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This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism;…
We explore convergence of deep neural networks with the popular ReLU activation function, as the depth of the networks tends to infinity. To this end, we introduce the notion of activation domains and activation matrices of a ReLU network.…
We consider the injectivity property of the ReLU networks layers. Determining the ReLU injectivity capacity (ratio of the number of layer's inputs and outputs) is established as isomorphic to determining the capacity of the so-called…
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified…
We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by $1/\sqrt{depth}$ (the only nontrivial scaling), result in the same covariance structure no matter how that limit…
{\em Hypernetworks} are architectures that produce the weights of a task-specific {\em primary network}. A notable application of hypernetworks in the recent literature involves learning to output functional representations. In these…
Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…
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,…
The implicit bias induced by the training of neural networks has become a topic of rigorous study. In the limit of gradient flow and gradient descent with appropriate step size, it has been shown that when one trains a deep linear network…
Amongst others, the adoption of Rectified Linear Units (ReLUs) is regarded as one of the ingredients of the success of deep learning. ReLU activation has been shown to mitigate the vanishing gradient issue, to encourage sparsity in the…
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…
Implicit deep learning has recently become popular in the machine learning community since these implicit models can achieve competitive performance with state-of-the-art deep networks while using significantly less memory and computational…
This article derives and validates three principles for initialization and architecture selection in finite width graph neural networks (GNNs) with ReLU activations. First, we theoretically derive what is essentially the unique…
Attention mechanisms lie at the heart of modern large language models (LLMs). Straightforward algorithms for forward and backward (gradient) computation take quadratic time, and a line of work initiated by [Alman and Song NeurIPS 2023] and…
In this paper, we study the generalization ability of the wide residual network on $\mathbb{S}^{d-1}$ with the ReLU activation function. We first show that as the width $m\rightarrow\infty$, the residual network kernel (RNK) uniformly…
Previous work has demonstrated that attention mechanisms are Turing complete. More recently, it has been shown that a looped 9-layer Transformer can function as a universal programmable computer. In contrast, the multi-layer perceptrons…
Multimodal large language models (MLLMs) often fail to transfer safety capabilities learned in the text modality to semantically equivalent non-text inputs, revealing a persistent multimodal safety gap. We study this gap from a…
The transparent formulation of explanation methods is essential for elucidating the predictions of neural networks, which are typically black-box models. Layer-wise Relevance Propagation (LRP) is a well-established method that transparently…
The transformer architecture has driven many successes in a variety of tasks within the field of deep learning, in particular the recent advances in natural language processing (NLP) culminating with large language models (LLM). Adding to…
Deep residual networks have emerged as a family of extremely deep architectures showing compelling accuracy and nice convergence behaviors. In this paper, we analyze the propagation formulations behind the residual building blocks, which…