{"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/facilitating-graph-neural-networks-with","title":"Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes","arxiv_id":"2310.19285","date":"2023-10-30","proceeding":"NeurIPS 2023 11","authors":["Cai Zhou","Xiyuan Wang","Muhan Zhang"],"abstract":"Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In the spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on the spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.","url_abs":"https://arxiv.org/abs/2310.19285v1","url_pdf":"https://arxiv.org/pdf/2310.19285v1.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":"facilitating-graph-neural-networks-with","repo_url":"https://github.com/zhouc20/hodgerandomwalk","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2310.19285","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.19285"}},"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/zhouc20/HodgeRandomWalk","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/zhouc20/hodgerandomwalk","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_draft_wrong":2,"ran":3,"unverified":6},"by_repo_kind":{"official":{"samples":11,"ran":5,"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":"a59edb7a016ef8b4","entry":"Delta_0","repo":"zhouc20/hodgerandomwalk","repo_kind":"official","path":"graphgps/transform/hodge_decomposition.py","file_url":"https://github.com/zhouc20/hodgerandomwalk/blob/HEAD/graphgps/transform/hodge_decomposition.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a59edb7a016ef8b4"}},{"code_sha256_prefix":"b888018e8acd3f1d","entry":"get_activation","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/layer/Exphormer.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/layer/Exphormer.py","link_basis":"harvester_set","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b888018e8acd3f1d"}},{"code_sha256_prefix":"1bb331bf70a78136","entry":"get_final_pretrained_ckpt","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/finetuning.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/finetuning.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1bb331bf70a78136"}},{"code_sha256_prefix":"b5c9e7acf599a98a","entry":"get_log_deg","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/layer/grit_layer.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/layer/grit_layer.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"b5c9e7acf599a98a"}},{"code_sha256_prefix":"9a4410b8a6c0cc47","entry":"init_model_from_pretrained","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/finetuning.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/finetuning.py","link_basis":"harvester_set","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9a4410b8a6c0cc47"}},{"code_sha256_prefix":"ae56bcfaae96da3c","entry":"apply_chunking_to_forward","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/layer/bigbird_layer.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/layer/bigbird_layer.py","link_basis":"harvester_set","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":"ae56bcfaae96da3c"}},{"code_sha256_prefix":"a0f064817b33d41f","entry":"divergence","repo":"zhouc20/hodgerandomwalk","repo_kind":"official","path":"graphgps/transform/hodge_decomposition.py","file_url":"https://github.com/zhouc20/hodgerandomwalk/blob/HEAD/graphgps/transform/hodge_decomposition.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":"a0f064817b33d41f"}},{"code_sha256_prefix":"c98a702be0660ac9","entry":"is_seed","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/agg_runs.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/agg_runs.py","link_basis":"harvester_set","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":"c98a702be0660ac9"}},{"code_sha256_prefix":"438635c08adfe2aa","entry":"is_split","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/agg_runs.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/agg_runs.py","link_basis":"harvester_set","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":"438635c08adfe2aa"}},{"code_sha256_prefix":"40e98e1ecbf39f34","entry":"join_list","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/agg_runs.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/agg_runs.py","link_basis":"harvester_set","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":"40e98e1ecbf39f34"}},{"code_sha256_prefix":"91c1f5bb90bbe0f3","entry":"load_pretrained_model_cfg","repo":"zhouc20/HodgeRandomWalk","repo_kind":"official","path":"graphgps/finetuning.py","file_url":"https://github.com/zhouc20/HodgeRandomWalk/blob/HEAD/graphgps/finetuning.py","link_basis":"harvester_set","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":"91c1f5bb90bbe0f3"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}