ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results

Adele Myers, Saiteja Utpala, Shubham Talbar, Sophia Sanborn, Christian Shewmake, Claire Donnat, Johan Mathe, Umberto Lupo, Rishi Sonthalia, Xinyue Cui, Tom Szwagier, Arthur Pignet, Andri Bergsson, Søren Hauberg, Dmitriy Nielsen, Stefan Sommer, David Klindt, Erik Hermansen, Melvin Vaupel, Benjamin Dunn et al. (8 additional authors not shown)

Abstract: This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learning". The competition asked participants to provide implementations of machine learning algorithms on manifolds that would respect the API of the open-source software Geomstats (manifold part) and Scikit-Learn (machine learning part) or PyTorch. The challenge attracted seven teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.