On Lyapunov exponents and adversarial perturbation

TL;DR

This paper discovers that Lyapunov exponents of 1-D time series representations of images can effectively distinguish adversarial examples from legitimate ones, serving as a pre-classification filter to improve CNN robustness.

Contribution

It introduces a novel use of Lyapunov exponents as a filtering defense against adversarial perturbations in image classification tasks.

Findings

Lyapunov exponents are highly discriminative features for adversarial detection.

The method can pre-classify images as adversarial or legitimate before CNN classification.

Potential false alarms occur with non-adversarial noisy images.

Abstract

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.