ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain
Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna, Federica Baccini, Mathilde Papillon, Miquel Ferriol-Galmés, Mustafa Hajij, Theodore Papamarkou, Maria Sofia Bucarelli, Olga Zaghen, Johan Mathe, Audun Myers, Scott Mahan, Hansen Lillemark, Sharvaree Vadgama, Erik Bekkers, Tim Doster, Tegan Emerson, Henry Kvinge, Katrina Agate, Nesreen K Ahmed, Pengfei Bai, Michael Banf, Claudio Battiloro, Maxim Beketov, Paul Bogdan, Martin Carrasco, Andrea Cavallo, Yun Young Choi, George Dasoulas, Matouš Elphick, Giordan Escalona, Dominik Filipiak, Halley Fritze, Thomas Gebhart, Manel Gil-Sorribes, Salvish Goomanee, Victor Guallar, Liliya Imasheva, Andrei Irimia, Hongwei Jin, Graham Johnson, Nikos Kanakaris, Boshko Koloski, Veljko Kovač, Manuel Lecha, Minho Lee, Pierrick Leroy, Theodore Long, German Magai, Alvaro Martinez, Marissa Masden, Sebastian Mežnar, Bertran Miquel-Oliver, Alexis Molina, Alexander Nikitin, Marco Nurisso, Matt Piekenbrock, Yu Qin, Patryk Rygiel, Alessandro Salatiello, Max Schattauer, Pavel Snopov, Julian Suk, Valentina Sánchez, Mauricio Tec, Francesco Vaccarino, Jonas Verhellen, Frederic Wantiez, Alexander Weers, Patrik Zajec, Blaž Škrlj, Nina Miolane
TL;DR
The paper documents the ICML 2024 Topological Deep Learning Challenge, which focuses on designing topological liftings between discrete topological domains to bridge traditional data forms (e.g., point clouds and graphs) with higher-order structures like simplicial, cellular, combinatorial complexes, and hypergraphs. It formalizes the task of topological liftings, outlines submission requirements, evaluation via a Condorcet framework, and software practices to ensure high-quality, reproducible implementations. The results include 52 valid submissions from 31 teams, with four non-mutually exclusive award categories and multiple prize positions, plus honorable mentions highlighting standout liftings and contributors. The findings demonstrate growing interest and a diverse set of lifting techniques, suggesting that topology-aware data representations can extend TDL applications to a wider range of structured datasets and pave the way for methodological benchmarks in this emerging field.
Abstract
This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.