Papers › MANTRA: The Manifold Triangulations Assemblage

MANTRA: The Manifold Triangulations Assemblage

3 Oct 2024arXiv:2410.02392archive 2025-07-28

Rubén Ballester, Ernst Röell, Daniel Bīn Schmid, Mathieu Alain, Sergio Escalera, Carles Casacuberta, Bastian Rieck

The rising interest in leveraging higher-order interactions present in complex systems has led 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 hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically higher-order dataset for benchmarking higher-order models, comprising over 43,000 and 250,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, leading the way for more effective higher-order models.

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