Certifying Robustness via Topological Representations
This addresses the challenge of ensuring robustness against adversarial attacks in machine learning, particularly for applications involving topological data, but it appears incremental as it builds on existing topological methods.
The paper tackled the problem of certifying robustness in adversarial learning by proposing a neural network architecture that learns Lipschitz-stable geometric representations from persistence diagrams, demonstrating this on the ORBIT5K dataset to certify ε-robustness.
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.