# A Singular Value Perspective on Model Robustness

arXiv: https://arxiv.org/abs/2012.03516 · HTML: https://mlsanity.com/paper/2012.03516/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [A Frequency Perspective of Adversarial Robustness](https://mlsanity.com/paper/2111.00861/) (2021)
- [A Unified Game-Theoretic Interpretation of Adversarial Robustness](https://mlsanity.com/paper/2111.03536/) (2021)
- [A Game-Theoretic Taxonomy of Visual Concepts in DNNs](https://mlsanity.com/paper/2106.10938/) (2021)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [A Unified Game-Theoretic Interpretation of Adversarial Robustness](https://mlsanity.com/paper/2103.07364/) (2021)
- [Benign Adversarial Attack: Tricking Models for Goodness](https://mlsanity.com/paper/2107.11986/) (2021)
- [Detecting Adversarial Data via Provable Adversarial Noise Amplification](https://mlsanity.com/paper/2605.02109/) (2026)

## Abstract (arXiv)

Convolutional Neural Networks (CNNs) have made significant progress on several computer vision benchmarks, but are fraught with numerous non-human biases such as vulnerability to adversarial samples. Their lack of explainability makes identification and rectification of these biases difficult, and understanding their generalization behavior remains an open problem. In this work we explore the relationship between the generalization behavior of CNNs and the Singular Value Decomposition (SVD) of images. We show that naturally trained and adversarially robust CNNs exploit highly different features for the same dataset. We demonstrate that these features can be disentangled by SVD for ImageNet and CIFAR-10 trained networks. Finally, we propose Rank Integrated Gradients (RIG), the first rank-based feature attribution method to understand the dependence of CNNs on image rank.