted Rasch scaling procedure integrates naturally with a multitask deep learning architecture for automated prediction on new data. The ratings on the theorized components of the target outcome are used as supervised, ordinal variables for the neural networks' internal concept learning. We test the use of an activation function (ordinal softmax) and loss function (ordinal cross-entropy) designed to exploit the structure of ordinal outcome variables. Our multitask architecture leads to a new form of model interpretation because each continuous prediction can be directly explained by the constituent components in the penultimate layer. We demonstrate this new method on a dataset of 50,000 social media comments sourced from YouTube, Twitter, and Reddit and labeled by 11,000 U.S.-based Amazon Mechanical Turk workers to measure a continuous spectrum from hate speech to counterspeech. We evaluate Universal Sentence Encoders, BERT, and RoBERTa as language representation models for the comment text, and compare our predictive accuracy to Google Jigsaw's Perspective API models, showing significant improvement over this standard benchmark.

Large Language Models (LLMs) have dramatically advanced AI applications, yet their deployment remains challenging due to their immense inference costs. Recent studies ameliorate the computational costs of LLMs by increasing their activation sparsity but suffer from significant performance degradation on downstream tasks. In this work, we introduce a new framework for sparsifying the activations of base LLMs and reducing inference costs, dubbed Contextually Aware Thresholding for Sparsity (CATS). CATS is relatively simple, easy to implement, and highly effective. At the heart of our framework is a new non-linear activation function. We demonstrate that CATS can be applied to various base models, including Mistral-7B and Llama2-7B, and outperforms existing sparsification techniques in downstream task performance. More precisely, CATS-based models often achieve downstream task performance within 1-2% of their base models without any fine-tuning and even at activation sparsity levels of 50%. Furthermore, CATS-based models converge faster and display better task performance than competing techniques when fine-tuning is applied. Finally, we develop a custom GPU kernel for efficient implementation of CATS that translates the activation of sparsity of CATS to real wall-clock time speedups. Our custom kernel implementation of CATS results in a ~15% improvement in wall-clock inference latency of token generation on both Llama-7B and Mistral-7B.

We propose a novel deep network structure called "Network In Network" (NIN) to enhance model discriminability for local patches within the receptive field. The conventional convolutional layer uses linear filters followed by a nonlinear activation function to scan the input. Instead, we build micro neural networks with more complex structures to abstract the data within the receptive field. We instantiate the micro neural network with a multilayer perceptron, which is a potent function approximator. The feature maps are obtained by sliding the micro networks over the input in a similar manner as CNN; they are then fed into the next layer. Deep NIN can be implemented by stacking mutiple of the above described structure. With enhanced local modeling via the micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is easier to interpret and less prone to overfitting than traditional fully connected layers. We demonstrated the state-of-the-art classification performances with NIN on CIFAR-10 and CIFAR-100, and reasonable performances on SVHN and MNIST datasets.

Large language models have achieved remarkable success in recent years, primarily due to the implementation of self-attention mechanisms. However, traditional Softmax attention suffers from numerical instability and reduced performance as the length of inference tokens increases. This paper addresses these issues by decomposing the Softmax operation into a non-linear transformation and the l_1-norm. We identify the latter as essential for maintaining model performance. By replacing the non-linear transformation with the Softplus activation function and introducing a dynamic scale factor for different token lengths based on invariance entropy, we create a novel attention mechanism with performance better than conventional Softmax attention across various inference lengths. To further improve the length extrapolation ability of the proposed attention mechanism, we introduce a fine-tuning-free re-weighting mechanism that amplifies significant attention weights while diminishing weaker ones, enabling the model to concentrate more effectively on relevant tokens without requiring retraining. When combined with our proposed attention mechanism, this approach demonstrates significant promise in managing longer sequences, maintaining nearly constant validation loss even at 16times the training token length while ensuring numerical stability. Our code is available at: https://github.com/iminfine/freeatten.

Sparse autoencoders (SAEs) are a promising approach to extracting features from neural networks, enabling model interpretability as well as causal interventions on model internals. SAEs generate sparse feature representations using a sparsifying activation function that implicitly defines a set of token-feature matches. We frame the token-feature matching as a resource allocation problem constrained by a total sparsity upper bound. For example, TopK SAEs solve this allocation problem with the additional constraint that each token matches with at most k features. In TopK SAEs, the k active features per token constraint is the same across tokens, despite some tokens being more difficult to reconstruct than others. To address this limitation, we propose two novel SAE variants, Feature Choice SAEs and Mutual Choice SAEs, which each allow for a variable number of active features per token. Feature Choice SAEs solve the sparsity allocation problem under the additional constraint that each feature matches with at most m tokens. Mutual Choice SAEs solve the unrestricted allocation problem where the total sparsity budget can be allocated freely between tokens and features. Additionally, we introduce a new auxiliary loss function, aux_zipf_loss, which generalises the aux_k_loss to mitigate dead and underutilised features. Our methods result in SAEs with fewer dead features and improved reconstruction loss at equivalent sparsity levels as a result of the inherent adaptive computation. More accurate and scalable feature extraction methods provide a path towards better understanding and more precise control of foundation models.

We train, for the first time, large language models using FP8 precision on datasets up to 2 trillion tokens -- a 20-fold increase over previous limits. Through these extended training runs, we uncover critical instabilities in FP8 training that were not observable in earlier works with shorter durations. We trace these instabilities to outlier amplification by the SwiGLU activation function. Interestingly, we show, both analytically and empirically, that this amplification happens only over prolonged training periods, and link it to a SwiGLU weight alignment process. To address this newly identified issue, we introduce Smooth-SwiGLU, a novel modification that ensures stable FP8 training without altering function behavior. We also demonstrate, for the first time, FP8 quantization of both Adam optimizer moments. Combining these innovations, we successfully train a 7B parameter model using FP8 precision on 256 Intel Gaudi2 accelerators, achieving on-par results with the BF16 baseline while delivering up to a sim 34 % throughput improvement.

In class incremental learning, neural networks typically suffer from catastrophic forgetting. We show that an MLP featuring a sparse activation function and an adaptive learning rate optimizer can compete with established regularization techniques in the Split-MNIST task. We highlight the effectiveness of the Adaptive SwisH (ASH) activation function in this context and introduce a novel variant, Hard Adaptive SwisH (Hard ASH) to further enhance the learning retention.

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or L^p function with the widths d_x+d_y+2 and max{d_x+1,d_y}, respectively, where the target function maps a finite sequence of vectors in R^{d_x} to a finite sequence of vectors in R^{d_y}. We also compute the additional width required if the activation function is tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

Text-to-3D generation, which aims to synthesize vivid 3D objects from text prompts, has attracted much attention from the computer vision community. While several existing works have achieved impressive results for this task, they mainly rely on a time-consuming optimization paradigm. Specifically, these methods optimize a neural field from scratch for each text prompt, taking approximately one hour or more to generate one object. This heavy and repetitive training cost impedes their practical deployment. In this paper, we propose a novel framework for fast text-to-3D generation, dubbed Instant3D. Once trained, Instant3D is able to create a 3D object for an unseen text prompt in less than one second with a single run of a feedforward network. We achieve this remarkable speed by devising a new network that directly constructs a 3D triplane from a text prompt. The core innovation of our Instant3D lies in our exploration of strategies to effectively inject text conditions into the network. Furthermore, we propose a simple yet effective activation function, the scaled-sigmoid, to replace the original sigmoid function, which speeds up the training convergence by more than ten times. Finally, to address the Janus (multi-head) problem in 3D generation, we propose an adaptive Perp-Neg algorithm that can dynamically adjust its concept negation scales according to the severity of the Janus problem during training, effectively reducing the multi-head effect. Extensive experiments on a wide variety of benchmark datasets demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods both qualitatively and quantitatively, while achieving significantly better efficiency. The project page is at https://ming1993li.github.io/Instant3DProj.

Most of the dominant approaches to continual learning are based on either memory replay, parameter isolation, or regularization techniques that require task boundaries to calculate task statistics. We propose a static architecture-based method that doesn't use any of these. We show that we can improve the continual learning performance by replacing the final layer of our networks with our pairwise interaction layer. The pairwise interaction layer uses sparse representations from a Winner-take-all style activation function to find the relevant correlations in the hidden layer representations. The networks using this architecture show competitive performance in MNIST and FashionMNIST-based continual image classification experiments. We demonstrate this in an online streaming continual learning setup where the learning system cannot access task labels or boundaries.

Convolutional neural networks (CNN) are built upon the classical McCulloch-Pitts neuron model, which is essentially a linear model, where the nonlinearity is provided by a separate activation function. Several researchers have proposed enhanced neuron models, including quadratic neurons, generalized operational neurons, generative neurons, and super neurons, with stronger nonlinearity than that provided by the pointwise activation function. There has also been a proposal to use Pade approximation as a generalized activation function. In this paper, we introduce a brand new neuron model called Pade neurons (Paons), inspired by the Pade approximants, which is the best mathematical approximation of a transcendental function as a ratio of polynomials with different orders. We show that Paons are a super set of all other proposed neuron models. Hence, the basic neuron in any known CNN model can be replaced by Paons. In this paper, we extend the well-known ResNet to PadeNet (built by Paons) to demonstrate the concept. Our experiments on the single-image super-resolution task show that PadeNets can obtain better results than competing architectures.

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.

We introduce the use of rectified linear units (ReLU) as the classification function in a deep neural network (DNN). Conventionally, ReLU is used as an activation function in DNNs, with Softmax function as their classification function. However, there have been several studies on using a classification function other than Softmax, and this study is an addition to those. We accomplish this by taking the activation of the penultimate layer h_{n - 1} in a neural network, then multiply it by weight parameters theta to get the raw scores o_{i}. Afterwards, we threshold the raw scores o_{i} by 0, i.e. f(o) = max(0, o_{i}), where f(o) is the ReLU function. We provide class predictions y through argmax function, i.e. argmax f(x).

Advanced diffusion models (DMs) perform impressively in image super-resolution (SR), but the high memory and computational costs hinder their deployment. Binarization, an ultra-compression algorithm, offers the potential for effectively accelerating DMs. Nonetheless, due to the model structure and the multi-step iterative attribute of DMs, existing binarization methods result in significant performance degradation. In this paper, we introduce a novel binarized diffusion model, BI-DiffSR, for image SR. First, for the model structure, we design a UNet architecture optimized for binarization. We propose the consistent-pixel-downsample (CP-Down) and consistent-pixel-upsample (CP-Up) to maintain dimension consistent and facilitate the full-precision information transfer. Meanwhile, we design the channel-shuffle-fusion (CS-Fusion) to enhance feature fusion in skip connection. Second, for the activation difference across timestep, we design the timestep-aware redistribution (TaR) and activation function (TaA). The TaR and TaA dynamically adjust the distribution of activations based on different timesteps, improving the flexibility and representation alability of the binarized module. Comprehensive experiments demonstrate that our BI-DiffSR outperforms existing binarization methods. Code is released at: https://github.com/zhengchen1999/BI-DiffSR.

