  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 practical
use in applications is often hindered by two major limitations: the
computational complexity required to compute such descriptors exactly, and
their sensitivity to even low-level proportions of outliers. In this work, we
propose to bypass these two burdens in a data-driven setting by entrusting the
estimation of (vectorization of) PDs built on top of point clouds to a neural
network architecture that we call RipsNet. Once trained on a given data set,
RipsNet can estimate topological descriptors on test data very efficiently with
generalization capacity. Furthermore, we prove that RipsNet is robust to input
perturbations in terms of the 1-Wasserstein distance, a major improvement over
the standard computation of PDs that only enjoys Hausdorff stability, yielding
RipsNet to substantially outperform exactly-computed PDs in noisy settings. We
showcase the use of RipsNet on both synthetic and real-world data. Our
open-source implementation is publicly available at
https://github.com/hensel-f/ripsnet and will be included in the Gudhi library.
