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Main Authors: Agerberg, Jens, Guidolin, Andrea, Martinelli, Andrea, Hoefgeest, Pepijn Roos, Eklund, David, Scolamiero, Martina
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.10876
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author Agerberg, Jens
Guidolin, Andrea
Martinelli, Andrea
Hoefgeest, Pepijn Roos
Eklund, David
Scolamiero, Martina
author_facet Agerberg, Jens
Guidolin, Andrea
Martinelli, Andrea
Hoefgeest, Pepijn Roos
Eklund, David
Scolamiero, Martina
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10876
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Certifying Robustness via Topological Representations
Agerberg, Jens
Guidolin, Andrea
Martinelli, Andrea
Hoefgeest, Pepijn Roos
Eklund, David
Scolamiero, Martina
Machine Learning
Computational Geometry
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.
title Certifying Robustness via Topological Representations
topic Machine Learning
Computational Geometry
url https://arxiv.org/abs/2501.10876