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Generative learning, recognized for its effective modeling of data distributions, offers inherent advantages in handling out-of-distribution instances, especially for enhancing robustness to adversarial attacks. Among these, diffusion…

Machine Learning · Computer Science 2025-02-25 Huanran Chen , Yinpeng Dong , Shitong Shao , Zhongkai Hao , Xiao Yang , Hang Su , Jun Zhu

We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…

Machine Learning · Computer Science 2019-04-15 Nicolas Couellan

The Lipschitz bound, a technique from robust statistics, can limit the maximum changes in the output concerning the input, taking into account associated irrelevant biased factors. It is an efficient and provable method for examining the…

Machine Learning · Computer Science 2023-12-13 Yaning Jia , Chunhui Zhang

This paper proposes a new regularization technique for reinforcement learning (RL) towards making policy and value functions smooth and stable. RL is known for the instability of the learning process and the sensitivity of the acquired…

Robotics · Computer Science 2023-07-04 Taisuke Kobayashi

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…

Machine Learning · Computer Science 2022-03-11 Guangyi Liu , Arash Amini , Martin Takac , Nader Motee

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

Neural networks are often highly sensitive to input and weight perturbations. This sensitivity has been linked to pathologies such as vulnerability to adversarial examples, divergent training, and overfitting. To combat these problems, past…

Machine Learning · Computer Science 2025-07-18 Laker Newhouse , R. Preston Hess , Franz Cesista , Andrii Zahorodnii , Jeremy Bernstein , Phillip Isola

For sensitive problems, such as medical imaging or fraud detection, Neural Network (NN) adoption has been slow due to concerns about their reliability, leading to a number of algorithms for explaining their decisions. NNs have also been…

Machine Learning · Computer Science 2019-11-06 Walt Woods , Jack Chen , Christof Teuscher

This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional…

Systems and Control · Electrical Eng. & Systems 2026-03-27 Daniele Ravasio , Danilo Saccani , Marcello Farina , Giancarlo Ferrari-Trecate

Research on adversarial examples in computer vision tasks has shown that small, often imperceptible changes to an image can induce misclassification, which has security implications for a wide range of image processing systems. Considering…

Computer Vision and Pattern Recognition · Computer Science 2019-04-05 Jérôme Rony , Luiz G. Hafemann , Luiz S. Oliveira , Ismail Ben Ayed , Robert Sabourin , Eric Granger

This note shows that, for a fixed Lipschitz constant $L > 0$, one layer neural networks that are $L$-Lipschitz are dense in the set of all $L$-Lipschitz functions with respect to the uniform norm on bounded sets.

Machine Learning · Statistics 2020-09-30 Stephan Eckstein

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

This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…

Optimization and Control · Mathematics 2021-12-08 Henk J. van Waarde , Rodolphe Sepulchre

Despite recent success, state-of-the-art learning-based models remain highly vulnerable to input changes such as adversarial examples. In order to obtain certifiable robustness against such perturbations, recent work considers…

Machine Learning · Computer Science 2023-09-13 Max Losch , David Stutz , Bernt Schiele , Mario Fritz

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

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

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead…

Machine Learning · Computer Science 2025-11-27 Erh-Chung Chen , Pin-Yu Chen , I-Hsin Chung , Che-Rung Lee

While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…

Machine Learning · Computer Science 2022-02-11 Zhenyu Zhu , Fabian Latorre , Grigorios G Chrysos , Volkan Cevher

A crucial problem in neural networks is to select the most appropriate number of hidden neurons and obtain tight statistical risk bounds. In this work, we present a new perspective towards the bias-variance tradeoff in neural networks. As…

Machine Learning · Computer Science 2020-10-05 Gen Li , Yuantao Gu , Jie Ding

Quantized neural network (NN) with a reduced bit precision is an effective solution to reduces the computational and memory resource requirements and plays a vital role in machine learning. However, it is still challenging to avoid the…

Machine Learning · Computer Science 2020-10-23 Xiaobin Li , Hongxu Jiang , Shuangxi Huang , Fangzheng Tian