Certifying Robustness via Topological Representations

TL;DR

This paper introduces a neural network architecture that leverages topological data analysis to learn stable geometric representations, enabling certification of robustness against adversarial perturbations.

Contribution

It presents a novel neural network design that learns stable topological representations with controllable Lipschitz constants for robustness certification.

Findings

Achieves Lipschitz stability in learned representations.

Enables certification of epsilon-robustness in adversarial settings.

Demonstrates effectiveness on the ORBIT5K dataset.

Abstract

We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis. The learned representations enjoy Lipschitz stability with a controllable Lipschitz constant. In adversarial learning, this stability can be used to certify $\epsilon$-robustness for samples in a dataset, which we demonstrate on the ORBIT5K dataset representing the orbits of a discrete dynamical system.