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This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization,…

Machine Learning · Computer Science 2020-11-10 Alexandre Araujo , Benjamin Negrevergne , Yann Chevaleyre , Jamal Atif

Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…

Optimization and Control · Mathematics 2020-06-23 Patrick L. Combettes , Jean-Christophe Pesquet

Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…

Machine Learning · Computer Science 2022-07-18 Sarosij Bose

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

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

Machine Learning · Computer Science 2021-04-30 Patricia Pauli , Anne Koch , Julian Berberich , Paul Kohler , Frank Allgöwer

In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity properties of convolutional, pooling, and fully connected layers…

Machine Learning · Computer Science 2023-06-21 Patricia Pauli , Dennis Gramlich , Frank Allgöwer

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…

Machine Learning · Computer Science 2024-05-16 Grigory Khromov , Sidak Pal Singh

Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…

Machine Learning · Computer Science 2024-11-01 Abulikemu Abuduweili , Changliu Liu

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the…

Information Theory · Computer Science 2018-08-07 Dongmian Zou , Radu Balan , Maneesh Singh

Deriving tight Lipschitz bounds for transformer-based architectures presents a significant challenge. The large input sizes and high-dimensional attention modules typically prove to be crucial bottlenecks during the training process and…

Machine Learning · Computer Science 2025-03-20 Rohan Menon , Nicola Franco , Stephan Günnemann

Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…

Machine Learning · Computer Science 2026-02-05 Róisín Luo

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…

Machine Learning · Computer Science 2024-02-23 Zhiyu Zhang , Heng Yang , Ashok Cutkosky , Ioannis Ch. Paschalidis

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

The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining…

Machine Learning · Computer Science 2021-07-07 Aritra Bhowmick , Meenakshi D'Souza , G. Srinivasa Raghavan

Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…

Machine Learning · Statistics 2021-03-15 Hisham Husain , Borja Balle

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the…

Machine Learning · Computer Science 2018-07-30 Kavosh Asadi , Dipendra Misra , Michael L. Littman

This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…

Machine Learning · Computer Science 2022-09-21 Patricia Pauli , Niklas Funcke , Dennis Gramlich , Mohamed Amine Msalmi , Frank Allgöwer

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural…

Machine Learning · Computer Science 2025-12-08 Marius F. R. Juston , Ramavarapu S. Sreenivas , Dustin Nottage , Ahmet Soylemezoglu

We present a novel local Lipschitz bound for self-attention blocks of transformers. This bound is based on a refined closed-form expression for the spectral norm of the softmax function. The resulting bound is not only more accurate than in…

Machine Learning · Computer Science 2025-07-11 Nikolay Yudin , Alexander Gaponov , Sergei Kudriashov , Maxim Rakhuba

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…

Machine Learning · Computer Science 2021-11-03 Yujia Huang , Huan Zhang , Yuanyuan Shi , J Zico Kolter , Anima Anandkumar