Certifying Robustness via Topological Representations

Jens Agerberg; Andrea Guidolin; Andrea Martinelli; Pepijn Roos Hoefgeest; David Eklund; Martina Scolamiero

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arXiv · 2501.10876

Certifying Robustness via Topological Representations

Jens Agerberg·Andrea Guidolin·Andrea Martinelli·Pepijn Roos Hoefgeest·David Eklund·Martina Scolamiero

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

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Jens Agerberg, Andrea Guidolin, Andrea Martinelli, Pepijn Roos Hoefgeest, David Eklund, Martina Scolamiero. 2025-01-18. Certifying Robustness via Topological Representations. https://arxiv.org/abs/2501.10876

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