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Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of…

Machine Learning · Computer Science 2019-04-03 Zhiming Zhou , Jian Shen , Yuxuan Song , Weinan Zhang , Yong Yu

This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th…

Machine Learning · Computer Science 2024-11-26 Patricia Pauli , Dennis Gramlich , Frank Allgöwer

Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees…

Machine Learning · Statistics 2020-05-04 Aman Sinha , Hongseok Namkoong , Riccardo Volpi , John Duchi

The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…

Machine Learning · Computer Science 2026-04-14 Yuezhu Xu , S. Sivaranjani

Spiking Neural Networks (SNNs) have attracted great attention for their energy-efficient operations and biologically inspired structures, offering potential advantages over Artificial Neural Networks (ANNs) in terms of energy efficiency and…

Neural and Evolutionary Computing · Computer Science 2024-06-03 Yujia Liu , Tong Bu , Jianhao Ding , Zecheng Hao , Tiejun Huang , Zhaofei Yu

Many state-of-the-art adversarial training methods for deep learning leverage upper bounds of the adversarial loss to provide security guarantees against adversarial attacks. Yet, these methods rely on convex relaxations to propagate lower…

Machine Learning · Computer Science 2023-04-07 Dimitris Bertsimas , Xavier Boix , Kimberly Villalobos Carballo , Dick den Hertog

Recently, Zhang et al. (2021) developed a new neural network architecture based on $\ell_\infty$-distance functions, which naturally possesses certified $\ell_\infty$ robustness by its construction. Despite the novel design and theoretical…

Machine Learning · Computer Science 2022-03-16 Bohang Zhang , Du Jiang , Di He , Liwei Wang

Optimizing deep neural networks is largely thought to be an empirical process, requiring manual tuning of several hyper-parameters, such as learning rate, weight decay, and dropout rate. Arguably, the learning rate is the most important of…

Machine Learning · Computer Science 2020-08-04 Rahul Yedida , Snehanshu Saha , Tejas Prashanth

The vulnerability to adversarial attacks has been a critical issue for deep neural networks. Addressing this issue requires a reliable way to evaluate the robustness of a network. Recently, several methods have been developed to compute…

Machine Learning · Computer Science 2019-05-20 Ching-Yun Ko , Zhaoyang Lyu , Tsui-Wei Weng , Luca Daniel , Ngai Wong , Dahua Lin

Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that…

Machine Learning · Computer Science 2019-02-19 Vincent Tjeng , Kai Xiao , Russ Tedrake

Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…

Machine Learning · Statistics 2026-05-28 Jürgen Dölz , Michael Multerer , Michele Palma

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

Machine Learning · Computer Science 2022-01-27 Saber Jafarpour , Alexander Davydov , Anton V. Proskurnikov , Francesco Bullo

The design of complex engineering systems leads to solving very large optimization problems involving different disciplines. Strategies allowing disciplines to optimize in parallel by providing sub-objectives and splitting the problem into…

Machine Learning · Computer Science 2021-06-14 Jean de Becdelievre , Ilan Kroo

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high…

Machine Learning · Computer Science 2017-11-07 Matthias Hein , Maksym Andriushchenko

In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…

Machine Learning · Computer Science 2021-09-01 Paul Hagemann , Sebastian Neumayer

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

Machine Learning · Computer Science 2020-02-28 Ankit Raj , Yoram Bresler , Bo Li

Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer…

Machine Learning · Statistics 2020-02-21 Amartya Sanyal , Philip H. S. Torr , Puneet K. Dokania

Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…

Machine Learning · Computer Science 2023-01-26 Brendon G. Anderson , Somayeh Sojoudi

This article provides a comprehensive understanding of optimization in deep learning, with a primary focus on the challenges of gradient vanishing and gradient exploding, which normally lead to diminished model representational ability and…

Machine Learning · Computer Science 2023-11-14 Xianbiao Qi , Jianan Wang , Lei Zhang