# Understanding robustness and generalization of artificial neural networks through Fourier masks

arXiv: https://arxiv.org/abs/2203.08822 · HTML: https://mlsanity.com/paper/2203.08822/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Torchattacks: A PyTorch Repository for Adversarial Attacks](https://mlsanity.com/paper/2010.01950/) (2020)
- [On the Effectiveness of Low Frequency Perturbations](https://mlsanity.com/paper/1903.00073/) (2019)
- [On the Structural Sensitivity of Deep Convolutional Networks to the Directions of Fourier Basis Functions](https://mlsanity.com/paper/1809.04098/) (2018)
- [Hold me tight! Influence of discriminative features on deep network boundaries](https://mlsanity.com/paper/2002.06349/) (2020)
- [Towards Frequency-Based Explanation for Robust CNN](https://mlsanity.com/paper/2005.03141/) (2020)
- [Neural Anisotropy Directions](https://mlsanity.com/paper/2006.09717/) (2020)
- [Local Convolutions Cause an Implicit Bias towards High Frequency Adversarial Examples](https://mlsanity.com/paper/2006.11440/) (2020)

## Built on by (most cited first, 3 of 3)

- [Which Frequencies do CNNs Need? Emergent Bottleneck Structure in Feature Learning](https://mlsanity.com/paper/2402.08010/) (2024)
- [Linking convolutional kernel size to generalization bias in face analysis CNNs](https://mlsanity.com/paper/2302.03750/) (2023)
- [Frequency maps reveal the correlation between Adversarial Attacks and Implicit Bias](https://mlsanity.com/paper/2305.15203/) (2023)

## Abstract (arXiv)

Despite the enormous success of artificial neural networks (ANNs) in many disciplines, the characterization of their computations and the origin of key properties such as generalization and robustness remain open questions. Recent literature suggests that robust networks with good generalization properties tend to be biased towards processing low frequencies in images. To explore the frequency bias hypothesis further, we develop an algorithm that allows us to learn modulatory masks highlighting the essential input frequencies needed for preserving a trained network's performance. We achieve this by imposing invariance in the loss with respect to such modulations in the input frequencies. We first use our method to test the low-frequency preference hypothesis of adversarially trained or data-augmented networks. Our results suggest that adversarially robust networks indeed exhibit a low-frequency bias but we find this bias is also dependent on directions in frequency space. However, this is not necessarily true for other types of data augmentation. Our results also indicate that the essential frequencies in question are effectively the ones used to achieve generalization in the first place. Surprisingly, images seen through these modulatory masks are not recognizable and resemble texture-like patterns.