# On Lyapunov exponents and adversarial perturbation

arXiv: https://arxiv.org/abs/1802.06927 · HTML: https://mlsanity.com/paper/1802.06927/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2018.

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

- [Chaos Theory and Adversarial Robustness](https://mlsanity.com/paper/2210.13235/) (2022)
- [Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs](https://mlsanity.com/paper/2602.09613/) (2026)
- [Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learning](https://mlsanity.com/paper/2412.17908/) (2024)

## Abstract (arXiv)

In this paper, we would like to disseminate a serendipitous discovery involving Lyapunov exponents of a 1-D time series and their use in serving as a filtering defense tool against a specific kind of deep adversarial perturbation. To this end, we use the state-of-the-art CleverHans library to generate adversarial perturbations against a standard Convolutional Neural Network (CNN) architecture trained on the MNIST as well as the Fashion-MNIST datasets. We empirically demonstrate how the Lyapunov exponents computed on the flattened 1-D vector representations of the images served as highly discriminative features that could be to pre-classify images as adversarial or legitimate before feeding the image into the CNN for classification. We also explore the issue of possible false-alarms when the input images are noisy in a non-adversarial sense.