Certifying Robustness via Topological Representations
Machine Learning
2025-01-22 v1 Computational Geometry
Machine Learning
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 -robustness for samples in a dataset, which we demonstrate on the ORBIT5K dataset representing the orbits of a discrete dynamical system.
Cite
@article{arxiv.2501.10876,
title = {Certifying Robustness via Topological Representations},
author = {Jens Agerberg and Andrea Guidolin and Andrea Martinelli and Pepijn Roos Hoefgeest and David Eklund and Martina Scolamiero},
journal= {arXiv preprint arXiv:2501.10876},
year = {2025}
}
Comments
Workshop on Symmetry and Geometry in Neural Representations (NeurReps) at NeurIPS 2024, Extended Abstract Track