Certifying Robustness via Topological Representations

Jens Agerberg, Andrea Guidolin, Andrea Martinelli, Pepijn Roos Hoefgeest, David Eklund +1 more
1/18/2025
stat.MLcs.CGcs.LG

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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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Cite this paper

@article{agerberg2025certifying,
  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},
  year   = {2025},
  eprint = {2501.10876},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2501.10876v1}
}

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