# A Spectral Perspective towards Understanding and Improving Adversarial Robustness

arXiv: https://arxiv.org/abs/2306.14262 · HTML: https://mlsanity.com/paper/2306.14262/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 41 references that are in the map.
- First posted on arXiv 25 Jun 2023.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (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)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (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)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Understanding and Improving Fast Adversarial Training](https://mlsanity.com/paper/2007.02617/) (2020)
- [LAS-AT: Adversarial Training with Learnable Attack Strategy](https://mlsanity.com/paper/2203.06616/) (2022)
- [Metric Learning for Adversarial Robustness](https://mlsanity.com/paper/1909.00900/) (2019)
- [Interpreting Adversarially Trained Convolutional Neural Networks](https://mlsanity.com/paper/1905.09797/) (2019)
- [Shield: Fast, Practical Defense and Vaccination for Deep Learning using JPEG Compression](https://mlsanity.com/paper/1802.06816/) (2018)
- [Guided Adversarial Attack for Evaluating and Enhancing Adversarial Defenses](https://mlsanity.com/paper/2011.14969/) (2020)
- [Efficient Adversarial Training with Transferable Adversarial Examples](https://mlsanity.com/paper/1912.11969/) (2019)
- [Consistency Regularization for Adversarial Robustness](https://mlsanity.com/paper/2103.04623/) (2021)

## Abstract (arXiv)

Deep neural networks (DNNs) are incredibly vulnerable to crafted, imperceptible adversarial perturbations. While adversarial training (AT) has proven to be an effective defense approach, the AT mechanism for robustness improvement is not fully understood. This work investigates AT from a spectral perspective, adding new insights to the design of effective defenses. In particular, we show that AT induces the deep model to focus more on the low-frequency region, which retains the shape-biased representations, to gain robustness. Further, we find that the spectrum of a white-box attack is primarily distributed in regions the model focuses on, and the perturbation attacks the spectral bands where the model is vulnerable. Based on this observation, to train a model tolerant to frequency-varying perturbation, we propose a spectral alignment regularization (SAR) such that the spectral output inferred by an attacked adversarial input stays as close as possible to its natural input counterpart. Experiments demonstrate that SAR and its weight averaging (WA) extension could significantly improve the robust accuracy by 1.14% ~ 3.87% relative to the standard AT, across multiple datasets (CIFAR-10, CIFAR-100 and Tiny ImageNet), and various attacks (PGD, C&W and Autoattack), without any extra data.