# Evaluating Adversarial Robustness in the Spatial Frequency Domain

arXiv: https://arxiv.org/abs/2405.06345 · HTML: https://mlsanity.com/paper/2405.06345/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 55 references that are in the map.
- First posted on arXiv 10 May 2024.

## 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)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [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)
- [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)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [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)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Delving into Transferable Adversarial Examples and Black-box Attacks](https://mlsanity.com/paper/1611.02770/) (2016)
- [Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples](https://mlsanity.com/paper/1605.07277/) (2016)
- [Rethinking Spatial Dimensions of Vision Transformers](https://mlsanity.com/paper/2103.16302/) (2021)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [FcaNet: Frequency Channel Attention Networks](https://mlsanity.com/paper/2012.11879/) (2020)
- [Disentangling Adversarial Robustness and Generalization](https://mlsanity.com/paper/1812.00740/) (2018)
- [FSDR: Frequency Space Domain Randomization for Domain Generalization](https://mlsanity.com/paper/2103.02370/) (2021)
- [AutoZOOM: Autoencoder-based Zeroth Order Optimization Method for Attacking Black-box Neural Networks](https://mlsanity.com/paper/1805.11770/) (2018)
- [Fast Algorithms for Convolutional Neural Networks](https://mlsanity.com/paper/1509.09308/) (2015)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have dominated the majority of computer vision tasks. However, CNNs' vulnerability to adversarial attacks has raised concerns about deploying these models to safety-critical applications. In contrast, the Human Visual System (HVS), which utilizes spatial frequency channels to process visual signals, is immune to adversarial attacks. As such, this paper presents an empirical study exploring the vulnerability of CNN models in the frequency domain. Specifically, we utilize the discrete cosine transform (DCT) to construct the Spatial-Frequency (SF) layer to produce a block-wise frequency spectrum of an input image and formulate Spatial Frequency CNNs (SF-CNNs) by replacing the initial feature extraction layers of widely-used CNN backbones with the SF layer. Through extensive experiments, we observe that SF-CNN models are more robust than their CNN counterparts under both white-box and black-box attacks. To further explain the robustness of SF-CNNs, we compare the SF layer with a trainable convolutional layer with identical kernel sizes using two mixing strategies to show that the lower frequency components contribute the most to the adversarial robustness of SF-CNNs. We believe our observations can guide the future design of robust CNN models.