mlsanityData to 14 Oct 2026

An Orthogonal Classifier for Improving the Adversarial Robustness of Neural Networks

arXiv 2105.09109 ↗First posted 19 May 2021cs.CVcited by 7

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Abstract (arXiv)

Neural networks are susceptible to artificially designed adversarial perturbations. Recent efforts have shown that imposing certain modifications on classification layer can improve the robustness of the neural networks. In this paper, we explicitly construct a dense orthogonal weight matrix whose entries have the same magnitude, thereby leading to a novel robust classifier. The proposed classifier avoids the undesired structural redundancy issue in previous work. Applying this classifier in standard training on clean data is sufficient to ensure the high accuracy and good robustness of the model. Moreover, when extra adversarial samples are used, better robustness can be further obtained with the help of a special worst-case loss. Experimental results show that our method is efficient and competitive to many state-of-the-art defensive approaches. Our code is available at urlhttps://github.com/MTandHJ/roboc.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 32 of its 44 references that are in the map. First posted on arXiv 19 May 2021.

Builds on

32 of 44 references.

References · 32

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  4. 2013Intriguing properties of neural networkscited by 5,155
  5. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  6. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  7. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,998
  8. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,517
  9. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,451
  10. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  11. 2015DeepFool: a simple and accurate method to fool deep neural networkscited by 1,318
  12. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
20 more
  1. 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 678
  2. 2020RobustBench: a standardized adversarial robustness benchmarkcited by 661
  3. 2019Adversarial Training for Free!cited by 643
  4. 2017Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networkscited by 486
  5. 2019On Evaluating Adversarial Robustnesscited by 447
  6. 2019Adversarial Examples Improve Image Recognitioncited by 286
  7. 2018Adversarial Logit Pairingcited by 224
  8. 2019Adversarial Training and Robustness for Multiple Perturbationscited by 183
  9. 2019You Only Propagate Once: Accelerating Adversarial Training via Maximal Principlecited by 183
  10. 2018Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Modelscited by 135
  11. 2019Orthogonal Convolutional Neural Networkscited by 123
  12. 2017Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networkscited by 92
  13. 2018Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?cited by 62
  14. 2017All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulationcited by 58
  15. 2019Adversarial Defense by Restricting the Hidden Space of Deep Neural Networkscited by 56
  16. 2018Rethinking Feature Distribution for Loss Functions in Image Classificationcited by 39
  17. 2017Foolbox: A Python toolbox to benchmark the robustness of machine learning modelscited by 20
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  19. 2018Adversarial classification: An adversarial risk analysis approachcited by 4
  20. 2020Improving adversarial robustness of deep neural networks by using semantic informationcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 1; 2024: 2; 2025: 1; 2026: 1.

7 papers.

  1. 2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 9
  2. 2024Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddingscited by 6
  3. 2023Group Orthogonalization Regularization For Vision Models Adaptation and Robustnesscited by 2
  4. 2025Deep Positive-Negative Prototypes for Adversarially Robust Discriminative Prototypical Learningcited by 1
  5. 2022Semantic Autoencoder and Its Potential Usage for Adversarial Attackcited by 0
  6. 2024Adversarial Attacks and Defense for Conversation Entailment Taskcited by 0
  7. 2026XtraLight-MedMamba for Classification of Neoplastic Tubular Adenomascited by 0