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Distributionally Robust (DR) optimization aims to certify worst-case risk within a Wasserstein uncertainty set. Current certifications typically rely either on global Lipschitz bounds, which are often conservative, or on local gradient…

Optimization and Control · Mathematics 2026-04-09 Hong T. M. Chu

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

Methodology · Statistics 2023-11-01 Juntong Chen

Training neural networks which are robust to adversarial attacks remains an important problem in deep learning, especially as heavily overparameterized models are adopted in safety-critical settings. Drawing from recent work which…

Machine Learning · Computer Science 2024-10-17 Daniel Kuelbs , Sanjay Lall , Mert Pilanci

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform…

Programming Languages · Computer Science 2019-05-02 Greg Anderson , Shankara Pailoor , Isil Dillig , Swarat Chaudhuri

Few-pixel attacks mislead a classifier by modifying a few pixels of an image. Their perturbation space is an $\ell_0$-ball, which is not convex, unlike $\ell_p$-balls for $p\geq1$. However, existing local robustness verifiers typically…

Machine Learning · Computer Science 2026-03-10 Yuval Shapira , Dana Drachsler-Cohen

Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust…

Machine Learning · Computer Science 2026-03-03 Wenxin Li , Wenchao Liu , Chuan Wang , Qi Gao , Yin Ma , Hai Wei , Kai Wen

Empirical evaluation of deep learning models against adversarial attacks entails solving nontrivial constrained optimization problems. Popular algorithms for solving these constrained problems rely on projected gradient descent (PGD) and…

Machine Learning · Computer Science 2022-11-15 Hengyue Liang , Buyun Liang , Ying Cui , Tim Mitchell , Ju Sun

Neural networks are prone to misclassify slightly modified input images. Recently, many defences have been proposed, but none have improved the robustness of neural networks consistently. Here, we propose to use adversarial attacks as a…

Neural and Evolutionary Computing · Computer Science 2021-06-11 Shashank Kotyan , Danilo Vasconcellos Vargas

Previous work has shown that a neural network with the rectified linear unit (ReLU) activation function leads to a convex polyhedral decomposition of the input space. These decompositions can be represented by a dual graph with vertices…

Computer Vision and Pattern Recognition · Computer Science 2022-12-06 Huma Jamil , Yajing Liu , Christina M. Cole , Nathaniel Blanchard , Emily J. King , Michael Kirby , Christopher Peterson

We develop a geometric approximation theory for deep feed-forward neural networks with ReLU activations. Given a $d$-dimensional hypersurface in $\mathbb{R}^{d+1}$ represented as the graph of a $C^2$-function $\phi$, we show that a deep…

Machine Learning · Computer Science 2024-07-08 Jonatan Vallin , Karl Larsson , Mats G. Larson

Formal verification of deep neural networks is increasingly required in safety-critical domains, yet exact reasoning over piecewise-linear (PWL) activations such as ReLU suffers from a combinatorial explosion of activation patterns. This…

Rings and Algebras · Mathematics 2026-01-01 Chandrasekhar Gokavarapu

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs)…

Optimization and Control · Mathematics 2024-05-22 Christopher Hojny , Shiqiang Zhang , Juan S. Campos , Ruth Misener

Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU…

Machine Learning · Computer Science 2026-02-23 Yuhao Mao , Yani Zhang , Martin Vechev

In recent years several adversarial attacks and defenses have been proposed. Often seemingly robust models turn out to be non-robust when more sophisticated attacks are used. One way out of this dilemma are provable robustness guarantees.…

Machine Learning · Computer Science 2020-04-27 Francesco Croce , Matthias Hein

We define the local complexity of a neural network with continuous piecewise linear activations as a measure of the density of linear regions over an input data distribution. We show theoretically that ReLU networks that learn…

Machine Learning · Computer Science 2025-07-15 Niket Patel , Guido Montufar

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Machine Learning · Computer Science 2025-11-11 Longqing Ye

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…

Machine Learning · Computer Science 2024-06-17 Matthias König , Xiyue Zhang , Holger H. Hoos , Marta Kwiatkowska , Jan N. van Rijn

We present a generic Reinforcement Learning (RL) framework optimized for crafting adversarial attacks on different model types spanning from ECG signal analysis (1D), image classification (2D), and video classification (3D). The framework…

Machine Learning · Computer Science 2024-04-23 Soumyendu Sarkar , Ashwin Ramesh Babu , Sajad Mousavi , Vineet Gundecha , Avisek Naug , Sahand Ghorbanpour

We develop fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions. Our work leverages a convex reformulation of the standard weight-decay penalized training problem as a set…

Machine Learning · Computer Science 2025-04-10 Aaron Mishkin , Arda Sahiner , Mert Pilanci

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Optimization and Control · Mathematics 2025-10-07 Rajiv Sambharya , Jinho Bok , Nikolai Matni , George Pappas