{"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/from-local-to-global-spectral-inspired-graph","title":"From Local to Global: Spectral-Inspired Graph Neural Networks","arxiv_id":"2209.12054","date":"2022-09-24","proceeding":null,"authors":["Ningyuan Huang","Soledad Villar","Carey E. Priebe","Da Zheng","Chengyue Huang","Lin Yang","Vladimir Braverman"],"abstract":"Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. Popular GNNs are message-passing algorithms (MPNNs) that aggregate and combine signals in a local graph neighborhood. However, shallow MPNNs tend to miss long-range signals and perform poorly on some heterophilous graphs, while deep MPNNs can suffer from issues like over-smoothing or over-squashing. To mitigate such issues, existing works typically borrow normalization techniques from training neural networks on Euclidean data or modify the graph structures. Yet these approaches are not well-understood theoretically and could increase the overall computational complexity. In this work, we draw inspirations from spectral graph embedding and propose $\\texttt{PowerEmbed}$ -- a simple layer-wise normalization technique to boost MPNNs. We show $\\texttt{PowerEmbed}$ can provably express the top-$k$ leading eigenvectors of the graph operator, which prevents over-smoothing and is agnostic to the graph topology; meanwhile, it produces a list of representations ranging from local features to global signals, which avoids over-squashing. We apply $\\texttt{PowerEmbed}$ in a wide range of simulated and real graphs and demonstrate its competitive performance, particularly for heterophilous graphs.","url_abs":"https://arxiv.org/abs/2209.12054v3","url_pdf":"https://arxiv.org/pdf/2209.12054v3.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":"from-local-to-global-spectral-inspired-graph","repo_url":"https://github.com/nhuang37/spectral-inspired-gnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-embedding","task_name":"Graph Embedding"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2209.12054","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2209.12054"}},"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":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/nhuang37/spectral-inspired-gnn","reach":null}],"summary":{"ran":2,"ran_fixture":1,"ran_draft_wrong":4},"by_repo_kind":{"official":{"samples":7,"ran":7,"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":7,"samples":[{"code_sha256_prefix":"784d7df8e3ae0b47","entry":"FeedForwardNet","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"power.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/power.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"784d7df8e3ae0b47"}},{"code_sha256_prefix":"78eaaf9b0dc8e3fc","entry":"SIGN_POWER","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"power.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/power.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"78eaaf9b0dc8e3fc"}},{"code_sha256_prefix":"15209c0c33d1fc91","entry":"power_iterate","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"power.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/power.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"15209c0c33d1fc91"}},{"code_sha256_prefix":"a08291d45482049d","entry":"run_model","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"power.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/power.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a08291d45482049d"}},{"code_sha256_prefix":"e4adcb63e82c82e0","entry":"run_model","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"baseline/gcn_variants_real_graph.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/baseline/gcn_variants_real_graph.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e4adcb63e82c82e0"}},{"code_sha256_prefix":"06321154c24315fa","entry":"test","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"power.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/power.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"06321154c24315fa"}},{"code_sha256_prefix":"0f53f615b042695b","entry":"test","repo":"nhuang37/spectral-inspired-gnn","repo_kind":"official","path":"baseline/gcn_variants_real_graph.py","file_url":"https://github.com/nhuang37/spectral-inspired-gnn/blob/HEAD/baseline/gcn_variants_real_graph.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"0f53f615b042695b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}