In this paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

This paper does not introduce a novel method. Instead, it offers a fairer and more comprehensive comparison of KAN and MLP models across various tasks, including machine learning, computer vision, audio processing, natural language processing, and symbolic formula representation. Specifically, we control the number of parameters and FLOPs to compare the performance of KAN and MLP. Our main observation is that, except for symbolic formula representation tasks, MLP generally outperforms KAN. We also conduct ablation studies on KAN and find that its advantage in symbolic formula representation mainly stems from its B-spline activation function. When B-spline is applied to MLP, performance in symbolic formula representation significantly improves, surpassing or matching that of KAN. However, in other tasks where MLP already excels over KAN, B-spline does not substantially enhance MLP's performance. Furthermore, we find that KAN's forgetting issue is more severe than that of MLP in a standard class-incremental continual learning setting, which differs from the findings reported in the KAN paper. We hope these results provide insights for future research on KAN and other MLP alternatives. Project link: https://github.com/yu-rp/KANbeFair

Sparse autoencoders (SAEs) are a promising unsupervised approach for identifying causally relevant and interpretable linear features in a language model's (LM) activations. To be useful for downstream tasks, SAEs need to decompose LM activations faithfully; yet to be interpretable the decomposition must be sparse -- two objectives that are in tension. In this paper, we introduce JumpReLU SAEs, which achieve state-of-the-art reconstruction fidelity at a given sparsity level on Gemma 2 9B activations, compared to other recent advances such as Gated and TopK SAEs. We also show that this improvement does not come at the cost of interpretability through manual and automated interpretability studies. JumpReLU SAEs are a simple modification of vanilla (ReLU) SAEs -- where we replace the ReLU with a discontinuous JumpReLU activation function -- and are similarly efficient to train and run. By utilising straight-through-estimators (STEs) in a principled manner, we show how it is possible to train JumpReLU SAEs effectively despite the discontinuous JumpReLU function introduced in the SAE's forward pass. Similarly, we use STEs to directly train L0 to be sparse, instead of training on proxies such as L1, avoiding problems like shrinkage.

Sparse autoencoders (SAEs) are a useful tool for uncovering human-interpretable features in the activations of large language models (LLMs). While some expect SAEs to find the true underlying features used by a model, our research shows that SAEs trained on the same model and data, differing only in the random seed used to initialize their weights, identify different sets of features. For example, in an SAE with 131K latents trained on a feedforward network in Llama 3 8B, only 30% of the features were shared across different seeds. We observed this phenomenon across multiple layers of three different LLMs, two datasets, and several SAE architectures. While ReLU SAEs trained with the L1 sparsity loss showed greater stability across seeds, SAEs using the state-of-the-art TopK activation function were more seed-dependent, even when controlling for the level of sparsity. Our results suggest that the set of features uncovered by an SAE should be viewed as a pragmatically useful decomposition of activation space, rather than an exhaustive and universal list of features "truly used" by the model.

There has been a debate about the superiority between vision Transformers and ConvNets, serving as the backbone of computer vision models. Although they are usually considered as two completely different architectures, in this paper, we interpret vision Transformers as ConvNets with dynamic convolutions, which enables us to characterize existing Transformers and dynamic ConvNets in a unified framework and compare their design choices side by side. In addition, our interpretation can also guide the network design as researchers now can consider vision Transformers from the design space of ConvNets and vice versa. We demonstrate such potential through two specific studies. First, we inspect the role of softmax in vision Transformers as the activation function and find it can be replaced by commonly used ConvNets modules, such as ReLU and Layer Normalization, which results in a faster convergence rate and better performance. Second, following the design of depth-wise convolution, we create a corresponding depth-wise vision Transformer that is more efficient with comparable performance. The potential of the proposed unified interpretation is not limited to the given examples and we hope it can inspire the community and give rise to more advanced network architectures.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as is. We believe that this work provides better understanding of neural networks and paves the way to tackle their black-box nature. We share equivalent trees of some neural networks and show that besides providing interpretability, tree representation can also achieve some computational advantages for small networks. The analysis holds both for fully connected and convolutional networks, which may or may not also include skip connections and/or normalizations.

This paper demonstrates that a single-layer neural network using Parametric Rectified Linear Unit (PReLU) activation can solve the XOR problem, a simple fact that has been overlooked so far. We compare this solution to the multi-layer perceptron (MLP) and the Growing Cosine Unit (GCU) activation function and explain why PReLU enables this capability. Our results show that the single-layer PReLU network can achieve 100\% success rate in a wider range of learning rates while using only three learnable parameters.

Deep encoder-decoder based CNNs have advanced image inpainting methods for hole filling. While existing methods recover structures and textures step-by-step in the hole regions, they typically use two encoder-decoders for separate recovery. The CNN features of each encoder are learned to capture either missing structures or textures without considering them as a whole. The insufficient utilization of these encoder features limit the performance of recovering both structures and textures. In this paper, we propose a mutual encoder-decoder CNN for joint recovery of both. We use CNN features from the deep and shallow layers of the encoder to represent structures and textures of an input image, respectively. The deep layer features are sent to a structure branch and the shallow layer features are sent to a texture branch. In each branch, we fill holes in multiple scales of the CNN features. The filled CNN features from both branches are concatenated and then equalized. During feature equalization, we reweigh channel attentions first and propose a bilateral propagation activation function to enable spatial equalization. To this end, the filled CNN features of structure and texture mutually benefit each other to represent image content at all feature levels. We use the equalized feature to supplement decoder features for output image generation through skip connections. Experiments on the benchmark datasets show the proposed method is effective to recover structures and textures and performs favorably against state-of-the-art approaches.

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

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

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.

Binary Neural Networks (BNNs) have emerged as a promising solution for reducing the memory footprint and compute costs of deep neural networks. BNNs, on the other hand, suffer from information loss because binary activations are limited to only two values, resulting in reduced accuracy. To improve the accuracy, previous studies have attempted to control the distribution of binary activation by manually shifting the threshold of the activation function or making the shift amount trainable. During the process, they usually depended on statistical information computed from a batch. We argue that using statistical data from a batch fails to capture the crucial information for each input instance in BNN computations, and the differences between statistical information computed from each instance need to be considered when determining the binary activation threshold of each instance. Based on the concept, we propose the Binary Neural Network with INSTAnce-aware threshold (INSTA-BNN), which decides the activation threshold value considering the difference between statistical data computed from a batch and each instance. The proposed INSTA-BNN outperforms the baseline by 2.5% and 2.3% on the ImageNet classification task with comparable computing cost, achieving 68.0% and 71.7% top-1 accuracy on ResNet-18 and MobileNetV1 based models, respectively.

Image dehazing is a representative low-level vision task that estimates latent haze-free images from hazy images. In recent years, convolutional neural network-based methods have dominated image dehazing. However, vision Transformers, which has recently made a breakthrough in high-level vision tasks, has not brought new dimensions to image dehazing. We start with the popular Swin Transformer and find that several of its key designs are unsuitable for image dehazing. To this end, we propose DehazeFormer, which consists of various improvements, such as the modified normalization layer, activation function, and spatial information aggregation scheme. We train multiple variants of DehazeFormer on various datasets to demonstrate its effectiveness. Specifically, on the most frequently used SOTS indoor set, our small model outperforms FFA-Net with only 25% #Param and 5% computational cost. To the best of our knowledge, our large model is the first method with the PSNR over 40 dB on the SOTS indoor set, dramatically outperforming the previous state-of-the-art methods. We also collect a large-scale realistic remote sensing dehazing dataset for evaluating the method's capability to remove highly non-homogeneous haze.

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons behind the delayed generalization and its dependence on regularization remain unclear. In this work, we argue that without regularization, grokking tasks push models to the edge of numerical stability, introducing floating point errors in the Softmax function, which we refer to as Softmax Collapse (SC). We demonstrate that SC prevents grokking and that mitigating SC enables grokking without regularization. Investigating the root cause of SC, we find that beyond the point of overfitting, the gradients strongly align with what we call the na\"ive loss minimization (NLM) direction. This component of the gradient does not alter the model's predictions but decreases the loss by scaling the logits, typically by scaling the weights along their current direction. We show that this scaling of the logits explains the delay in generalization characteristic of grokking and eventually leads to SC, halting further learning. To validate our hypotheses, we introduce two key contributions that address the challenges in grokking tasks: StableMax, a new activation function that prevents SC and enables grokking without regularization, and perpGrad, a training algorithm that promotes quick generalization in grokking tasks by preventing NLM altogether. These contributions provide new insights into grokking, elucidating its delayed generalization, reliance on regularization, and the effectiveness of existing grokking-inducing methods. Code for this paper is available at https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability.

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering only activation values and not the effect those activations have on downstream computations. This limits the information available to learn features, and biases the autoencoder towards neglecting features which are represented with small activation values but strongly influence model outputs. To address this, we introduce Gradient SAEs (g-SAEs), which modify the k-sparse autoencoder architecture by augmenting the TopK activation function to rely on the gradients of the input activation when selecting the k elements. For a given sparsity level, g-SAEs produce reconstructions that are more faithful to original network performance when propagated through the network. Additionally, we find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts. By considering the downstream effects of activations, our approach leverages the dual nature of neural network features as both representations, retrospectively, and actions, prospectively. While previous methods have approached the problem of feature discovery primarily focused on the former aspect, g-SAEs represent a step towards accounting for the latter as well.

This study introduces BrainTransformers, an innovative Large Language Model (LLM) implemented using Spiking Neural Networks (SNN). Our key contributions include: (1) designing SNN-compatible Transformer components such as SNNMatmul, SNNSoftmax, and SNNSiLU; (2) implementing an SNN approximation of the SiLU activation function; and (3) developing a Synapsis module to simulate synaptic plasticity. Our 3-billion parameter model, BrainTransformers-3B-Chat, demonstrates competitive performance across various benchmarks, including MMLU (63.2), BBH (54.1), ARC-C (54.3), and GSM8K (76.3), while potentially offering improved energy efficiency and biological plausibility. The model employs a three-stage training approach, including SNN-specific neuronal synaptic plasticity training. This research opens new avenues for brain-like AI systems in natural language processing and neuromorphic computing. Future work will focus on hardware optimization, developing specialized SNN fine-tuning tools, and exploring practical applications in energy-efficient computing environments.

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.

