# Enhancing Robustness of Neural Networks through Fourier Stabilization

arXiv: https://arxiv.org/abs/2106.04435 · HTML: https://mlsanity.com/paper/2106.04435/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [A Benchmark Dataset for Learning to Intervene in Online Hate Speech](https://mlsanity.com/paper/1909.04251/) (2019)
- [Defending Against Physically Realizable Attacks on Image Classification](https://mlsanity.com/paper/1909.09552/) (2019)
- [Accurate, reliable and fast robustness evaluation](https://mlsanity.com/paper/1907.01003/) (2019)
- [Adversarial Perturbations Against Deep Neural Networks for Malware Classification](https://mlsanity.com/paper/1606.04435/) (2016)
- [Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution](https://mlsanity.com/paper/1810.12272/) (2018)
- [Attacking Binarized Neural Networks](https://mlsanity.com/paper/1711.00449/) (2017)
- [Improving Robustness of ML Classifiers against Realizable Evasion Attacks Using Conserved Features](https://mlsanity.com/paper/1708.08327/) (2017)
- [CodNN -- Robust Neural Networks From Coded Classification](https://mlsanity.com/paper/2004.10700/) (2020)

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

- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [DFT-Based Adversarial Attack Detection in MRI Brain Imaging: Enhancing Diagnostic Accuracy in Alzheimer's Case Studies](https://mlsanity.com/paper/2408.08489/) (2024)

## Abstract (arXiv)

Despite the considerable success of neural networks in security settings such as malware detection, such models have proved vulnerable to evasion attacks, in which attackers make slight changes to inputs (e.g., malware) to bypass detection. We propose a novel approach, Fourier stabilization, for designing evasion-robust neural networks with binary inputs. This approach, which is complementary to other forms of defense, replaces the weights of individual neurons with robust analogs derived using Fourier analytic tools. The choice of which neurons to stabilize in a neural network is then a combinatorial optimization problem, and we propose several methods for approximately solving it. We provide a formal bound on the per-neuron drop in accuracy due to Fourier stabilization, and experimentally demonstrate the effectiveness of the proposed approach in boosting robustness of neural networks in several detection settings. Moreover, we show that our approach effectively composes with adversarial training.