# Phase-shifted Adversarial Training

arXiv: https://arxiv.org/abs/2301.04785 · HTML: https://mlsanity.com/paper/2301.04785/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [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)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (2020)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Adversarial Robustness through Local Linearization](https://mlsanity.com/paper/1907.02610/) (2019)
- [AugMax: Adversarial Composition of Random Augmentations for Robust Training](https://mlsanity.com/paper/2110.13771/) (2021)
- [Guided Adversarial Attack for Evaluating and Enhancing Adversarial Defenses](https://mlsanity.com/paper/2011.14969/) (2020)
- [Random Noise Defense Against Query-Based Black-Box Attacks](https://mlsanity.com/paper/2104.11470/) (2021)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems](https://mlsanity.com/paper/1909.11759/) (2019)

## Abstract (arXiv)

Adversarial training has been considered an imperative component for safely deploying neural network-based applications to the real world. To achieve stronger robustness, existing methods primarily focus on how to generate strong attacks by increasing the number of update steps, regularizing the models with the smoothed loss function, and injecting the randomness into the attack. Instead, we analyze the behavior of adversarial training through the lens of response frequency. We empirically discover that adversarial training causes neural networks to have low convergence to high-frequency information, resulting in highly oscillated predictions near each data. To learn high-frequency contents efficiently and effectively, we first prove that a universal phenomenon of frequency principle, i.e., textitlower frequencies are learned first, still holds in adversarial training. Based on that, we propose phase-shifted adversarial training (PhaseAT) in which the model learns high-frequency components by shifting these frequencies to the low-frequency range where the fast convergence occurs. For evaluations, we conduct the experiments on CIFAR-10 and ImageNet with the adaptive attack carefully designed for reliable evaluation. Comprehensive results show that PhaseAT significantly improves the convergence for high-frequency information. This results in improved adversarial robustness by enabling the model to have smoothed predictions near each data.