Transformer, composed of self-attention and Feed-Forward Network, has revolutionized the landscape of network design across various vision tasks. FFN is a versatile operator seamlessly integrated into nearly all AI models to effectively harness rich representations. Recent works also show that FFN functions like key-value memories. Thus, akin to the query-key-value mechanism within self-attention, FFN can be viewed as a memory network, where the input serves as query and the two projection weights operate as keys and values, respectively. We hypothesize that the importance lies in query-key-value framework itself rather than in self-attention. To verify this, we propose converting self-attention into a more FFN-like efficient token mixer with only convolutions while retaining query-key-value framework, namely FFNification. Specifically, FFNification replaces query-key and attention coefficient-value interactions with large kernel convolutions and adopts GELU activation function instead of softmax. The derived token mixer, FFNified attention, serves as key-value memories for detecting locally distributed spatial patterns, and operates in the opposite dimension to the ConvNeXt block within each corresponding sub-operation of the query-key-value framework. Building upon the above two modules, we present a family of Fast-Forward Networks. Our FFNet achieves remarkable performance improvements over previous state-of-the-art methods across a wide range of tasks. The strong and general performance of our proposed method validates our hypothesis and leads us to introduce MetaMixer, a general mixer architecture that does not specify sub-operations within the query-key-value framework. We show that using only simple operations like convolution and GELU in the MetaMixer can achieve superior performance.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.

Numerous adversarial attack methods have been developed to generate imperceptible image perturbations that can cause erroneous predictions of state-of-the-art machine learning (ML) models, in particular, deep neural networks (DNNs). Despite intense research on adversarial attacks, little effort was made to uncover 'arcana' carried in adversarial attacks. In this work, we ask whether it is possible to infer data-agnostic victim model (VM) information (i.e., characteristics of the ML model or DNN used to generate adversarial attacks) from data-specific adversarial instances. We call this 'model parsing of adversarial attacks' - a task to uncover 'arcana' in terms of the concealed VM information in attacks. We approach model parsing via supervised learning, which correctly assigns classes of VM's model attributes (in terms of architecture type, kernel size, activation function, and weight sparsity) to an attack instance generated from this VM. We collect a dataset of adversarial attacks across 7 attack types generated from 135 victim models (configured by 5 architecture types, 3 kernel size setups, 3 activation function types, and 3 weight sparsity ratios). We show that a simple, supervised model parsing network (MPN) is able to infer VM attributes from unseen adversarial attacks if their attack settings are consistent with the training setting (i.e., in-distribution generalization assessment). We also provide extensive experiments to justify the feasibility of VM parsing from adversarial attacks, and the influence of training and evaluation factors in the parsing performance (e.g., generalization challenge raised in out-of-distribution evaluation). We further demonstrate how the proposed MPN can be used to uncover the source VM attributes from transfer attacks, and shed light on a potential connection between model parsing and attack transferability.

AnalogVNN, a simulation framework built on PyTorch which can simulate the effects of optoelectronic noise, limited precision, and signal normalization present in photonic neural network accelerators. We use this framework to train and optimize linear and convolutional neural networks with up to 9 layers and ~1.7 million parameters, while gaining insights into how normalization, activation function, reduced precision, and noise influence accuracy in analog photonic neural networks. By following the same layer structure design present in PyTorch, the AnalogVNN framework allows users to convert most digital neural network models to their analog counterparts with just a few lines of code, taking full advantage of the open-source optimization, deep learning, and GPU acceleration libraries available through PyTorch. Code is available at https://analogvnn.github.io

Due to the increased demand for music streaming/recommender services and the recent developments of music information retrieval frameworks, Music Genre Classification (MGC) has attracted the community's attention. However, convolutional-based approaches are known to lack the ability to efficiently encode and localize temporal features. In this paper, we study the broadcast-based neural networks aiming to improve the localization and generalizability under a small set of parameters (about 180k) and investigate twelve variants of broadcast networks discussing the effect of block configuration, pooling method, activation function, normalization mechanism, label smoothing, channel interdependency, LSTM block inclusion, and variants of inception schemes. Our computational experiments using relevant datasets such as GTZAN, Extended Ballroom, HOMBURG, and Free Music Archive (FMA) show state-of-the-art classification accuracies in Music Genre Classification. Our approach offers insights and the potential to enable compact and generalizable broadcast networks for music and audio classification.

In the last few years, deep learning has led to very good performance on a variety of problems, such as visual recognition, speech recognition and natural language processing. Among different types of deep neural networks, convolutional neural networks have been most extensively studied. Leveraging on the rapid growth in the amount of the annotated data and the great improvements in the strengths of graphics processor units, the research on convolutional neural networks has been emerged swiftly and achieved state-of-the-art results on various tasks. In this paper, we provide a broad survey of the recent advances in convolutional neural networks. We detailize the improvements of CNN on different aspects, including layer design, activation function, loss function, regularization, optimization and fast computation. Besides, we also introduce various applications of convolutional neural networks in computer vision, speech and natural language processing.

Several variants of the Long Short-Term Memory (LSTM) architecture for recurrent neural networks have been proposed since its inception in 1995. In recent years, these networks have become the state-of-the-art models for a variety of machine learning problems. This has led to a renewed interest in understanding the role and utility of various computational components of typical LSTM variants. In this paper, we present the first large-scale analysis of eight LSTM variants on three representative tasks: speech recognition, handwriting recognition, and polyphonic music modeling. The hyperparameters of all LSTM variants for each task were optimized separately using random search, and their importance was assessed using the powerful fANOVA framework. In total, we summarize the results of 5400 experimental runs (approx 15 years of CPU time), which makes our study the largest of its kind on LSTM networks. Our results show that none of the variants can improve upon the standard LSTM architecture significantly, and demonstrate the forget gate and the output activation function to be its most critical components. We further observe that the studied hyperparameters are virtually independent and derive guidelines for their efficient adjustment.

Gradients can be employed for sensitivity analysis. Here, we leverage the advantages of the Loss Landscape to comprehend which independent variables impact the dependent variable. We seek to grasp the loss landscape by utilizing first, second, and third derivatives through automatic differentiation. we know that Spearman's rank correlation coefficient can detect the monotonic relationship between two variables. However, I have found that second-order gradients, with certain configurations and parameters, provide information that can be visualized similarly to Spearman results, In this approach, we incorporate a loss function with an activation function, resulting in a non-linear pattern. Each exploration of the loss landscape through retraining yields new valuable information. Furthermore, the first and third derivatives are also beneficial, as they indicate the extent to which independent variables influence the dependent variable.

Deep neural networks (DNNs) have demonstrated state-of-the-art results on many pattern recognition tasks, especially vision classification problems. Understanding the inner workings of such computational brains is both fascinating basic science that is interesting in its own right - similar to why we study the human brain - and will enable researchers to further improve DNNs. One path to understanding how a neural network functions internally is to study what each of its neurons has learned to detect. One such method is called activation maximization (AM), which synthesizes an input (e.g. an image) that highly activates a neuron. Here we dramatically improve the qualitative state of the art of activation maximization by harnessing a powerful, learned prior: a deep generator network (DGN). The algorithm (1) generates qualitatively state-of-the-art synthetic images that look almost real, (2) reveals the features learned by each neuron in an interpretable way, (3) generalizes well to new datasets and somewhat well to different network architectures without requiring the prior to be relearned, and (4) can be considered as a high-quality generative method (in this case, by generating novel, creative, interesting, recognizable images).

A neuroscience method to understanding the brain is to find and study the preferred stimuli that highly activate an individual cell or groups of cells. Recent advances in machine learning enable a family of methods to synthesize preferred stimuli that cause a neuron in an artificial or biological brain to fire strongly. Those methods are known as Activation Maximization (AM) or Feature Visualization via Optimization. In this chapter, we (1) review existing AM techniques in the literature; (2) discuss a probabilistic interpretation for AM; and (3) review the applications of AM in debugging and explaining networks.

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Taken together, our findings suggest that LLMs contain internal abstractions of general-purpose functions that can be invoked in a variety of contexts.

We can better understand deep neural networks by identifying which features each of their neurons have learned to detect. To do so, researchers have created Deep Visualization techniques including activation maximization, which synthetically generates inputs (e.g. images) that maximally activate each neuron. A limitation of current techniques is that they assume each neuron detects only one type of feature, but we know that neurons can be multifaceted, in that they fire in response to many different types of features: for example, a grocery store class neuron must activate either for rows of produce or for a storefront. Previous activation maximization techniques constructed images without regard for the multiple different facets of a neuron, creating inappropriate mixes of colors, parts of objects, scales, orientations, etc. Here, we introduce an algorithm that explicitly uncovers the multiple facets of each neuron by producing a synthetic visualization of each of the types of images that activate a neuron. We also introduce regularization methods that produce state-of-the-art results in terms of the interpretability of images obtained by activation maximization. By separately synthesizing each type of image a neuron fires in response to, the visualizations have more appropriate colors and coherent global structure. Multifaceted feature visualization thus provides a clearer and more comprehensive description of the role of each neuron.

A long standing goal in neuroscience has been to elucidate the functional organization of the brain. Within higher visual cortex, functional accounts have remained relatively coarse, focusing on regions of interest (ROIs) and taking the form of selectivity for broad categories such as faces, places, bodies, food, or words. Because the identification of such ROIs has typically relied on manually assembled stimulus sets consisting of isolated objects in non-ecological contexts, exploring functional organization without robust a priori hypotheses has been challenging. To overcome these limitations, we introduce a data-driven approach in which we synthesize images predicted to activate a given brain region using paired natural images and fMRI recordings, bypassing the need for category-specific stimuli. Our approach -- Brain Diffusion for Visual Exploration ("BrainDiVE") -- builds on recent generative methods by combining large-scale diffusion models with brain-guided image synthesis. Validating our method, we demonstrate the ability to synthesize preferred images with appropriate semantic specificity for well-characterized category-selective ROIs. We then show that BrainDiVE can characterize differences between ROIs selective for the same high-level category. Finally we identify novel functional subdivisions within these ROIs, validated with behavioral data. These results advance our understanding of the fine-grained functional organization of human visual cortex, and provide well-specified constraints for further examination of cortical organization using hypothesis-driven methods.

We explore the effects of various plasticity functions on assemblies of neurons. To bridge the gap between experimental and computational theories we make use of a conceptual framework, the Assembly Calculus, which is a formal system for the description of brain function based on assemblies of neurons. The Assembly Calculus includes operations for projecting, associating, and merging assemblies of neurons. Our research is focused on simulating different plasticity functions with Assembly Calculus. Our main contribution is the modification and evaluation of the projection operation. We experiment with Oja's and Spike Time-Dependent Plasticity (STDP) rules and test the effect of various hyper-parameters.

