{"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/continuous-simplicial-neural-networks","title":"Continuous Simplicial Neural Networks","arxiv_id":"2503.12919","date":"2025-03-17","proceeding":null,"authors":["Aref Einizade","Dorina Thanou","Fragkiskos D. Malliaros","Jhony H. Giraldo"],"abstract":"Simplicial complexes provide a powerful framework for modeling high-order interactions in structured data, making them particularly suitable for applications such as trajectory prediction and mesh processing. However, existing simplicial neural networks (SNNs), whether convolutional or attention-based, rely primarily on discrete filtering techniques, which can be restrictive. In contrast, partial differential equations (PDEs) on simplicial complexes offer a principled approach to capture continuous dynamics in such structures. In this work, we introduce continuous simplicial neural network (COSIMO), a novel SNN architecture derived from PDEs on simplicial complexes. We provide theoretical and experimental justifications of COSIMO's stability under simplicial perturbations. Furthermore, we investigate the over-smoothing phenomenon, a common issue in geometric deep learning, demonstrating that COSIMO offers better control over this effect than discrete SNNs. Our experiments on real-world datasets demonstrate that COSIMO achieves competitive performance compared to state-of-the-art SNNs in complex and noisy environments.","url_abs":"https://arxiv.org/abs/2503.12919v2","url_pdf":"https://arxiv.org/pdf/2503.12919v2.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":[],"tasks":[{"task_slug":"trajectory-prediction","task_name":"Trajectory Prediction"}],"methods":[{"method_slug":"snn","method_name":"SNN"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2503.12919","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2503.12919"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"deterministic:regex_extraction","url":"https://github.com/ArefEinizade2/COSIMO","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"found_in_text":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"bd1403e0e2313344","entry":"COSIMO_Layer","repo":"ArefEinizade2/COSIMO","repo_kind":"found_in_text","path":"Mesh_Shrec16/COSIMO_layer.py","file_url":"https://github.com/ArefEinizade2/COSIMO/blob/HEAD/Mesh_Shrec16/COSIMO_layer.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"bd1403e0e2313344"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}