# Towards Understanding the Regularization of Adversarial Robustness on Neural Networks

arXiv: https://arxiv.org/abs/2011.07478 · HTML: https://mlsanity.com/paper/2011.07478/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2020.

## Built on by (most cited first, 12 of 12)

- [Enhance the Visual Representation via Discrete Adversarial Training](https://mlsanity.com/paper/2209.07735/) (2022)
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- [Understanding the robustness difference between stochastic gradient descent and adaptive gradient methods](https://mlsanity.com/paper/2308.06703/) (2023)
- [Certified Defense via Latent Space Randomized Smoothing with Orthogonal Encoders](https://mlsanity.com/paper/2108.00491/) (2021)
- [Disentangled Contrastive Learning for Learning Robust Textual Representations](https://mlsanity.com/paper/2104.04907/) (2021)
- [On the Interaction of Compressibility and Adversarial Robustness](https://mlsanity.com/paper/2507.17725/) (2025)
- [GGT: Graph-Guided Testing for Adversarial Sample Detection of Deep Neural Network](https://mlsanity.com/paper/2107.07043/) (2021)
- [Provable Robust Saliency-based Explanations](https://mlsanity.com/paper/2212.14106/) (2022)
- [Advances in Electron Microscopy with Deep Learning](https://mlsanity.com/paper/2101.01178/) (2021)
- [Robust Ranking Explanations](https://mlsanity.com/paper/2307.04024/) (2023)
- [Omnipotent Adversarial Training in the Wild](https://mlsanity.com/paper/2307.08596/) (2023)

## Abstract (arXiv)

The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be it ε-adversarially robust (AR); that is, to require the model not to change predicted labels when any given input examples are perturbed within a certain range. However, it is observed that such methods would lead to standard performance degradation, i.e., the degradation on natural examples. In this work, we study the degradation through the regularization perspective. We identify quantities from generalization analysis of NNs; with the identified quantities we empirically find that AR is achieved by regularizing/biasing NNs towards less confident solutions by making the changes in the feature space (induced by changes in the instance space) of most layers smoother uniformly in all directions; so to a certain extent, it prevents sudden change in prediction w.r.t. perturbations. However, the end result of such smoothing concentrates samples around decision boundaries, resulting in less confident solutions, and leads to worse standard performance. Our studies suggest that one might consider ways that build AR into NNs in a gentler way to avoid the problematic regularization.