How neuronal circuits achieve credit assignment remains a central unsolved question in systems neuroscience. Various studies have suggested plausible solutions for back-propagating error signals through multi-layer networks. These purely functionally motivated models assume distinct neuronal compartments to represent local error signals that determine the sign of synaptic plasticity. However, this explicit error modulation is inconsistent with phenomenological plasticity models in which the sign depends primarily on postsynaptic activity. Here we show how a plausible microcircuit model and Hebbian learning rule derived within an adaptive control theory framework can resolve this discrepancy. Assuming errors are encoded in top-down dis-inhibitory synaptic afferents, we show that error-modulated learning emerges naturally at the circuit level when recurrent inhibition explicitly influences Hebbian plasticity. The same learning rule accounts for experimentally observed plasticity in the absence of inhibition and performs comparably to back-propagation of error (BP) on several non-linearly separable benchmarks. Our findings bridge the gap between functional and experimentally observed plasticity rules and make concrete predictions on inhibitory modulation of excitatory plasticity.

The truthfulness of existing explanation methods in authentically elucidating the underlying model's decision-making process has been questioned. Existing methods have deviated from faithfully representing the model, thus susceptible to adversarial attacks. To address this, we propose a novel eXplainable AI (XAI) method called SRD (Sharing Ratio Decomposition), which sincerely reflects the model's inference process, resulting in significantly enhanced robustness in our explanations. Different from the conventional emphasis on the neuronal level, we adopt a vector perspective to consider the intricate nonlinear interactions between filters. We also introduce an interesting observation termed Activation-Pattern-Only Prediction (APOP), letting us emphasize the importance of inactive neurons and redefine relevance encapsulating all relevant information including both active and inactive neurons. Our method, SRD, allows for the recursive decomposition of a Pointwise Feature Vector (PFV), providing a high-resolution Effective Receptive Field (ERF) at any layer.

We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.

The out-of-distribution (OOD) problem generally arises when neural networks encounter data that significantly deviates from the training data distribution, i.e., in-distribution (InD). In this paper, we study the OOD problem from a neuron activation view. We first formulate neuron activation states by considering both the neuron output and its influence on model decisions. Then, to characterize the relationship between neurons and OOD issues, we introduce the neuron activation coverage (NAC) -- a simple measure for neuron behaviors under InD data. Leveraging our NAC, we show that 1) InD and OOD inputs can be largely separated based on the neuron behavior, which significantly eases the OOD detection problem and beats the 21 previous methods over three benchmarks (CIFAR-10, CIFAR-100, and ImageNet-1K). 2) a positive correlation between NAC and model generalization ability consistently holds across architectures and datasets, which enables a NAC-based criterion for evaluating model robustness. Compared to prevalent InD validation criteria, we show that NAC not only can select more robust models, but also has a stronger correlation with OOD test performance.

Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

In the pursuit to understand the intricacies of human brain's visual processing, reconstructing dynamic visual experiences from brain activities emerges as a challenging yet fascinating endeavor. While recent advancements have achieved success in reconstructing static images from non-invasive brain recordings, the domain of translating continuous brain activities into video format remains underexplored. In this work, we introduce NeuroCine, a novel dual-phase framework to targeting the inherent challenges of decoding fMRI data, such as noises, spatial redundancy and temporal lags. This framework proposes spatial masking and temporal interpolation-based augmentation for contrastive learning fMRI representations and a diffusion model enhanced by dependent prior noise for video generation. Tested on a publicly available fMRI dataset, our method shows promising results, outperforming the previous state-of-the-art models by a notable margin of {20.97%}, {31.00%} and {12.30%} respectively on decoding the brain activities of three subjects in the fMRI dataset, as measured by SSIM. Additionally, our attention analysis suggests that the model aligns with existing brain structures and functions, indicating its biological plausibility and interpretability.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Mechanistic interpretability aims to understand the behavior of neural networks by reverse-engineering their internal computations. However, current methods struggle to find clear interpretations of neural network activations because a decomposition of activations into computational features is missing. Individual neurons or model components do not cleanly correspond to distinct features or functions. We present a novel interpretability method that aims to overcome this limitation by transforming the activations of the network into a new basis - the Local Interaction Basis (LIB). LIB aims to identify computational features by removing irrelevant activations and interactions. Our method drops irrelevant activation directions and aligns the basis with the singular vectors of the Jacobian matrix between adjacent layers. It also scales features based on their importance for downstream computation, producing an interaction graph that shows all computationally-relevant features and interactions in a model. We evaluate the effectiveness of LIB on modular addition and CIFAR-10 models, finding that it identifies more computationally-relevant features that interact more sparsely, compared to principal component analysis. However, LIB does not yield substantial improvements in interpretability or interaction sparsity when applied to language models. We conclude that LIB is a promising theory-driven approach for analyzing neural networks, but in its current form is not applicable to large language models.

A basic question within the emerging field of mechanistic interpretability is the degree to which neural networks learn the same underlying mechanisms. In other words, are neural mechanisms universal across different models? In this work, we study the universality of individual neurons across GPT2 models trained from different initial random seeds, motivated by the hypothesis that universal neurons are likely to be interpretable. In particular, we compute pairwise correlations of neuron activations over 100 million tokens for every neuron pair across five different seeds and find that 1-5\% of neurons are universal, that is, pairs of neurons which consistently activate on the same inputs. We then study these universal neurons in detail, finding that they usually have clear interpretations and taxonomize them into a small number of neuron families. We conclude by studying patterns in neuron weights to establish several universal functional roles of neurons in simple circuits: deactivating attention heads, changing the entropy of the next token distribution, and predicting the next token to (not) be within a particular set.

Note: This paper describes an older version of DeepLIFT. See https://arxiv.org/abs/1704.02685 for the newer version. Original abstract follows: The purported "black box" nature of neural networks is a barrier to adoption in applications where interpretability is essential. Here we present DeepLIFT (Learning Important FeaTures), an efficient and effective method for computing importance scores in a neural network. DeepLIFT compares the activation of each neuron to its 'reference activation' and assigns contribution scores according to the difference. We apply DeepLIFT to models trained on natural images and genomic data, and show significant advantages over gradient-based methods.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the particularity of linear function class, while real-world practice usually adopts general non-linear representation functions like neural networks. This significantly reduces its applicability. In this work, we extend the analysis to general function class representations. Specifically, we consider an agent playing M contextual bandits (or MDPs) concurrently and extracting a shared representation function phi from a specific function class Phi using our proposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP for the first time. Lastly, we conduct experiments to demonstrate the effectiveness of our algorithm with neural net representation.

Activation compressed training provides a solution towards reducing the memory cost of training deep neural networks~(DNNs). However, state-of-the-art work combines a search of quantization bit-width with the training, which makes the procedure complicated and less transparent. To this end, we propose a simple and effective method to compress DNN training. Our method is motivated by an instructive observation: DNN backward propagation mainly utilizes the low-frequency component (LFC) of the activation maps, while the majority of memory is for caching the high-frequency component (HFC) during the training. This indicates the HFC of activation maps is highly redundant and compressible during DNN training, which inspires our proposed Dual Activation Precision (DIVISION). During the training, DIVISION preserves the high-precision copy of LFC and compresses the HFC into a light-weight copy with low numerical precision. This can significantly reduce the memory cost without negatively affecting the precision of backward propagation such that DIVISION maintains competitive model accuracy. Experiment results show DIVISION has better comprehensive performance than state-of-the-art methods, including over 10x compression of activation maps and competitive training throughput, without loss of model accuracy.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

We interpret the function of individual neurons in CLIP by automatically describing them using text. Analyzing the direct effects (i.e. the flow from a neuron through the residual stream to the output) or the indirect effects (overall contribution) fails to capture the neurons' function in CLIP. Therefore, we present the "second-order lens", analyzing the effect flowing from a neuron through the later attention heads, directly to the output. We find that these effects are highly selective: for each neuron, the effect is significant for <2% of the images. Moreover, each effect can be approximated by a single direction in the text-image space of CLIP. We describe neurons by decomposing these directions into sparse sets of text representations. The sets reveal polysemantic behavior - each neuron corresponds to multiple, often unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we mass-produce "semantic" adversarial examples by generating images with concepts spuriously correlated to the incorrect class. Additionally, we use the second-order effects for zero-shot segmentation and attribute discovery in images. Our results indicate that a scalable understanding of neurons can be used for model deception and for introducing new model capabilities.

Brain decoding, a pivotal field in neuroscience, aims to reconstruct stimuli from acquired brain signals, primarily utilizing functional magnetic resonance imaging (fMRI). Currently, brain decoding is confined to a per-subject-per-model paradigm, limiting its applicability to the same individual for whom the decoding model is trained. This constraint stems from three key challenges: 1) the inherent variability in input dimensions across subjects due to differences in brain size; 2) the unique intrinsic neural patterns, influencing how different individuals perceive and process sensory information; 3) limited data availability for new subjects in real-world scenarios hampers the performance of decoding models. In this paper, we present a novel approach, MindBridge, that achieves cross-subject brain decoding by employing only one model. Our proposed framework establishes a generic paradigm capable of addressing these challenges by introducing biological-inspired aggregation function and novel cyclic fMRI reconstruction mechanism for subject-invariant representation learning. Notably, by cycle reconstruction of fMRI, MindBridge can enable novel fMRI synthesis, which also can serve as pseudo data augmentation. Within the framework, we also devise a novel reset-tuning method for adapting a pretrained model to a new subject. Experimental results demonstrate MindBridge's ability to reconstruct images for multiple subjects, which is competitive with dedicated subject-specific models. Furthermore, with limited data for a new subject, we achieve a high level of decoding accuracy, surpassing that of subject-specific models. This advancement in cross-subject brain decoding suggests promising directions for wider applications in neuroscience and indicates potential for more efficient utilization of limited fMRI data in real-world scenarios. Project page: https://littlepure2333.github.io/MindBridge

Objective: fMRI and derived measures such as functional connectivity (FC) have been used to predict brain age, general fluid intelligence, psychiatric disease status, and preclinical neurodegenerative disease. However, it is not always clear that all demographic confounds, such as age, sex, and race, have been removed from fMRI data. Additionally, many fMRI datasets are restricted to authorized researchers, making dissemination of these valuable data sources challenging. Methods: We create a variational autoencoder (VAE)-based model, DemoVAE, to decorrelate fMRI features from demographics and generate high-quality synthetic fMRI data based on user-supplied demographics. We train and validate our model using two large, widely used datasets, the Philadelphia Neurodevelopmental Cohort (PNC) and Bipolar and Schizophrenia Network for Intermediate Phenotypes (BSNIP). Results: We find that DemoVAE recapitulates group differences in fMRI data while capturing the full breadth of individual variations. Significantly, we also find that most clinical and computerized battery fields that are correlated with fMRI data are not correlated with DemoVAE latents. An exception are several fields related to schizophrenia medication and symptom severity. Conclusion: Our model generates fMRI data that captures the full distribution of FC better than traditional VAE or GAN models. We also find that most prediction using fMRI data is dependent on correlation with, and prediction of, demographics. Significance: Our DemoVAE model allows for generation of high quality synthetic data conditioned on subject demographics as well as the removal of the confounding effects of demographics. We identify that FC-based prediction tasks are highly influenced by demographic confounds.

Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.

Recent work in activation steering has demonstrated the potential to better control the outputs of Large Language Models (LLMs), but it involves finding steering vectors. This is difficult because engineers do not typically know how features are represented in these models. We seek to address this issue by applying the idea of mean-centring to steering vectors. We find that taking the average of activations associated with a target dataset, and then subtracting the mean of all training activations, results in effective steering vectors. We test this method on a variety of models on natural language tasks by steering away from generating toxic text, and steering the completion of a story towards a target genre. We also apply mean-centring to extract function vectors, more effectively triggering the execution of a range of natural language tasks by a significant margin (compared to previous baselines). This suggests that mean-centring can be used to easily improve the effectiveness of activation steering in a wide range of contexts.

We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i.e., those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1.25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures.

Mammalian brains handle complex reasoning tasks in a gestalt manner by integrating information from regions of the brain that are specialised to individual sensory modalities. This allows for improved robustness and better generalisation ability. In contrast, deep neural networks are usually designed to process one particular information stream and susceptible to various types of adversarial perturbations. While many methods exist for detecting and defending against adversarial attacks, they do not generalise across a range of attacks and negatively affect performance on clean, unperturbed data. We developed a fusion model using a combination of background and foreground features extracted in parallel from Places-CNN and Imagenet-CNN. We tested the benefits of the fusion approach on preserving adversarial robustness for human perceivable (e.g., Gaussian blur) and network perceivable (e.g., gradient-based) attacks for CIFAR-10 and MS COCO data sets. For gradient based attacks, our results show that fusion allows for significant improvements in classification without decreasing performance on unperturbed data and without need to perform adversarial retraining. Our fused model revealed improvements for Gaussian blur type perturbations as well. The increase in performance from fusion approach depended on the variability of the image contexts; larger increases were seen for classes of images with larger differences in their contexts. We also demonstrate the effect of regularization to bias the classifier decision in the presence of a known adversary. We propose that this biologically inspired approach to integrate information across multiple modalities provides a new way to improve adversarial robustness that can be complementary to current state of the art approaches.

Activation sparsity improves compute efficiency and resource utilization in sparsity-aware neural network accelerators. As the predominant operation in DNNs is multiply-accumulate (MAC) of activations with weights to compute inner products, skipping operations where (at least) one of the two operands is zero can make inference more efficient in terms of latency and power. Spatial sparsification of activations is a popular topic in DNN literature and several methods have already been established to bias a DNN for it. On the other hand, temporal sparsity is an inherent feature of bio-inspired spiking neural networks (SNNs), which neuromorphic processing exploits for hardware efficiency. Introducing and exploiting spatio-temporal sparsity, is a topic much less explored in DNN literature, but in perfect resonance with the trend in DNN, to shift from static signal processing to more streaming signal processing. Towards this goal, in this paper we introduce a new DNN layer (called Delta Activation Layer), whose sole purpose is to promote temporal sparsity of activations during training. A Delta Activation Layer casts temporal sparsity into spatial activation sparsity to be exploited when performing sparse tensor multiplications in hardware. By employing delta inference and ``the usual'' spatial sparsification heuristics during training, the resulting model learns to exploit not only spatial but also temporal activation sparsity (for a given input data distribution). One may use the Delta Activation Layer either during vanilla training or during a refinement phase. We have implemented Delta Activation Layer as an extension of the standard Tensoflow-Keras library, and applied it to train deep neural networks on the Human Action Recognition (UCF101) dataset. We report an almost 3x improvement of activation sparsity, with recoverable loss of model accuracy after longer training.

Recent advancements in both representation learning and function learning have demonstrated substantial promise across diverse domains of artificial intelligence. However, the effective integration of these paradigms poses a significant challenge, particularly in cases where users must manually decide whether to apply a representation learning or function learning model based on dataset characteristics. To address this issue, we introduce MLP-KAN, a unified method designed to eliminate the need for manual model selection. By integrating Multi-Layer Perceptrons (MLPs) for representation learning and Kolmogorov-Arnold Networks (KANs) for function learning within a Mixture-of-Experts (MoE) architecture, MLP-KAN dynamically adapts to the specific characteristics of the task at hand, ensuring optimal performance. Embedded within a transformer-based framework, our work achieves remarkable results on four widely-used datasets across diverse domains. Extensive experimental evaluation demonstrates its superior versatility, delivering competitive performance across both deep representation and function learning tasks. These findings highlight the potential of MLP-KAN to simplify the model selection process, offering a comprehensive, adaptable solution across various domains. Our code and weights are available at https://github.com/DLYuanGod/MLP-KAN.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

Protein function prediction is a crucial task in bioinformatics, with significant implications for understanding biological processes and disease mechanisms. While the relationship between sequence and function has been extensively explored, translating protein structure to function continues to present substantial challenges. Various models, particularly, CNN and graph-based deep learning approaches that integrate structural and functional data, have been proposed to address these challenges. However, these methods often fall short in elucidating the functional significance of key residues essential for protein functionality, as they predominantly adopt a retrospective perspective, leading to suboptimal performance. Inspired by region proposal networks in computer vision, we introduce the Protein Region Proposal Network (ProteinRPN) for accurate protein function prediction. Specifically, the region proposal module component of ProteinRPN identifies potential functional regions (anchors) which are refined through the hierarchy-aware node drop pooling layer favoring nodes with defined secondary structures and spatial proximity. The representations of the predicted functional nodes are enriched using attention mechanisms and subsequently fed into a Graph Multiset Transformer, which is trained with supervised contrastive (SupCon) and InfoNCE losses on perturbed protein structures. Our model demonstrates significant improvements in predicting Gene Ontology (GO) terms, effectively localizing functional residues within protein structures. The proposed framework provides a robust, scalable solution for protein function annotation, advancing the understanding of protein structure-function relationships in computational biology.

This position paper explores the rapid development of Foundation Models (FMs) in AI and their implications for intelligence and reasoning. It examines the characteristics of FMs, including their training on vast datasets and use of embedding spaces to capture semantic relationships. The paper discusses recent advancements in FMs' reasoning abilities which we argue cannot be attributed to increased model size but to novel training techniques which yield learning phenomena like grokking. It also addresses the challenges in benchmarking FMs and compares their structure to the human brain. We argue that while FMs show promising developments in reasoning and knowledge representation, understanding their inner workings remains a significant challenge, similar to ongoing efforts in neuroscience to comprehend human brain function. Despite having some similarities, fundamental differences between FMs and the structure of human brain warn us against making direct comparisons or expecting neuroscience to provide immediate insights into FM function.

State-of-the-art systems neuroscience experiments yield large-scale multimodal data, and these data sets require new tools for analysis. Inspired by the success of large pretrained models in vision and language domains, we reframe the analysis of large-scale, cellular-resolution neuronal spiking data into an autoregressive spatiotemporal generation problem. Neuroformer is a multimodal, multitask generative pretrained transformer (GPT) model that is specifically designed to handle the intricacies of data in systems neuroscience. It scales linearly with feature size, can process an arbitrary number of modalities, and is adaptable to downstream tasks, such as predicting behavior. We first trained Neuroformer on simulated datasets, and found that it both accurately predicted simulated neuronal circuit activity, and also intrinsically inferred the underlying neural circuit connectivity, including direction. When pretrained to decode neural responses, the model predicted the behavior of a mouse with only few-shot fine-tuning, suggesting that the model begins learning how to do so directly from the neural representations themselves, without any explicit supervision. We used an ablation study to show that joint training on neuronal responses and behavior boosted performance, highlighting the model's ability to associate behavioral and neural representations in an unsupervised manner. These findings show that Neuroformer can analyze neural datasets and their emergent properties, informing the development of models and hypotheses associated with the brain.

Deep implicit functions have been found to be an effective tool for efficiently encoding all manner of natural signals. Their attractiveness stems from their ability to compactly represent signals with little to no off-line training data. Instead, they leverage the implicit bias of deep networks to decouple hidden redundancies within the signal. In this paper, we explore the hypothesis that additional compression can be achieved by leveraging the redundancies that exist between layers. We propose to use a novel run-time decoder-only hypernetwork - that uses no offline training data - to better model this cross-layer parameter redundancy. Previous applications of hyper-networks with deep implicit functions have applied feed-forward encoder/decoder frameworks that rely on large offline datasets that do not generalize beyond the signals they were trained on. We instead present a strategy for the initialization of run-time deep implicit functions for single-instance signals through a Decoder-Only randomly projected Hypernetwork (D'OH). By directly changing the dimension of a latent code to approximate a target implicit neural architecture, we provide a natural way to vary the memory footprint of neural representations without the costly need for neural architecture search on a space of alternative low-rate structures.

Mechanistic interpretability seeks to understand the internal mechanisms of machine learning models, where localization -- identifying the important model components -- is a key step. Activation patching, also known as causal tracing or interchange intervention, is a standard technique for this task (Vig et al., 2020), but the literature contains many variants with little consensus on the choice of hyperparameters or methodology. In this work, we systematically examine the impact of methodological details in activation patching, including evaluation metrics and corruption methods. In several settings of localization and circuit discovery in language models, we find that varying these hyperparameters could lead to disparate interpretability results. Backed by empirical observations, we give conceptual arguments for why certain metrics or methods may be preferred. Finally, we provide recommendations for the best practices of activation patching going forwards.

Conventional supervised learning typically assumes that the learning task can be solved by learning a single function since the data is sampled from a fixed distribution. However, this assumption is invalid in open-ended environments where no task-level data partitioning is available. In this paper, we present a novel supervised learning framework of learning from open-ended data, which is modeled as data implicitly sampled from multiple domains with the data in each domain obeying a domain-specific target function. Since different domains may possess distinct target functions, open-ended data inherently requires multiple functions to capture all its input-output relations, rendering training a single global model problematic. To address this issue, we devise an Open-ended Supervised Learning (OSL) framework, of which the key component is a subjective function that allocates the data among multiple candidate models to resolve the "conflict" between the data from different domains, exhibiting a natural hierarchy. We theoretically analyze the learnability and the generalization error of OSL, and empirically validate its efficacy in both open-ended regression and classification tasks.

Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of deep neural networks. In this article, we present a relatively new mathematical framework that provides the beginning of a deeper understanding of deep learning. This framework precisely characterizes the functional properties of neural networks that are trained to fit to data. The key mathematical tools which support this framework include transform-domain sparse regularization, the Radon transform of computed tomography, and approximation theory, which are all techniques deeply rooted in signal processing. This framework explains the effect of weight decay regularization in neural network training, the use of skip connections and low-rank weight matrices in network architectures, the role of sparsity in neural networks, and explains why neural networks can perform well in high-dimensional problems.

Neural decoding, the process of understanding how brain activity corresponds to different stimuli, has been a primary objective in cognitive sciences. Over the past three decades, advancements in functional Magnetic Resonance Imaging and machine learning have greatly improved our ability to map visual stimuli to brain activity, especially in the visual cortex. Concurrently, research has expanded into decoding more complex processes like language and memory across the whole brain, utilizing techniques to handle greater variability and improve signal accuracy. We argue that "seeing" involves more than just mapping visual stimuli onto the visual cortex; it engages the entire brain, as various emotions and cognitive states can emerge from observing different scenes. In this paper, we develop algorithms to enhance our understanding of visual processes by incorporating whole-brain activation maps while individuals are exposed to visual stimuli. We utilize large-scale fMRI encoders and Image generative models pre-trained on large public datasets, which are then fine-tuned through Image-fMRI contrastive learning. Our models hence can decode visual experience across the entire cerebral cortex, surpassing the traditional confines of the visual cortex. We first compare our method with state-of-the-art approaches to decoding visual processing and show improved predictive semantic accuracy by 43%. A network ablation analysis suggests that beyond the visual cortex, the default mode network contributes most to decoding stimuli, in line with the proposed role of this network in sense-making and semantic processing. Additionally, we implemented zero-shot imagination decoding on an extra validation dataset, achieving a p-value of 0.0206 for mapping the reconstructed images and ground-truth text stimuli, which substantiates the model's capability to capture semantic meanings across various scenarios.

This paper considers the Pointer Value Retrieval (PVR) benchmark introduced in [ZRKB21], where a 'reasoning' function acts on a string of digits to produce the label. More generally, the paper considers the learning of logical functions with gradient descent (GD) on neural networks. It is first shown that in order to learn logical functions with gradient descent on symmetric neural networks, the generalization error can be lower-bounded in terms of the noise-stability of the target function, supporting a conjecture made in [ZRKB21]. It is then shown that in the distribution shift setting, when the data withholding corresponds to freezing a single feature (referred to as canonical holdout), the generalization error of gradient descent admits a tight characterization in terms of the Boolean influence for several relevant architectures. This is shown on linear models and supported experimentally on other models such as MLPs and Transformers. In particular, this puts forward the hypothesis that for such architectures and for learning logical functions such as PVR functions, GD tends to have an implicit bias towards low-degree representations, which in turn gives the Boolean influence for the generalization error under quadratic loss.

Identifying cell types and understanding their functional properties is crucial for unraveling the mechanisms underlying perception and cognition. In the retina, functional types can be identified by carefully selected stimuli, but this requires expert domain knowledge and biases the procedure towards previously known cell types. In the visual cortex, it is still unknown what functional types exist and how to identify them. Thus, for unbiased identification of the functional cell types in retina and visual cortex, new approaches are needed. Here we propose an optimization-based clustering approach using deep predictive models to obtain functional clusters of neurons using Most Discriminative Stimuli (MDS). Our approach alternates between stimulus optimization with cluster reassignment akin to an expectation-maximization algorithm. The algorithm recovers functional clusters in mouse retina, marmoset retina and macaque visual area V4. This demonstrates that our approach can successfully find discriminative stimuli across species, stages of the visual system and recording techniques. The resulting most discriminative stimuli can be used to assign functional cell types fast and on the fly, without the need to train complex predictive models or show a large natural scene dataset, paving the way for experiments that were previously limited by experimental time. Crucially, MDS are interpretable: they visualize the distinctive stimulus patterns that most unambiguously identify a specific type of neuron.

The interpretation of deep learning models is a challenge due to their size, complexity, and often opaque internal state. In addition, many systems, such as image classifiers, operate on low-level features rather than high-level concepts. To address these challenges, we introduce Concept Activation Vectors (CAVs), which provide an interpretation of a neural net's internal state in terms of human-friendly concepts. The key idea is to view the high-dimensional internal state of a neural net as an aid, not an obstacle. We show how to use CAVs as part of a technique, Testing with CAVs (TCAV), that uses directional derivatives to quantify the degree to which a user-defined concept is important to a classification result--for example, how sensitive a prediction of "zebra" is to the presence of stripes. Using the domain of image classification as a testing ground, we describe how CAVs may be used to explore hypotheses and generate insights for a standard image classification network as well as a medical application.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

In the past five years, the use of generative and foundational AI systems has greatly improved the decoding of brain activity. Visual perception, in particular, can now be decoded from functional Magnetic Resonance Imaging (fMRI) with remarkable fidelity. This neuroimaging technique, however, suffers from a limited temporal resolution (approx0.5 Hz) and thus fundamentally constrains its real-time usage. Here, we propose an alternative approach based on magnetoencephalography (MEG), a neuroimaging device capable of measuring brain activity with high temporal resolution (approx5,000 Hz). For this, we develop an MEG decoding model trained with both contrastive and regression objectives and consisting of three modules: i) pretrained embeddings obtained from the image, ii) an MEG module trained end-to-end and iii) a pretrained image generator. Our results are threefold: Firstly, our MEG decoder shows a 7X improvement of image-retrieval over classic linear decoders. Second, late brain responses to images are best decoded with DINOv2, a recent foundational image model. Third, image retrievals and generations both suggest that high-level visual features can be decoded from MEG signals, although the same approach applied to 7T fMRI also recovers better low-level features. Overall, these results, while preliminary, provide an important step towards the decoding -- in real-time -- of the visual processes continuously unfolding within the human brain.

Predicting gene function from its DNA sequence is a fundamental challenge in biology. Many deep learning models have been proposed to embed DNA sequences and predict their enzymatic function, leveraging information in public databases linking DNA sequences to an enzymatic function label. However, much of the scientific community's knowledge of biological function is not represented in these categorical labels, and is instead captured in unstructured text descriptions of mechanisms, reactions, and enzyme behavior. These descriptions are often captured alongside DNA sequences in biological databases, albeit in an unstructured manner. Deep learning of models predicting enzymatic function are likely to benefit from incorporating this multi-modal data encoding scientific knowledge of biological function. There is, however, no dataset designed for machine learning algorithms to leverage this multi-modal information. Here we propose a novel dataset and benchmark suite that enables the exploration and development of large multi-modal neural network models on gene DNA sequences and natural language descriptions of gene function. We present baseline performance on benchmarks for both unsupervised and supervised tasks that demonstrate the difficulty of this modeling objective, while demonstrating the potential benefit of incorporating multi-modal data types in function prediction compared to DNA sequences alone. Our dataset is at: https://hoarfrost-lab.github.io/BioTalk/.

Activation patching is a popular mechanistic interpretability technique, but has many subtleties regarding how it is applied and how one may interpret the results. We provide a summary of advice and best practices, based on our experience using this technique in practice. We include an overview of the different ways to apply activation patching and a discussion on how to interpret the results. We focus on what evidence patching experiments provide about circuits, and on the choice of metric and associated pitfalls.

Selecting appropriate datasets is critical in modern computer vision. However, no general-purpose tools exist to evaluate the extent to which two datasets differ. For this, we propose representing images - and by extension datasets - using Distributions of Neuron Activations (DNAs). DNAs fit distributions, such as histograms or Gaussians, to activations of neurons in a pre-trained feature extractor through which we pass the image(s) to represent. This extractor is frozen for all datasets, and we rely on its generally expressive power in feature space. By comparing two DNAs, we can evaluate the extent to which two datasets differ with granular control over the comparison attributes of interest, providing the ability to customise the way distances are measured to suit the requirements of the task at hand. Furthermore, DNAs are compact, representing datasets of any size with less than 15 megabytes. We demonstrate the value of DNAs by evaluating their applicability on several tasks, including conditional dataset comparison, synthetic image evaluation, and transfer learning, and across diverse datasets, ranging from synthetic cat images to celebrity faces and urban driving scenes.

TD-learning is a foundation reinforcement learning (RL) algorithm for value prediction. Critical to the accuracy of value predictions is the quality of state representations. In this work, we consider the question: how does end-to-end TD-learning impact the representation over time? Complementary to prior work, we provide a set of analysis that sheds further light on the representation dynamics under TD-learning. We first show that when the environments are reversible, end-to-end TD-learning strictly decreases the value approximation error over time. Under further assumptions on the environments, we can connect the representation dynamics with spectral decomposition over the transition matrix. This latter finding establishes fitting multiple value functions from randomly generated rewards as a useful auxiliary task for representation learning, as we empirically validate on both tabular and Atari game suites.

In-context learning is a powerful emergent ability in transformer models. Prior work in mechanistic interpretability has identified a circuit element that may be critical for in-context learning -- the induction head (IH), which performs a match-and-copy operation. During training of large transformers on natural language data, IHs emerge around the same time as a notable phase change in the loss. Despite the robust evidence for IHs and this interesting coincidence with the phase change, relatively little is known about the diversity and emergence dynamics of IHs. Why is there more than one IH, and how are they dependent on each other? Why do IHs appear all of a sudden, and what are the subcircuits that enable them to emerge? We answer these questions by studying IH emergence dynamics in a controlled setting by training on synthetic data. In doing so, we develop and share a novel optogenetics-inspired causal framework for modifying activations throughout training. Using this framework, we delineate the diverse and additive nature of IHs. By clamping subsets of activations throughout training, we then identify three underlying subcircuits that interact to drive IH formation, yielding the phase change. Furthermore, these subcircuits shed light on data-dependent properties of formation, such as phase change timing, already showing the promise of this more in-depth understanding of subcircuits that need to "go right" for an induction head.

When trying to gain better visibility into a machine learning model in order to understand and mitigate the associated risks, a potentially valuable source of evidence is: which training examples most contribute to a given behavior? Influence functions aim to answer a counterfactual: how would the model's parameters (and hence its outputs) change if a given sequence were added to the training set? While influence functions have produced insights for small models, they are difficult to scale to large language models (LLMs) due to the difficulty of computing an inverse-Hessian-vector product (IHVP). We use the Eigenvalue-corrected Kronecker-Factored Approximate Curvature (EK-FAC) approximation to scale influence functions up to LLMs with up to 52 billion parameters. In our experiments, EK-FAC achieves similar accuracy to traditional influence function estimators despite the IHVP computation being orders of magnitude faster. We investigate two algorithmic techniques to reduce the cost of computing gradients of candidate training sequences: TF-IDF filtering and query batching. We use influence functions to investigate the generalization patterns of LLMs, including the sparsity of the influence patterns, increasing abstraction with scale, math and programming abilities, cross-lingual generalization, and role-playing behavior. Despite many apparently sophisticated forms of generalization, we identify a surprising limitation: influences decay to near-zero when the order of key phrases is flipped. Overall, influence functions give us a powerful new tool for studying the generalization properties of LLMs.

