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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

Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that…

Machine Learning · Computer Science 2019-02-19 Vincent Tjeng , Kai Xiao , Russ Tedrake

Deep neural networks are capable of training fast and generalizing well within many domains. Despite their promising performance, deep networks have shown sensitivities to perturbations of their inputs (e.g., adversarial examples) and their…

Machine Learning · Computer Science 2020-07-09 Justin Goodwin , Olivia Brown , Victoria Helus

In recent years, neural networks have demonstrated outstanding effectiveness in a large amount of applications.However, recent works have shown that neural networks are susceptible to adversarial examples, indicating possible flaws…

Machine Learning · Computer Science 2018-06-08 Fuxun Yu , Zirui Xu , Yanzhi Wang , Chenchen Liu , Xiang Chen

Training neural networks with verifiable robustness guarantees is challenging. Several existing approaches utilize linear relaxation based neural network output bounds under perturbation, but they can slow down training by a factor of…

Machine Learning · Computer Science 2019-11-28 Huan Zhang , Hongge Chen , Chaowei Xiao , Sven Gowal , Robert Stanforth , Bo Li , Duane Boning , Cho-Jui Hsieh

As spiking neural networks (SNNs) are deployed increasingly in real-world efficiency critical applications, the security concerns in SNNs attract more attention. Currently, researchers have already demonstrated an SNN can be attacked with…

Neural and Evolutionary Computing · Computer Science 2022-05-04 Ling Liang , Kaidi Xu , Xing Hu , Lei Deng , Yuan Xie

Verifiable training has shown success in creating neural networks that are provably robust to a given amount of noise. However, despite only enforcing a single robustness criterion, its performance scales poorly with dataset complexity. On…

Machine Learning · Computer Science 2020-12-16 Shiqi Wang , Kevin Eykholt , Taesung Lee , Jiyong Jang , Ian Molloy

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…

Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…

Machine Learning · Computer Science 2023-09-06 Ruihan Zhang , Peixin Zhang , Jun Sun

Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small $\ell_\infty$-noise). For other perturbations, these defenses offer no guarantees and, at times, even…

Machine Learning · Computer Science 2019-10-21 Florian Tramèr , Dan Boneh

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…

Machine Learning · Computer Science 2019-11-12 Bai Li , Changyou Chen , Wenlin Wang , Lawrence Carin

Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We…

Machine Learning · Computer Science 2021-02-03 Akhilan Boopathy , Tsui-Wei Weng , Sijia Liu , Pin-Yu Chen , Gaoyuan Zhang , Luca Daniel

Neural network robustness has become a central topic in machine learning in recent years. Most training algorithms that improve the model's robustness to adversarial and common corruptions also introduce a large computational overhead,…

Machine Learning · Computer Science 2021-12-07 Weizhe Hua , Yichi Zhang , Chuan Guo , Zhiru Zhang , G. Edward Suh

Neural Networks (NNs) are vulnerable to adversarial examples. Such inputs differ only slightly from their benign counterparts yet provoke misclassifications of the attacked NNs. The required perturbations to craft the examples are often…

Cryptography and Security · Computer Science 2020-09-30 Philip Sperl , Konstantin Böttinger

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

Machine Learning · Computer Science 2021-12-13 Saber Jafarpour , Matthew Abate , Alexander Davydov , Francesco Bullo , Samuel Coogan

Adversarial training is arguably the most popular way to provide empirical robustness against specific adversarial examples. While variants based on multi-step attacks incur significant computational overhead, single-step variants are…

Machine Learning · Computer Science 2025-03-25 Alessandro De Palma , Serge Durand , Zakaria Chihani , François Terrier , Caterina Urban

Mixup is a procedure for data augmentation that trains networks to make smoothly interpolated predictions between datapoints. Adversarial training is a strong form of data augmentation that optimizes for worst-case predictions in a compact…

Machine Learning · Computer Science 2021-03-23 Jason Bunk , Srinjoy Chattopadhyay , B. S. Manjunath , Shivkumar Chandrasekaran

Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness…

Machine Learning · Computer Science 2025-08-06 Lukas Koller , Tobias Ladner , Matthias Althoff

Lifted neural networks (i.e. neural architectures explicitly optimizing over respective network potentials to determine the neural activities) can be combined with a type of adversarial training to gain robustness for internal as well as…

Machine Learning · Computer Science 2025-03-12 Christopher Zach
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