mlsanityData to 7 Oct 2026

Improving Adversarial Robustness with Hypersphere Embedding and Angular-based Regularizations

arXiv 2303.08289 ↗First posted 15 Mar 2023cs.LG cs.AI cs.CVcited by 5

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Abstract (arXiv)

Adversarial training (AT) methods have been found to be effective against adversarial attacks on deep neural networks. Many variants of AT have been proposed to improve its performance. Pang et al. [1] have recently shown that incorporating hypersphere embedding (HE) into the existing AT procedures enhances robustness. We observe that the existing AT procedures are not designed for the HE framework, and thus fail to adequately learn the angular discriminative information available in the HE framework. In this paper, we propose integrating HE into AT with regularization terms that exploit the rich angular information available in the HE framework. Specifically, our method, termed angular-AT, adds regularization terms to AT that explicitly enforce weight-feature compactness and inter-class separation; all expressed in terms of angular features. Experimental results show that angular-AT further improves adversarial robustness.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 19 of its 26 references that are in the map. First posted on arXiv 15 Mar 2023.

Builds on

19 of 26 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  4. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  5. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  6. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  7. 2018CosFace: Large Margin Cosine Loss for Deep Face Recognitioncited by 968
  8. 2017SphereFace: Deep Hypersphere Embedding for Face Recognitioncited by 733
  9. 2019Unlabeled Data Improves Adversarial Robustnesscited by 415
  10. 2016Large-Margin Softmax Loss for Convolutional Neural Networkscited by 296
  11. 2017NormFace: L2 Hypersphere Embedding for Face Verificationcited by 237
  12. 2018Adversarial Logit Pairingcited by 224
7 more
  1. 2018Adversarial Risk and the Dangers of Evaluating Against Weak Attackscited by 221
  2. 2022(Certified!!) Adversarial Robustness for Free!cited by 130
  3. 2020Boosting Adversarial Training with Hypersphere Embeddingcited by 97
  4. 2019Hyperspherical Prototype Networkscited by 85
  5. 2020Improving Adversarial Robustness via Probabilistically Compact Loss with Logit Constraintscited by 10
  6. 2021Anomaly Detection of Adversarial Examples using Class-conditional Generative Adversarial Networkscited by 3
  7. 2019PR Product: A Substitute for Inner Product in Neural Networkscited by 1

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Cited by year

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

5 papers.

  1. 2023Fast Certification of Vision-Language Models Using Incremental Randomized Smoothingcited by 4
  2. 2023Vulnerability-Aware Instance Reweighting For Adversarial Trainingcited by 2
  3. 2024Improving Adversarial Training using Vulnerability-Aware Perturbation Budgetcited by 1
  4. 2024Standard-Deviation-Inspired Regularization for Improving Adversarial Robustnesscited by 0
  5. 2025Sharpness-Aware Geometric Defense for Robust Out-Of-Distribution Detectioncited by 0