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

Brain-Computer Interface (BCI) systems allow users to perform actions by translating their brain activity into commands. Such systems usually need a training phase, consisting in training a classification algorithm to discriminate between mental states using specific features from the recorded signals. This phase of feature selection and training is crucial for BCI performance and presents specific constraints to be met in a clinical context, such as post-stroke rehabilitation. In this paper, we present HappyFeat, a software making Motor Imagery (MI) based BCI experiments easier, by gathering all necessary manipulations and analysis in a single convenient GUI and via automation of experiment or analysis parameters. The resulting workflow allows for effortlessly selecting the best features, helping to achieve good BCI performance in time-constrained environments. Alternative features based on Functional Connectivity can be used and compared or combined with Power Spectral Density, allowing a network-oriented approach. We then give details of HappyFeat's main mechanisms, and a review of its performances in typical use cases. We also show that it can be used as an efficient tool for comparing different metrics extracted from the signals, to train the classification algorithm. To this end, we show a comparison between the commonly-used Power Spectral Density and network metrics based on Functional Connectivity. HappyFeat is available as an open-source project which can be freely downloaded on GitHub.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Recent work has shown that feed-forward networks (FFNs) in pre-trained Transformers are a key component, storing various linguistic and factual knowledge. However, the computational patterns of FFNs are still unclear. In this work, we study the computational patterns of FFNs and observe that most inputs only activate a tiny ratio of neurons of FFNs. This phenomenon is similar to the sparsity of the human brain, which drives research on functional partitions of the human brain. To verify whether functional partitions also emerge in FFNs, we propose to convert a model into its MoE version with the same parameters, namely MoEfication. Specifically, MoEfication consists of two phases: (1) splitting the parameters of FFNs into multiple functional partitions as experts, and (2) building expert routers to decide which experts will be used for each input. Experimental results show that MoEfication can conditionally use 10% to 30% of FFN parameters while maintaining over 95% original performance for different models on various downstream tasks. Besides, MoEfication brings two advantages: (1) it significantly reduces the FLOPS of inference, i.e., 2x speedup with 25% of FFN parameters, and (2) it provides a fine-grained perspective to study the inner mechanism of FFNs. The source code of this paper can be obtained from https://github.com/thunlp/MoEfication.

Deep neural networks are ubiquitous due to the ease of developing models and their influence on other domains. At the heart of this progress is convolutional neural networks (CNNs) that are capable of learning representations or features given a set of data. Making sense of such complex models (i.e., millions of parameters and hundreds of layers) remains challenging for developers as well as the end-users. This is partially due to the lack of tools or interfaces capable of providing interpretability and transparency. A growing body of literature, for example, class activation map (CAM), focuses on making sense of what a model learns from the data or why it behaves poorly in a given task. This paper builds on previous ideas to cope with the increasing demand for interpretable, robust, and transparent models. Our approach provides a simpler and intuitive (or familiar) way of generating CAM. The proposed Eigen-CAM computes and visualizes the principle components of the learned features/representations from the convolutional layers. Empirical studies were performed to compare the Eigen-CAM with the state-of-the-art methods (such as Grad-CAM, Grad-CAM++, CNN-fixations) by evaluating on benchmark datasets such as weakly-supervised localization and localizing objects in the presence of adversarial noise. Eigen-CAM was found to be robust against classification errors made by fully connected layers in CNNs, does not rely on the backpropagation of gradients, class relevance score, maximum activation locations, or any other form of weighting features. In addition, it works with all CNN models without the need to modify layers or retrain models. Empirical results show up to 12% improvement over the best method among the methods compared on weakly supervised object localization.

The causalimages R package enables causal inference with image and image sequence data, providing new tools for integrating novel data sources like satellite and bio-medical imagery into the study of cause and effect. One set of functions enables image-based causal inference analyses. For example, one key function decomposes treatment effect heterogeneity by images using an interpretable Bayesian framework. This allows for determining which types of images or image sequences are most responsive to interventions. A second modeling function allows researchers to control for confounding using images. The package also allows investigators to produce embeddings that serve as vector summaries of the image or video content. Finally, infrastructural functions are also provided, such as tools for writing large-scale image and image sequence data as sequentialized byte strings for more rapid image analysis. causalimages therefore opens new capabilities for causal inference in R, letting researchers use informative imagery in substantive analyses in a fast and accessible manner.

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

In this work we identify the dormant neuron phenomenon in deep reinforcement learning, where an agent's network suffers from an increasing number of inactive neurons, thereby affecting network expressivity. We demonstrate the presence of this phenomenon across a variety of algorithms and environments, and highlight its effect on learning. To address this issue, we propose a simple and effective method (ReDo) that Recycles Dormant neurons throughout training. Our experiments demonstrate that ReDo maintains the expressive power of networks by reducing the number of dormant neurons and results in improved performance.

In this study, we present a technique that spans multi-scale views (global scale -- meaning brain network-level and local scale -- examining each individual ROI that constitutes the network) applied to resting-state fMRI volumes. Deep learning based classification is utilized in understanding neurodegeneration. The novelty of the proposed approach lies in utilizing two extreme scales of analysis. One branch considers the entire network within graph-analysis framework. Concurrently, the second branch scrutinizes each ROI within a network independently, focusing on evolution of dynamics. For each subject, graph-based approach employs partial correlation to profile the subject in a single graph where each ROI is a node, providing insights into differences in levels of participation. In contrast, non-linear analysis employs recurrence plots to profile a subject as a multichannel 2D image, revealing distinctions in underlying dynamics. The proposed approach is employed for classification of a cohort of 50 healthy control (HC) and 50 Mild Cognitive Impairment (MCI), sourced from ADNI dataset. Results point to: (1) reduced activity in ROIs such as PCC in MCI (2) greater activity in occipital in MCI, which is not seen in HC (3) when analysed for dynamics, all ROIs in MCI show greater predictability in time-series.

We present a simple mathematical model for the mammalian low visual pathway, taking into account its key elements: retina, lateral geniculate nucleus (LGN), primary visual cortex (V1). The analogies between the cortical level of the visual system and the structure of popular CNNs, used in image classification tasks, suggests the introduction of an additional preliminary convolutional module inspired to precortical neuronal circuits to improve robustness with respect to global light intensity and contrast variations in the input images. We validate our hypothesis on the popular databases MNIST, FashionMNIST and SVHN, obtaining significantly more robust CNNs with respect to these variations, once such extra module is added.

Advancements in LLMs have recently unveiled challenges tied to computational efficiency and continual scalability due to their requirements of huge parameters, making the applications and evolution of these models on devices with limited computation resources and scenarios requiring various abilities increasingly cumbersome. Inspired by modularity within the human brain, there is a growing tendency to decompose LLMs into numerous functional modules, allowing for inference with part of modules and dynamic assembly of modules to tackle complex tasks, such as mixture-of-experts. To highlight the inherent efficiency and composability of the modular approach, we coin the term brick to represent each functional module, designating the modularized structure as configurable foundation models. In this paper, we offer a comprehensive overview and investigation of the construction, utilization, and limitation of configurable foundation models. We first formalize modules into emergent bricks - functional neuron partitions that emerge during the pre-training phase, and customized bricks - bricks constructed via additional post-training to improve the capabilities and knowledge of LLMs. Based on diverse functional bricks, we further present four brick-oriented operations: retrieval and routing, merging, updating, and growing. These operations allow for dynamic configuration of LLMs based on instructions to handle complex tasks. To verify our perspective, we conduct an empirical analysis on widely-used LLMs. We find that the FFN layers follow modular patterns with functional specialization of neurons and functional neuron partitions. Finally, we highlight several open issues and directions for future research. Overall, this paper aims to offer a fresh modular perspective on existing LLM research and inspire the future creation of more efficient and scalable foundational models.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to individual examples. However, these measures are susceptible to noise and spurious correlations encoded in the model during the training phase (e.g., biased inputs, model overfitting, or misspecification). Moreover, this process has proven to result in noisy and unstable attributions that prevent any transparent understanding of the model's behavior. In this paper, we develop a robust interventional-based method grounded by causal analysis to capture cause-effect mechanisms in pre-trained neural networks and their relation to the prediction. Our novel approach relies on path interventions to infer the causal mechanisms within hidden layers and isolate relevant and necessary information (to model prediction), avoiding noisy ones. The result is task-specific causal explanatory graphs that can audit model behavior and express the actual causes underlying its performance. We apply our method to vision models trained on classification tasks. On image classification tasks, we provide extensive quantitative experiments to show that our approach can capture more stable and faithful explanations than standard attribution-based methods. Furthermore, the underlying causal graphs reveal the neural interactions in the model, making it a valuable tool in other applications (e.g., model repair).

Fast feedforward networks (FFFs) are a class of neural networks that exploit the observation that different regions of the input space activate distinct subsets of neurons in wide networks. FFFs partition the input space into separate sections using a differentiable binary tree of neurons and during inference descend the binary tree in order to improve computational efficiency. Inspired by Mixture of Experts (MoE) research, we propose the incorporation of load balancing and Master Leaf techniques into the FFF architecture to improve performance and simplify the training process. We reproduce experiments found in literature and present results on FFF models enhanced using these techniques. The proposed architecture and training recipe achieves up to 16.3% and 3% absolute classification accuracy increase in training and test accuracy, respectively, compared to the original FFF architecture. Additionally, we observe a smaller variance in the results compared to those reported in prior research. These findings demonstrate the potential of integrating MoE-inspired techniques into FFFs for developing more accurate and efficient models.

