# Lower Difficulty and Better Robustness: A Bregman Divergence Perspective for Adversarial Training

arXiv: https://arxiv.org/abs/2208.12511 · HTML: https://mlsanity.com/paper/2208.12511/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Adversarial Examples Improve Image Recognition](https://mlsanity.com/paper/1911.09665/) (2019)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [On Detecting Adversarial Perturbations](https://mlsanity.com/paper/1702.04267/) (2017)
- [Understanding and Improving Fast Adversarial Training](https://mlsanity.com/paper/2007.02617/) (2020)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [MMA Training: Direct Input Space Margin Maximization through Adversarial Training](https://mlsanity.com/paper/1812.02637/) (2018)
- [Are Labels Required for Improving Adversarial Robustness?](https://mlsanity.com/paper/1905.13725/) (2019)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Models](https://mlsanity.com/paper/1808.01688/) (2018)
- [Robustness and Accuracy Could Be Reconcilable by (Proper) Definition](https://mlsanity.com/paper/2202.10103/) (2022)
- [Universal Adversarial Training](https://mlsanity.com/paper/1811.11304/) (2018)
- [Revisiting Adversarial Robustness Distillation: Robust Soft Labels Make Student Better](https://mlsanity.com/paper/2108.07969/) (2021)

## Abstract (arXiv)

In this paper, we investigate on improving the adversarial robustness obtained in adversarial training (AT) via reducing the difficulty of optimization. To better study this problem, we build a novel Bregman divergence perspective for AT, in which AT can be viewed as the sliding process of the training data points on the negative entropy curve. Based on this perspective, we analyze the learning objectives of two typical AT methods, i.e., PGD-AT and TRADES, and we find that the optimization process of TRADES is easier than PGD-AT for that TRADES separates PGD-AT. In addition, we discuss the function of entropy in TRADES, and we find that models with high entropy can be better robustness learners. Inspired by the above findings, we propose two methods, i.e., FAIT and MER, which can both not only reduce the difficulty of optimization under the 10-step PGD adversaries, but also provide better robustness. Our work suggests that reducing the difficulty of optimization under the 10-step PGD adversaries is a promising approach for enhancing the adversarial robustness in AT.