MANTRA: The Manifold Triangulations Assemblage

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

Keywords: simplicial complex, topological deep learning, high-order, high-order dataset, simplicial complex learning

TL;DR: We introduce MANTRA, the first large-scale, diverse, and intrinsically high-order dataset for testing graph and topological models.

Abstract:

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, paving the way towards more effective
higher-order models.

Primary Area: datasets and benchmarks

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Submission Number: 10845