# Subspace Defense: Discarding Adversarial Perturbations by Learning a Subspace for Clean Signals

arXiv: https://arxiv.org/abs/2403.16176 · HTML: https://mlsanity.com/paper/2403.16176/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 24 Mar 2024.

## Builds on (most cited first, 29 of 29)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailment](https://mlsanity.com/paper/1907.11932/) (2019)
- [BERT-ATTACK: Adversarial Attack Against BERT Using BERT](https://mlsanity.com/paper/2004.09984/) (2020)
- [Generating Natural Language Adversarial Examples](https://mlsanity.com/paper/1804.07998/) (2018)
- [TextBugger: Generating Adversarial Text Against Real-world Applications](https://mlsanity.com/paper/1812.05271/) (2018)
- [Black-box Generation of Adversarial Text Sequences to Evade Deep Learning Classifiers](https://mlsanity.com/paper/1801.04354/) (2018)
- [BAE: BERT-based Adversarial Examples for Text Classification](https://mlsanity.com/paper/2004.01970/) (2020)
- [Adversarial Example Generation with Syntactically Controlled Paraphrase Networks](https://mlsanity.com/paper/1804.06059/) (2018)
- [FreeLB: Enhanced Adversarial Training for Natural Language Understanding](https://mlsanity.com/paper/1909.11764/) (2019)
- [Feature Purification: How Adversarial Training Performs Robust Deep Learning](https://mlsanity.com/paper/2005.10190/) (2020)
- [InfoBERT: Improving Robustness of Language Models from An Information Theoretic Perspective](https://mlsanity.com/paper/2010.02329/) (2020)
- [A Boundary Tilting Persepective on the Phenomenon of Adversarial Examples](https://mlsanity.com/paper/1608.07690/) (2016)
- [How Robust is GPT-3.5 to Predecessors? A Comprehensive Study on Language Understanding Tasks](https://mlsanity.com/paper/2303.00293/) (2023)
- [Generating Natural Language Attacks in a Hard Label Black Box Setting](https://mlsanity.com/paper/2012.14956/) (2020)
- [Defense against Universal Adversarial Perturbations](https://mlsanity.com/paper/1711.05929/) (2017)
- [CAT-Gen: Improving Robustness in NLP Models via Controlled Adversarial Text Generation](https://mlsanity.com/paper/2010.02338/) (2020)
- [Distilling Robust and Non-Robust Features in Adversarial Examples by Information Bottleneck](https://mlsanity.com/paper/2204.02735/) (2022)
- [Using Adversarial Attacks to Reveal the Statistical Bias in Machine Reading Comprehension Models](https://mlsanity.com/paper/2105.11136/) (2021)
- [Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery](https://mlsanity.com/paper/1711.09492/) (2017)
- [CEB Improves Model Robustness](https://mlsanity.com/paper/2002.05380/) (2020)

## Built on by (most cited first, 1 of 1)

- [Breaking the Adversarial Robustness-Performance Trade-off in Text Classification via Manifold Purification](https://mlsanity.com/paper/2511.07888/) (2025)

## Abstract (arXiv)

Deep neural networks (DNNs) are notoriously vulnerable to adversarial attacks that place carefully crafted perturbations on normal examples to fool DNNs. To better understand such attacks, a characterization of the features carried by adversarial examples is needed. In this paper, we tackle this challenge by inspecting the subspaces of sample features through spectral analysis. We first empirically show that the features of either clean signals or adversarial perturbations are redundant and span in low-dimensional linear subspaces respectively with minimal overlap, and the classical low-dimensional subspace projection can suppress perturbation features out of the subspace of clean signals. This makes it possible for DNNs to learn a subspace where only features of clean signals exist while those of perturbations are discarded, which can facilitate the distinction of adversarial examples. To prevent the residual perturbations that is inevitable in subspace learning, we propose an independence criterion to disentangle clean signals from perturbations. Experimental results show that the proposed strategy enables the model to inherently suppress adversaries, which not only boosts model robustness but also motivates new directions of effective adversarial defense.