# Robust Adversarial Defense by Tensor Factorization

arXiv: https://arxiv.org/abs/2309.01077 · HTML: https://mlsanity.com/paper/2309.01077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 3 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [CP-decomposition with Tensor Power Method for Convolutional Neural Networks Compression](https://mlsanity.com/paper/1701.07148/) (2017)
- [Learning Low-Rank Approximation for CNNs](https://mlsanity.com/paper/1905.10145/) (2019)
- [L1-norm Tucker Tensor Decomposition](https://mlsanity.com/paper/1904.06455/) (2019)
- [Applying Tensor Decomposition to image for Robustness against Adversarial Attack](https://mlsanity.com/paper/2002.12913/) (2020)
- [Defensive Tensorization](https://mlsanity.com/paper/2110.13859/) (2021)

## Built on by (most cited first, 2 of 2)

- [LoRID: Low-Rank Iterative Diffusion for Adversarial Purification](https://mlsanity.com/paper/2409.08255/) (2024)
- [Model-Free Adversarial Purification via Coarse-To-Fine Tensor Network Representation](https://mlsanity.com/paper/2502.17972/) (2025)

## Abstract (arXiv)

As machine learning techniques become increasingly prevalent in data analysis, the threat of adversarial attacks has surged, necessitating robust defense mechanisms. Among these defenses, methods exploiting low-rank approximations for input data preprocessing and neural network (NN) parameter factorization have shown potential. Our work advances this field further by integrating the tensorization of input data with low-rank decomposition and tensorization of NN parameters to enhance adversarial defense. The proposed approach demonstrates significant defense capabilities, maintaining robust accuracy even when subjected to the strongest known auto-attacks. Evaluations against leading-edge robust performance benchmarks reveal that our results not only hold their ground against the best defensive methods available but also exceed all current defense strategies that rely on tensor factorizations. This study underscores the potential of integrating tensorization and low-rank decomposition as a robust defense against adversarial attacks in machine learning.