Part of International Conference on Representation Learning 2025 (ICLR 2025) Conference
Rubén Ballester, Ernst Roell, Daniel Bin Schmid, Mathieu Alain, Sergio Escalera, Carles Casacuberta, Bastian Rieck
The rising interest in leveraging higher-order interactions present in complex systems hasled to a surge in more expressive models exploiting higher-order structures in the data,especially in topological deep learning (TDL), which designs neural networks on higher-order domains such as simplicial complexes. However, progress in this field is hinderedby the scarcity of datasets for benchmarking these architectures. To address this gap, weintroduce MANTRA, the first large-scale, diverse, and intrinsically higher-order dataset forbenchmarking higher-order models, comprising over 43,000 and 250,000 triangulationsof surfaces and three-dimensional manifolds, respectively. With MANTRA, we assessseveral graph- and simplicial complex-based models on three topological classificationtasks. We demonstrate that while simplicial complex-based neural networks generallyoutperform their graph-based counterparts in capturing simple topological invariants, theyalso struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark forassessing and advancing topological methods, paving the way towards more effectivehigher-order models.