# Certifying Robustness via Topological Representations

arXiv: https://arxiv.org/abs/2501.10876 · HTML: https://mlsanity.com/paper/2501.10876/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2025.

## Abstract (arXiv)

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 ε-robustness for samples in a dataset, which we demonstrate on the ORBIT5K dataset representing the orbits of a discrete dynamical system.