{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/generalized-simplicial-attention-neural","title":"Generalized Simplicial Attention Neural Networks","arxiv_id":"2309.02138","date":"2023-09-05","proceeding":null,"authors":["Claudio Battiloro","Lucia Testa","Lorenzo Giusti","Stefania Sardellitti","Paolo Di Lorenzo","Sergio Barbarossa"],"abstract":"Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to model the data on higher-order combinatorial topological spaces, such as Simplicial Complexes (SCs) or Cell Complexes. For this reason, we introduce Generalized Simplicial Attention Neural Networks (GSANs), novel neural network architectures designed to process data living on simplicial complexes using masked self-attentional layers. Hinging on topological signal processing principles, we devise a series of principled self-attention mechanisms able to process data associated with simplices of various order, such as nodes, edges, triangles, and beyond. These schemes learn how to combine data associated with neighbor simplices of consecutive order in a task-oriented fashion, leveraging on the simplicial Dirac operator and its Dirac decomposition. We also prove that GSAN satisfies two fundamental properties: permutation equivariance and simplicial-awareness. Finally, we illustrate how our approach compares favorably with other simplicial and graph models when applied to several (inductive and transductive) tasks such as trajectory prediction, missing data imputation, graph classification, and simplex prediction.","url_abs":"https://arxiv.org/abs/2309.02138v2","url_pdf":"https://arxiv.org/pdf/2309.02138v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"generalized-simplicial-attention-neural","repo_url":"https://github.com/luciatesta97/generalized-simplicial-attention-neural-networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-classification","task_name":"Graph Classification"},{"task_slug":"imputation","task_name":"Imputation"},{"task_slug":"trajectory-prediction","task_name":"Trajectory Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2309.02138","atlas_url":"https://app.syntology.ai/?focus=2309.02138","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2309.02138"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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