Certifying Robustness via Topological Representations
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912193737392128 |
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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 |