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A constrained optimization approach to improve robustness of neural networks

arXiv 2409.13770 ↗First posted 18 Sep 2024cs.LG math.OCcited by 0

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Abstract (arXiv)

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 adversary-correction constraints to ensure correct classification of adversarial data and minimizes changes to the model parameters. We propose an efficient cutting-plane-based algorithm to iteratively solve the large-scale nonconvex optimization problem by approximating the feasible region through polyhedral cuts and balancing between robustness and accuracy. Computational experiments on standard datasets such as MNIST and CIFAR10 demonstrate that the proposed approach significantly improves robustness, even with a very small set of adversarial data, while maintaining minimal impact on accuracy.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 41 references that are in the map. First posted on arXiv 18 Sep 2024.

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24 of 41 references.

References · 24

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  3. 2013Intriguing properties of neural networkscited by 5,155
  4. 2016Adversarial Machine Learning at Scalecited by 936
  5. 2016Practical Black-Box Attacks against Machine Learningcited by 903
  6. 2017Ensemble Adversarial Training: Attacks and Defensescited by 840
  7. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  8. 2017Defense against Adversarial Attacks Using High-Level Representation Guided Denoisercited by 329
  9. 2018Certified Defenses against Adversarial Examplescited by 306
  10. 2019Adversarial Robustness through Local Linearizationcited by 146
  11. 2016Technical Report on the CleverHans v2.1.0 Adversarial Examples Librarycited by 124
  12. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
12 more
  1. 2019Training Robust Deep Neural Networks via Adversarial Noise Propagationcited by 62
  2. 2019Certifiable Robustness and Robust Training for Graph Convolutional Networkscited by 59
  3. 2020Adversarial Machine Learning in Image Classification: A Survey Towards the Defender's Perspectivecited by 59
  4. 2021Fast Certified Robust Training with Short Warmupcited by 46
  5. 2022The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networkscited by 41
  6. 2021Partition-based formulations for mixed-integer optimization of trained ReLU neural networkscited by 39
  7. 2024Certified Robustness to Data Poisoning in Gradient-Based Trainingcited by 18
  8. 2020Understanding and Increasing Efficiency of Frank-Wolfe Adversarial Trainingcited by 14
  9. 2018A Survey of Safety and Trustworthiness of Deep Neural Networks: Verification, Testing, Adversarial Attack and Defence, and Interpretabilitycited by 8
  10. 2020Optimal training of integer-valued neural networks with mixed integer programmingcited by 6
  11. 2023Taming Binarized Neural Networks and Mixed-Integer Programscited by 4
  12. 2023Model-based feature selection for neural networks: A mixed-integer programming approachcited by 2

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