ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain

TL;DR

This paper presents the second ICML Topological Deep Learning Challenge, focusing on developing methods to represent and connect various discrete topological data structures, advancing the integration of topological methods with structured datasets.

Contribution

It introduces a new challenge aimed at designing topological liftings between different data structures, encouraging progress in topological deep learning methods.

Findings

52 submissions met the challenge requirements

Participants developed novel topological liftings

The challenge fostered advancements in topological data representations

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.