Can we pre-train a generalist agent from a large amount of unlabeled offline trajectories such that it can be immediately adapted to any new downstream tasks in a zero-shot manner? In this work, we present a functional reward encoding (FRE) as a general, scalable solution to this zero-shot RL problem. Our main idea is to learn functional representations of any arbitrary tasks by encoding their state-reward samples using a transformer-based variational auto-encoder. This functional encoding not only enables the pre-training of an agent from a wide diversity of general unsupervised reward functions, but also provides a way to solve any new downstream tasks in a zero-shot manner, given a small number of reward-annotated samples. We empirically show that FRE agents trained on diverse random unsupervised reward functions can generalize to solve novel tasks in a range of simulated robotic benchmarks, often outperforming previous zero-shot RL and offline RL methods. Code for this project is provided at: https://github.com/kvfrans/fre

A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help practitioners know when to use which explanation function. This paper proposes quantitative evaluation criteria for feature-based explanations: low sensitivity, high faithfulness, and low complexity. We devise a framework for aggregating explanation functions. We develop a procedure for learning an aggregate explanation function with lower complexity and then derive a new aggregate Shapley value explanation function that minimizes sensitivity.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Attention Deficit Hyperactive Disorder (ADHD) is a common behavioral problem affecting children. In this work, we investigate the automatic classification of ADHD subjects using the resting state Functional Magnetic Resonance Imaging (fMRI) sequences of the brain. We show that the brain can be modeled as a functional network, and certain properties of the networks differ in ADHD subjects from control subjects. We compute the pairwise correlation of brain voxels' activity over the time frame of the experimental protocol which helps to model the function of a brain as a network. Different network features are computed for each of the voxels constructing the network. The concatenation of the network features of all the voxels in a brain serves as the feature vector. Feature vectors from a set of subjects are then used to train a PCA-LDA (principal component analysis-linear discriminant analysis) based classifier. We hypothesized that ADHD-related differences lie in some specific regions of the brain and using features only from those regions is sufficient to discriminate ADHD and control subjects. We propose a method to create a brain mask that includes the useful regions only and demonstrate that using the feature from the masked regions improves classification accuracy on the test data set. We train our classifier with 776 subjects and test on 171 subjects provided by The Neuro Bureau for the ADHD-200 challenge. We demonstrate the utility of graph-motif features, specifically the maps that represent the frequency of participation of voxels in network cycles of length 3. The best classification performance (69.59%) is achieved using 3-cycle map features with masking. Our proposed approach holds promise in being able to diagnose and understand the disorder.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Prior studies on the emergence in large models have primarily focused on how the functional capabilities of large language models (LLMs) scale with model size. Our research, however, transcends this traditional paradigm, aiming to deepen our understanding of the emergence within LLMs by placing a special emphasis not just on the model size but more significantly on the complex behavior of neuron interactions during the training process. By introducing the concepts of "self-organization" and "multifractal analysis," we explore how neuron interactions dynamically evolve during training, leading to "emergence," mirroring the phenomenon in natural systems where simple micro-level interactions give rise to complex macro-level behaviors. To quantitatively analyze the continuously evolving interactions among neurons in large models during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA). Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent behavior in LLMs through the lens of both model size and training process, paving new avenues for research into the emergence in large models.

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose Mutual Feature Regularization (MFR), a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate MFR by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that MFR can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale MFR to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that MFR can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

As one of the energy-efficient alternatives of conventional neural networks (CNNs), spiking neural networks (SNNs) have gained more and more interest recently. To train the deep models, some effective batch normalization (BN) techniques are proposed in SNNs. All these BNs are suggested to be used after the convolution layer as usually doing in CNNs. However, the spiking neuron is much more complex with the spatio-temporal dynamics. The regulated data flow after the BN layer will be disturbed again by the membrane potential updating operation before the firing function, i.e., the nonlinear activation. Therefore, we advocate adding another BN layer before the firing function to normalize the membrane potential again, called MPBN. To eliminate the induced time cost of MPBN, we also propose a training-inference-decoupled re-parameterization technique to fold the trained MPBN into the firing threshold. With the re-parameterization technique, the MPBN will not introduce any extra time burden in the inference. Furthermore, the MPBN can also adopt the element-wised form, while these BNs after the convolution layer can only use the channel-wised form. Experimental results show that the proposed MPBN performs well on both popular non-spiking static and neuromorphic datasets. Our code is open-sourced at https://github.com/yfguo91/MPBN{MPBN}.

We analyze the storage and recall of factual associations in autoregressive transformer language models, finding evidence that these associations correspond to localized, directly-editable computations. We first develop a causal intervention for identifying neuron activations that are decisive in a model's factual predictions. This reveals a distinct set of steps in middle-layer feed-forward modules that mediate factual predictions while processing subject tokens. To test our hypothesis that these computations correspond to factual association recall, we modify feed-forward weights to update specific factual associations using Rank-One Model Editing (ROME). We find that ROME is effective on a standard zero-shot relation extraction (zsRE) model-editing task, comparable to existing methods. To perform a more sensitive evaluation, we also evaluate ROME on a new dataset of counterfactual assertions, on which it simultaneously maintains both specificity and generalization, whereas other methods sacrifice one or another. Our results confirm an important role for mid-layer feed-forward modules in storing factual associations and suggest that direct manipulation of computational mechanisms may be a feasible approach for model editing. The code, dataset, visualizations, and an interactive demo notebook are available at https://rome.baulab.info/

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks implement specific target functions, this paper explores a complementary question -- why do networks arrive at particular computational strategies? Our inquiry focuses on the algebraic learning tasks of modular addition, sparse parities, and finite group operations. Our primary theoretical findings analytically characterize the features learned by stylized neural networks for these algebraic tasks. Notably, our main technique demonstrates how the principle of margin maximization alone can be used to fully specify the features learned by the network. Specifically, we prove that the trained networks utilize Fourier features to perform modular addition and employ features corresponding to irreducible group-theoretic representations to perform compositions in general groups, aligning closely with the empirical observations of Nanda et al. and Chughtai et al. More generally, we hope our techniques can help to foster a deeper understanding of why neural networks adopt specific computational strategies.

A key method for creating Artificial Intelligence (AI) agents is Reinforcement Learning (RL). However, constructing a standalone RL policy that maps perception to action directly encounters severe problems, chief among them being its lack of generality across multiple tasks and the need for a large amount of training data. The leading cause is that it cannot effectively integrate prior information into the perception-action cycle when devising the policy. Large language models (LLMs) emerged as a fundamental way to incorporate cross-domain knowledge into AI agents but lack crucial learning and adaptation toward specific decision problems. This paper presents a general framework model for integrating and learning structured reasoning into AI agents' policies. Our methodology is motivated by the modularity found in the human brain. The framework utilises the construction of intrinsic and extrinsic functions to add previous understandings of reasoning structures. It also provides the adaptive ability to learn models inside every module or function, consistent with the modular structure of cognitive processes. We describe the framework in-depth and compare it with other AI pipelines and existing frameworks. The paper explores practical applications, covering experiments that show the effectiveness of our method. Our results indicate that AI agents perform and adapt far better when organised reasoning and prior knowledge are embedded. This opens the door to more resilient and general AI agent systems.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

One of the roadblocks to a better understanding of neural networks' internals is polysemanticity, where neurons appear to activate in multiple, semantically distinct contexts. Polysemanticity prevents us from identifying concise, human-understandable explanations for what neural networks are doing internally. One hypothesised cause of polysemanticity is superposition, where neural networks represent more features than they have neurons by assigning features to an overcomplete set of directions in activation space, rather than to individual neurons. Here, we attempt to identify those directions, using sparse autoencoders to reconstruct the internal activations of a language model. These autoencoders learn sets of sparsely activating features that are more interpretable and monosemantic than directions identified by alternative approaches, where interpretability is measured by automated methods. Ablating these features enables precise model editing, for example, by removing capabilities such as pronoun prediction, while disrupting model behaviour less than prior techniques. This work indicates that it is possible to resolve superposition in language models using a scalable, unsupervised method. Our method may serve as a foundation for future mechanistic interpretability work, which we hope will enable greater model transparency and steerability.

Electroencephalography (EEG) signals, known for convenient non-invasive acquisition but low signal-to-noise ratio, have recently gained substantial attention due to the potential to decode natural images. This paper presents a self-supervised framework to demonstrate the feasibility of learning image representations from EEG signals, particularly for object recognition. The framework utilizes image and EEG encoders to extract features from paired image stimuli and EEG responses. Contrastive learning aligns these two modalities by constraining their similarity. With the framework, we attain significantly above-chance results on a comprehensive EEG-image dataset, achieving a top-1 accuracy of 15.6% and a top-5 accuracy of 42.8% in challenging 200-way zero-shot tasks. Moreover, we perform extensive experiments to explore the biological plausibility by resolving the temporal, spatial, spectral, and semantic aspects of EEG signals. Besides, we introduce attention modules to capture spatial correlations, providing implicit evidence of the brain activity perceived from EEG data. These findings yield valuable insights for neural decoding and brain-computer interfaces in real-world scenarios. The code will be released on https://github.com/eeyhsong/NICE-EEG.

Invasive brain-computer interfaces have garnered significant attention due to their high performance. The current intracranial stereoElectroEncephaloGraphy (sEEG) foundation models typically build univariate representations based on a single channel. Some of them further use Transformer to model the relationship among channels. However, due to the locality and specificity of brain computation, their performance on more difficult tasks, e.g., speech decoding, which demands intricate processing in specific brain regions, is yet to be fully investigated. We hypothesize that building multi-variate representations within certain brain regions can better capture the specific neural processing. To explore this hypothesis, we collect a well-annotated Chinese word-reading sEEG dataset, targeting language-related brain networks, over 12 subjects. Leveraging this benchmark dataset, we developed the Du-IN model that can extract contextual embeddings from specific brain regions through discrete codebook-guided mask modeling. Our model achieves SOTA performance on the downstream 61-word classification task, surpassing all baseline models. Model comparison and ablation analysis reveal that our design choices, including (i) multi-variate representation by fusing channels in vSMC and STG regions and (ii) self-supervision by discrete codebook-guided mask modeling, significantly contribute to these performances. Collectively, our approach, inspired by neuroscience findings, capitalizing on multi-variate neural representation from specific brain regions, is suitable for invasive brain modeling. It marks a promising neuro-inspired AI approach in BCI.

The ability to predict upcoming events has been hypothesized to comprise a key aspect of natural and machine cognition. This is supported by trends in deep reinforcement learning (RL), where self-supervised auxiliary objectives such as prediction are widely used to support representation learning and improve task performance. Here, we study the effects predictive auxiliary objectives have on representation learning across different modules of an RL system and how these mimic representational changes observed in the brain. We find that predictive objectives improve and stabilize learning particularly in resource-limited architectures, and we identify settings where longer predictive horizons better support representational transfer. Furthermore, we find that representational changes in this RL system bear a striking resemblance to changes in neural activity observed in the brain across various experiments. Specifically, we draw a connection between the auxiliary predictive model of the RL system and hippocampus, an area thought to learn a predictive model to support memory-guided behavior. We also connect the encoder network and the value learning network of the RL system to visual cortex and striatum in the brain, respectively. This work demonstrates how representation learning in deep RL systems can provide an interpretable framework for modeling multi-region interactions in the brain. The deep RL perspective taken here also suggests an additional role of the hippocampus in the brain -- that of an auxiliary learning system that benefits representation learning in other regions.