Ballester, Rubén Röell, Ernst Schmid, Daniel Bīn Alain, Mathieu Casacuberta, Carles Escalera, Sergio Rieck, Bastian 2024 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. application/pdf https://folia.unifr.ch/global/documents/331315 https://folia.unifr.ch/documents/331315/files/10845_mantra_the_manifold_tria.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.5281/zenodo.14103581 info:eu-repo/semantics/openAccess License undefined 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 info:eu-repo/classification/udc/004 MANTRA: The Manifold Triangulations Assemblage http://purl.org/coar/resource_type/c_5794