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This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity…

Machine Learning · Computer Science 2024-03-15 Thomas Pethick , Wanyun Xie , Volkan Cevher

While existing work in robust deep learning has focused on small pixel-level norm-based perturbations, this may not account for perturbations encountered in several real-world settings. In many such cases although test data might not be…

Computer Vision and Pattern Recognition · Computer Science 2021-04-09 Tejas Gokhale , Rushil Anirudh , Bhavya Kailkhura , Jayaraman J. Thiagarajan , Chitta Baral , Yezhou Yang

A globally robust deep neural network resists perturbations on all meaningful inputs. Current robustness certification methods emphasize local robustness, struggling to scale and generalize. This paper presents a systematic and efficient…

Machine Learning · Computer Science 2024-06-03 You Li , Guannan Zhao , Shuyu Kong , Yunqi He , Hai Zhou

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

Machine Learning · Computer Science 2022-01-27 Saber Jafarpour , Alexander Davydov , Anton V. Proskurnikov , Francesco Bullo

Existing machine learning-based surrogate modeling methods for transient stability constrained-optimal power flow (TSC-OPF) lack certifications in the presence of unseen disturbances or uncertainties. This may lead to divergence of TSC-OPF…

Systems and Control · Electrical Eng. & Systems 2025-06-12 Tong Su , Junbo Zhao

Adversarial examples pose a security threat to many critical systems built on neural networks. While certified training improves robustness, it also decreases accuracy noticeably. Despite various proposals for addressing this issue, the…

Machine Learning · Statistics 2024-06-21 Ruihan Zhang , Jun Sun

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

Machine Learning · Computer Science 2021-04-30 Patricia Pauli , Anne Koch , Julian Berberich , Paul Kohler , Frank Allgöwer

Post-hoc explanation methods are used with the intent of providing insights about neural networks and are sometimes said to help engender trust in their outputs. However, popular explanations methods have been found to be fragile to minor…

Machine Learning · Computer Science 2022-12-19 Matthew Wicker , Juyeon Heo , Luca Costabello , Adrian Weller

Conformal Prediction (CP) has proven to be an effective post-hoc method for improving the trustworthiness of neural networks by providing prediction sets with finite-sample guarantees. However, under adversarial attacks, classical conformal…

Deep neural networks (DNNs) are vulnerable to adversarial examples, in which DNNs are misled to false outputs due to inputs containing imperceptible perturbations. Adversarial training, a reliable and effective method of defense, may…

Computer Vision and Pattern Recognition · Computer Science 2025-11-14 Zongyuan Zhang , Qingwen Bu , Tianyang Duan , Zheng Lin , Yuhao Qing , Zihan Fang , Heming Cui , Dong Huang

Certified defense using randomized smoothing is a popular technique to provide robustness guarantees for deep neural networks against l2 adversarial attacks. Existing works use this technique to provably secure a pretrained non-robust model…

Machine Learning · Computer Science 2022-10-18 Gaurav Kumar Nayak , Ruchit Rawal , Anirban Chakraborty

Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this…

Machine Learning · Computer Science 2018-11-26 Eric Wong , Frank R. Schmidt , Jan Hendrik Metzen , J. Zico Kolter

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

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

State-of-the-art NLP models can often be fooled by adversaries that apply seemingly innocuous label-preserving transformations (e.g., paraphrasing) to input text. The number of possible transformations scales exponentially with text length,…

Computation and Language · Computer Science 2019-09-04 Robin Jia , Aditi Raghunathan , Kerem Göksel , Percy Liang

Reinforcement learning often uses neural networks to solve complex control tasks. However, neural networks are sensitive to input perturbations, which makes their deployment in safety-critical environments challenging. This work lifts…

Machine Learning · Computer Science 2024-08-20 Manuel Wendl , Lukas Koller , Tobias Ladner , Matthias Althoff

We present a new algorithm to train a robust neural network against adversarial attacks. Our algorithm is motivated by the following two ideas. First, although recent work has demonstrated that fusing randomness can improve the robustness…

Machine Learning · Computer Science 2019-05-07 Xuanqing Liu , Yao Li , Chongruo Wu , Cho-Jui Hsieh

In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…

Machine Learning · Computer Science 2021-07-28 Yejiang Yang , Weiming Xiang

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Machine Learning · Computer Science 2024-10-28 Shudian Zhao , Jan Kronqvist

Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based…

Optimization and Control · Mathematics 2020-02-11 Ren Liu , Xiaoqun Zhang
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