{"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/geometric-knowledge-distillation-topology","title":"Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks","arxiv_id":"2210.13014","date":"2022-10-24","proceeding":null,"authors":["Chenxiao Yang","Qitian Wu","Junchi Yan"],"abstract":"We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) by distilling knowledge from a teacher GNN model trained on a complete graph to a student GNN model operating on a smaller or sparser graph. To this end, we revisit the connection between thermodynamics and the behavior of GNN, based on which we propose Neural Heat Kernel (NHK) to encapsulate the geometric property of the underlying manifold concerning the architecture of GNNs. A fundamental and principled solution is derived by aligning NHKs on teacher and student models, dubbed as Geometric Knowledge Distillation. We develop non- and parametric instantiations and demonstrate their efficacy in various experimental settings for knowledge distillation regarding different types of privileged topological information and teacher-student schemes.","url_abs":"https://arxiv.org/abs/2210.13014v2","url_pdf":"https://arxiv.org/pdf/2210.13014v2.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":"geometric-knowledge-distillation-topology","repo_url":"https://github.com/chr26195/gkd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"geometric-knowledge-distillation-topology","repo_url":"https://github.com/chr26195/pmlp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"knowledge-distillation","task_name":"Knowledge Distillation"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[{"method_slug":"knowledge-distillation","method_name":"Knowledge Distillation"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2210.13014","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2210.13014"}},"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/chr26195/GKD","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/chr26195/gkd","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/chr26195/pmlp","reach":{"status":"ok"}}],"summary":{"ran":1,"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1},"listed":{"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":2,"samples":[{"code_sha256_prefix":"2c61d3e4a79a64b1","entry":"Kernel","repo":"chr26195/gkd","repo_kind":"official","path":"kernels.py","file_url":"https://github.com/chr26195/gkd/blob/HEAD/kernels.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"2c61d3e4a79a64b1"}},{"code_sha256_prefix":"eb415acecb87c3bb","entry":"heat_kernel","repo":"chr26195/pmlp","repo_kind":"listed","path":"vA_3_in_1/conv.py","file_url":"https://github.com/chr26195/pmlp/blob/HEAD/vA_3_in_1/conv.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"eb415acecb87c3bb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}