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The use of topological descriptors in modern machine learning applications,such as Persistence Diagrams (PDs) arising from Topological Data Analysis(TDA), has shown great potential in various domains. However, their practicaluse in applications is often hindered by two major limitations: thecomputational complexity required to compute such descriptors exactly, andtheir sensitivity to even low-level proportions of outliers. In this work, wepropose to bypass these two burdens in a data-driven setting by entrusting theestimation of (vectorization of) PDs built on top of point clouds to a neuralnetwork architecture that we call RipsNet. Once trained on a given data set,RipsNet can estimate topological descriptors on test data very efficiently withgeneralization capacity. Furthermore, we prove that RipsNet is robust to inputperturbations in terms of the 1-Wasserstein distance, a major improvement overthe standard computation of PDs that only enjoys Hausdorff stability, yieldingRipsNet to substantially outperform exactly-computed PDs in noisy settings. Weshowcase the use of RipsNet on both synthetic and real-world data. Ouropen-source implementation is publicly available athttps://github.com/hensel-f/ripsnet and will be included in the Gudhi library.

RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds