[2505.17939] Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding

Computer Science > Machine Learning arXiv:2505.17939 (cs) [Submitted on 23 May 2025 (v1), last revised 2 Mar 2026 (this version, v3)] Title:Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding Authors:Manuel Lecha, Andrea Cavallo, Francesca Dominici, Ran Levi, Alessio Del Bue, Elvin Isufi, Pietro Morerio, Claudio Battiloro View a PDF of the paper titled Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding, by Manuel Lecha and 7 other authors View PDF Abstract:Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces. However, existing TDL models are restricted to undirected settings and fail to capture the higher-order directed patterns prevalent in many complex systems, e.g., brain networks, where such interactions are both abundant and functionally significant. To fill this gap, we introduce Semi-Simplicial Neural Networks (SSNs), a principled class of TDL models that operate on semi-simplicial sets -- combinatorial structures that encode directed higher-order motifs and their directional relationships. To enhance scalability, we propose Routing-SSNs, which dynamically select the most informative relations in a learnable manner. We prove that SSNs are strictly more expressive than standard graph and TDL models. We then introduce a new princi...