No Triangulation Without Representation: Generalization in Topological Deep Learning
Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated by the fact that topological objects permit operations, such as structural refinements, that are not appropriate for graph data. In this work, we extend MANTRA, a benchmark dataset containing manifold triangulations, to a larger class of manifolds with more diverse homeomorphism types. We show that, unlike prior claims, both graph neural networks (GNNs) and higher-order message passing (HOMP) methods can saturate the benchmark. However, we find that this is contingent on the right representation and feature ass...
| Authors | Johannes S. Schmidt, Martin Carrasco, Ernst Röell et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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