Deep learning models are known to be vulnerable to small malicious perturbations producing so-called adversarial examples. Vulnerability to adversarial examples is of particular concern in the case of models developed to operate in security- and safety-critical situations. As a consequence, the study of robustness properties of deep learning models has recently attracted significant attention.

In this talk we discuss how the stability results for the invariants of Topological Data Analysis can be exploited to design machine learning models with robustness guarantees. We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams. The learned representations enjoy Lipschitz stability with a controllable Lipschitz constant. In adversarial learning, this stability can be used to certify robustness for samples in a dataset, as we demonstrate on synthetic data.