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Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to…

Machine Learning · Computer Science 2022-10-17 Zhouxing Shi , Yihan Wang , Huan Zhang , Zico Kolter , Cho-Jui Hsieh

We consider the problem of certified robustness for sequence classification against edit distance perturbations. Naturally occurring inputs of varying lengths (e.g., sentences in natural language processing tasks) present a challenge to…

Computation and Language · Computer Science 2025-11-13 Zhuoqun Huang , Neil G. Marchant , Olga Ohrimenko , Benjamin I. P. Rubinstein

Robustness is a fundamental pillar of Machine Learning (ML) classifiers, substantially determining their reliability. Methods for assessing classifier robustness are therefore essential. In this work, we address the challenge of evaluating…

Machine Learning · Computer Science 2026-01-19 Georg Siedel , Silvia Vock , Andrey Morozov , Stefan Voß

Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class…

Machine Learning · Statistics 2018-09-06 Zac Cranko , Simon Kornblith , Zhan Shi , Richard Nock

As deep learning models continue to advance and are increasingly utilized in real-world systems, the issue of robustness remains a major challenge. Existing certified training methods produce models that achieve high provable robustness…

Machine Learning · Computer Science 2023-07-26 Zhakshylyk Nurlanov , Frank R. Schmidt , Florian Bernard

We propose a principled framework that combines adversarial training and provable robustness verification for training certifiably robust neural networks. We formulate the training problem as a joint optimization problem with both empirical…

Machine Learning · Computer Science 2021-06-08 Jiameng Fan , Wenchao Li

Randomized Smoothing (RS), being one of few provable defenses, has been showing great effectiveness and scalability in terms of defending against $\ell_2$-norm adversarial perturbations. However, the cost of MC sampling needed in RS for…

Machine Learning · Computer Science 2021-08-03 Huimin Zeng , Jiahao Su , Furong Huang

The language models, especially the basic text classification models, have been shown to be susceptible to textual adversarial attacks such as synonym substitution and word insertion attacks. To defend against such attacks, a growing body…

Cryptography and Security · Computer Science 2024-06-12 Xinyu Zhang , Hanbin Hong , Yuan Hong , Peng Huang , Binghui Wang , Zhongjie Ba , Kui Ren

Certifiable local robustness, which rigorously precludes small-norm adversarial examples, has received significant attention as a means of addressing security concerns in deep learning. However, for some classification problems, local…

Machine Learning · Computer Science 2021-06-15 Klas Leino , Matt Fredrikson

Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…

Machine Learning · Computer Science 2019-07-01 Daniel Zügner , Stephan Günnemann

This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of…

Artificial Intelligence · Computer Science 2019-02-07 Haifeng Qian , Mark N. Wegman

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the…

Formal Languages and Automata Theory · Computer Science 2014-10-08 Thomas A. Henzinger , Jan Otop , Roopsha Samanta

We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…

Optimization and Control · Mathematics 2015-09-23 Timothy C. Y. Chan , Philip Allen Mar

It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying…

Machine Learning · Computer Science 2026-02-18 Tom A. Splittgerber

Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the…

Machine Learning · Computer Science 2021-11-18 Jongheon Jeong , Sejun Park , Minkyu Kim , Heung-Chang Lee , Doguk Kim , Jinwoo Shin

We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell\_p$ ball for $p \in [1, \infty]$ and Gaussian noise with an arbitrary covariance matrix. We…

Machine Learning · Computer Science 2018-06-25 Jean-Yves Franceschi , Alhussein Fawzi , Omar Fawzi

It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. One of the fundamental problems in adversarial machine learning is to quantify how much training data is needed in the…

Machine Learning · Computer Science 2023-08-24 Pascale Gourdeau

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…

Information Theory · Computer Science 2025-12-15 Alan J. X. Guo , Sihan Sun , Xiang Wei , Mengyi Wei , Xin Chen

Reachability analysis of neural networks, which seeks to compute or bound the set of outputs attainable over a given input domain, is central to certifying safety and robustness in learning-enabled physical systems. Since exact reachable…

Machine Learning · Computer Science 2026-05-12 Taha Entesari , Mahyar Fazlyab

We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…

Machine Learning · Computer Science 2025-11-11 Peter Blohm , Patrick Indri , Thomas Gärtner , Sagar Malhotra