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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

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

Deep neural networks are easily fooled by small perturbations known as adversarial attacks. Adversarial Training (AT) is a technique aimed at learning features robust to such attacks and is widely regarded as a very effective defense.…

Machine Learning · Computer Science 2020-09-11 Theodoros Tsiligkaridis , Jay Roberts

The progress in the last decade has enabled machine learning models to achieve impressive performance across a wide range of tasks in Computer Vision. However, a plethora of works have demonstrated the susceptibility of these models to…

Machine Learning · Computer Science 2020-02-06 B. S. Vivek , R. Venkatesh Babu

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness…

Machine Learning · Computer Science 2019-03-11 Francesco Croce , Maksym Andriushchenko , Matthias Hein

Recent studies indicate that current adversarial attack methods are flawed and easy to fail when encountering some deliberately designed defense. Sometimes even a slight modification in the model details will invalidate the attack. We find…

Computer Vision and Pattern Recognition · Computer Science 2020-09-18 Chaohao Fu , Hongbin Chen , Na Ruan , Weijia Jia

Adversarial training is one of the most popular ways to learn robust models but is usually attack-dependent and time costly. In this paper, we propose the MACER algorithm, which learns robust models without using adversarial training but…

Machine Learning · Computer Science 2022-03-15 Runtian Zhai , Chen Dan , Di He , Huan Zhang , Boqing Gong , Pradeep Ravikumar , Cho-Jui Hsieh , Liwei Wang

This paper proposes a new algorithmic framework, predictor-verifier training, to train neural networks that are verifiable, i.e., networks that provably satisfy some desired input-output properties. The key idea is to simultaneously train…

Generative Adversarial Networks (GANs) are known to be difficult to train, despite considerable research effort. Several regularization techniques for stabilizing training have been proposed, but they introduce non-trivial computational…

Machine Learning · Computer Science 2020-02-20 Han Zhang , Zizhao Zhang , Augustus Odena , Honglak Lee

Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper…

Machine Learning · Computer Science 2025-04-10 Blaise Delattre , Paul Caillon , Quentin Barthélemy , Erwan Fagnou , Alexandre Allauzen

Graph Laplacian (GL)-based semi-supervised learning is one of the most used approaches for classifying nodes in a graph. Understanding and certifying the adversarial robustness of machine learning (ML) algorithms has attracted large amounts…

Machine Learning · Computer Science 2021-04-23 Matthew Thorpe , Bao Wang

Deep Neural Networks, despite their great success in diverse domains, are provably sensitive to small perturbations on correctly classified examples and lead to erroneous predictions. Recently, it was proposed that this behavior can be…

Machine Learning · Computer Science 2020-09-29 Nan Xu , Oluwaseyi Feyisetan , Abhinav Aggarwal , Zekun Xu , Nathanael Teissier

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

Machine Learning · Computer Science 2025-09-24 Steffen Schotthöfer , H. Lexie Yang , Stefan Schnake

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

Machine Learning · Computer Science 2022-06-09 Alexander Robey , Luiz F. O. Chamon , George J. Pappas , Hamed Hassani

Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…

Machine Learning · Computer Science 2023-07-18 Aounon Kumar , Alexander Levine , Tom Goldstein , Soheil Feizi

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

Adversarial training is widely used to improve the robustness of deep neural networks to adversarial attack. However, adversarial training is prone to overfitting, and the cause is far from clear. This work sheds light on the mechanisms…

Machine Learning · Computer Science 2022-12-12 Lin Li , Michael Spratling

Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…

Machine Learning · Computer Science 2025-07-16 Stefan Balauca , Mark Niklas Müller , Yuhao Mao , Maximilian Baader , Marc Fischer , Martin Vechev

Training certifiably robust neural networks remains a notoriously hard problem. On one side, adversarial training optimizes under-approximations of the worst-case loss, which leads to insufficient regularization for certification, while on…

Machine Learning · Computer Science 2023-10-26 Yuhao Mao , Mark Niklas Müller , Marc Fischer , Martin Vechev

Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…

Machine Learning · Computer Science 2024-04-29 Emmanouil Seferis , Stefanos Kollias , Chih-Hong Cheng