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10845_mantra_the_manifold_tria
Conference paper (in proceedings)

MANTRA: The Manifold Triangulations Assemblage

DOKPE

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  • 2024
Published in:
  • OpenReview.net. - Singapore :ICLR 2025: The Thirteenth International Conference on Learning Representations. - 2024, p. 1-30
topological data analysis
topological deep learning
geometric deep learning
data set
simplicial complex
simplicial complex learning
high-order dataset
high-order
English 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 higherorder 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.
Faculty
Faculté des sciences et de médecine
Department
Département d'Informatique
Language
  • English
Classification
Computer science and technology
License
License undefined
Open access status
green
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/331315
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