Related papers: Robustness in deep learning: The good (width), the…

Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples. In this work we focus on two-layer neural networks trained using data which lie on a low…

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore,…

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

Neural networks are very successful at detecting patterns in noisy data, and have become the technology of choice in many fields. However, their usefulness is hampered by their susceptibility to adversarial attacks. Recently, many methods…

Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

Substantial work indicates that the dynamics of neural networks (NNs) is closely related to their initialization of parameters. Inspired by the phase diagram for two-layer ReLU NNs with infinite width (Luo et al., 2021), we make a step…

We present a theoretical study of the robustness of parameterized networks to random input perturbations. Specifically, we analyze local robustness at a given network input by quantifying the probability that a small additive random…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…

We study the effect of width on the dynamics of feature-learning neural networks across a variety of architectures and datasets. Early in training, wide neural networks trained on online data have not only identical loss curves but also…

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Adversarial training can considerably robustify deep neural networks to resist adversarial attacks. However, some works suggested that adversarial training might comprise the privacy-preserving and generalization abilities. This paper…

In recent years, deep learning has made remarkable progress in a wide range of domains, with a particularly notable impact on natural language processing tasks. One of the challenges associated with training deep neural networks in the…

We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior…

Deep neural networks (DNNs) are vulnerable to adversarial noises, which motivates the benchmark of model robustness. Existing benchmarks mainly focus on evaluating defenses, but there are no comprehensive studies of how architecture design…

Deep learning models have proven to be successful in a wide range of machine learning tasks. Yet, they are often highly sensitive to perturbations on the input data which can lead to incorrect decisions with high confidence, hampering their…

The implicit biases of gradient-based optimization algorithms are conjectured to be a major factor in the success of modern deep learning. In this work, we investigate the implicit bias of gradient flow and gradient descent in two-layer…

This work studies the (non)robustness of two-layer neural networks in various high-dimensional linearized regimes. We establish fundamental trade-offs between memorization and robustness, as measured by the Sobolev-seminorm of the model…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…