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Fast and precise Lipschitz constant estimation of neural networks is an important task for deep learning. Researchers have recently found an intrinsic trade-off between the accuracy and smoothness of neural networks, so training a network…

Machine Learning · Computer Science 2022-10-12 Zi Wang , Gautam Prakriya , Somesh Jha

Deep Reinforcement Learning (DRL) has achieved remarkable advances in sequential decision tasks. However, recent works have revealed that DRL agents are susceptible to slight perturbations in observations. This vulnerability raises concerns…

Machine Learning · Computer Science 2023-12-15 Buqing Nie , Jingtian Ji , Yangqing Fu , Yue Gao

Recent studies have highlighted the potential of Lipschitz-based methods for training certifiably robust neural networks against adversarial attacks. A key challenge, supported both theoretically and empirically, is that robustness demands…

Machine Learning · Computer Science 2024-06-25 Kai Hu , Klas Leino , Zifan Wang , Matt Fredrikson

Deep Neural Networks are vulnerable to small perturbations that can drastically alter their predictions for perceptually unchanged inputs. The literature on adversarially robust Deep Learning attempts to either enhance the robustness of…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Thomas Massena , Corentin Friedrich , Franck Mamalet , Mathieu Serrurier

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

Machine Learning · Statistics 2020-08-11 Henry Gouk , Eibe Frank , Bernhard Pfahringer , Michael J. Cree

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

Adversarial training is an effective methodology for training deep neural networks that are robust against adversarial, norm-bounded perturbations. However, the computational cost of adversarial training grows prohibitively as the size of…

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…

Machine Learning · Computer Science 2018-07-26 Todd Huster , Cho-Yu Jason Chiang , Ritu Chadha

Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation…

Machine Learning · Computer Science 2021-07-07 Sungyoon Lee , Hoki Kim , Jaewook Lee

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…

Computer Vision and Pattern Recognition · Computer Science 2018-11-02 Yusuke Tsuzuku , Issei Sato , Masashi Sugiyama

Deep neural networks are notorious for being sensitive to small well-chosen perturbations, and estimating the regularity of such architectures is of utmost importance for safe and robust practical applications. In this paper, we investigate…

Machine Learning · Statistics 2019-10-28 Kevin Scaman , Aladin Virmaux

Quantized neural networks (NN) are the common standard to efficiently deploy deep learning models on tiny hardware platforms. However, we notice that quantized NNs are as vulnerable to adversarial attacks as the full-precision models. With…

Machine Learning · Computer Science 2021-05-17 Lorena Qendro , Sangwon Ha , René de Jong , Partha Maji

Dynamic DNN optimization techniques such as layer-skipping offer increased adaptability and efficiency gains but can lead to i) a larger memory footprint as in decision gates, ii) increased training complexity (e.g., with non-differentiable…

Machine Learning · Computer Science 2025-05-26 Guilherme Korol , Antonio Carlos Schneider Beck , Jeronimo Castrillon

This paper presents a study of robust policy networks in deep reinforcement learning. We investigate the benefits of policy parameterizations that naturally satisfy constraints on their Lipschitz bound, analyzing their empirical performance…

Machine Learning · Computer Science 2025-02-07 Nicholas H. Barbara , Ruigang Wang , Ian R. Manchester

Despite its popularity, deep neural networks are easily fooled. To alleviate this deficiency, researchers are actively developing new training strategies, which encourage models that are robust to small input perturbations. Several…

Machine Learning · Computer Science 2021-10-28 Jingyue Lu , M. Pawan Kumar

Neural network quantization is becoming an industry standard to efficiently deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and FPGAs. However, we observe that the conventional quantization approaches are…

Machine Learning · Computer Science 2019-04-19 Ji Lin , Chuang Gan , Song Han

Robustness certification against bounded input noise or adversarial perturbations is increasingly important for deployment recurrent neural networks (RNNs) in safety-critical control applications. To address this challenge, we present…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Paul Hamelbeck , Johannes Schiffer

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Machine Learning · Computer Science 2020-04-21 Fabian Latorre , Paul Rolland , Volkan Cevher

This paper investigates a family of methods for defending against adversarial attacks that owe part of their success to creating a noisy, discontinuous, or otherwise rugged loss landscape that adversaries find difficult to navigate. A…

Machine Learning · Computer Science 2022-08-08 Panagiotis Eustratiadis , Henry Gouk , Da Li , Timothy Hospedales

Deep neural networks have been shown to suffer from critical vulnerabilities under adversarial attacks. This phenomenon stimulated the creation of different attack and defense strategies similar to those adopted in cyberspace security. The…

Cryptography and Security · Computer Science 2021-05-07 Ruoxi Qin , Linyuan Wang , Xingyuan Chen , Xuehui Du , Bin Yan