arXiv research

The paper analyzes deep ReLU CNNs' approximation properties in 2D space.

Polynomial-time convex optimization for CNNs with ReLU activations.

2D CNNs approximate Korobov functions with near-optimal rates.

Paper studies the expressivity of Convolutional Neural Networks (CNNs).

Optimal rates for shallow ReLU networks in nonparametric regression.

In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is $\mathit{~locally~strongly~convex}$ in a basin of attraction…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear conve…

Two-layer CNNs can overfit well if initialized correctly.

In this paper, we analyze efficacy of the fast gradient sign method (FGSM) and the Carlini-Wagner's L2 (CW-L2) attack. We prove that, within a certain regime, the untargeted FGSM can fool any convolutional neural nets (CNNs) with ReLU activation; the targeted FGSM can mislead any CNNs with ReLU activation to classify a…

Improved generalization bounds for CNNs using Rademacher complexity.

Study analyzes error in ReLU networks with local connections.

SPLASH units improve deep neural network accuracy and adversarial robustness.

Kernel sparsity ("dying ReLUs") and lack of diversity are commonly observed in CNN kernels, which decreases model capacity. Drawing inspiration from information theory and wireless communications, we demonstrate the intersection of coding theory and deep learning through the Grassmannian subspace packing problem in CNN…

Very deep CNNs achieve state-of-the-art results in both computer vision and speech recognition, but are difficult to train. The most popular way to train very deep CNNs is to use shortcut connections (SC) together with batch normalization (BN). Inspired by Self- Normalizing Neural Networks, we propose the self-normaliz…

New Lipschitz bound for ReLU networks resists weight rescaling.

Computer vision performances have been significantly improved in recent years by Convolutional Neural Networks(CNN). Currently, applications using CNN algorithms are deployed mainly on general purpose hardwares, such as CPUs, GPUs or FPGAs. However, power consumption, speed, accuracy, memory footprint, and die size sho…

Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP…

In order to classify linearly non-separable data, neurons are typically organized into multi-layer neural networks that are equipped with at least one hidden layer. Inspired by some recent discoveries in neuroscience, we propose a new model of artificial neuron along with a novel activation function enabling the learni…

We analyze why some models resist unlearning using linear stability theory.

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these net…

Paper analyzes weak-to-strong generalization in CNNs, identifying data-scarce and data-abundant regimes.

DP-GD improves CNN training accuracy with privacy, especially with low signal-to-noise ratios.

We investigate filter level sparsity that emerges in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. We conduct an extensive experimental study casting our initial findings into hy…

We propose a new way of thinking about deep neural networks, in which the linear and non-linear components of the network are naturally derived and justified in terms of principles in probability theory. In particular, the models constructed in our framework assign probabilities to uncertain realizations, leading to Ku…

We show implicit filter level sparsity manifests in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. Through an extensive empirical study (Mehta et al., 2019) we hypothesize the mec…

This study connects ReLU neural networks to toric geometry to analyze function realization.

The paper investigates how target normalization and momentum affect dying ReLUs in neural networks.

Single ReLU neuron's gradient dynamics reveal support vectors as key to generalization.

Large deviation principle for deep neural networks with ReLU activation.

Study shows efficient neural network approach for stochastic bandits.

The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die. However, little is known about its theoretical analysis. In this paper, we rigorously prove that a deep ReLU network will eventually die in…

Proves existence of optimal shallow neural networks with ReLU activation.

Gradient descent learns ReLU functions with non-zero bias efficiently.

Deep ReLU networks can be simplified to a three-layer model.

This article concerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width $w_{\text{min}}(d)$ so that ReLU nets of width $w_{\text{min}}(d)$ (and arbitrary depth) can approximate any continuous functio…

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural networks with one hidden layer. The theory of multi-layer networks remains largely …

Modified ReLU networks improve regression estimation rates.

Bayesian ReLU nets fix asymptotic overconfidence with infinite features.

We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let $\mathsf{opt} < 1$ be the population loss of the best-fitting ReLU. We prove: 1. Finding a ReLU wit…

Improved bounds on neural network expressivity.

Despite their prevalence in neural networks we still lack a thorough theoretical characterization of ReLU layers. This paper aims to further our understanding of ReLU layers by studying how the activation function ReLU interacts with the linear component of the layer and what role this interaction plays in the success …

Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.

Transformers use ReLUs to approximate softmax efficiently.

PHP connects to ReLU neural networks for scalable Bayesian inference.

We study the approximation properties of random ReLU features through their reproducing kernel Hilbert space (RKHS). We first prove a universality theorem for the RKHS induced by random features whose feature maps are of the form of nodes in neural networks. The universality result implies that the random ReLU features…

Paper analyzes GLM-tron for high-dimensional ReLU regression, providing upper and lower bounds.

The paper explores how ReLU DNNs can represent MPC policies and vice versa.

We study algebraic varieties of ReLU networks to understand their representable functions.