{"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/weisfeiler-and-leman-go-loopy-a-new-hierarchy","title":"Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning","arxiv_id":"2403.13749","date":"2024-03-20","proceeding":null,"authors":["Raffaele Paolino","Sohir Maskey","Pascal Welke","Gitta Kutyniok"],"abstract":"We introduce $r$-loopy Weisfeiler-Leman ($r$-$\\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\\ell{}$MPNN, that can count cycles up to length $r + 2$. Most notably, we show that $r$-$\\ell{}$WL can count homomorphisms of cactus graphs. This strictly extends classical 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of the proposed $r$-$\\ell{}$MPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy","url_abs":"https://arxiv.org/abs/2403.13749v2","url_pdf":"https://arxiv.org/pdf/2403.13749v2.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":"weisfeiler-and-leman-go-loopy-a-new-hierarchy","repo_url":"https://github.com/rpaolino/loopy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2403.13749","atlas_url":"https://app.syntology.ai/?focus=2403.13749","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2403.13749"}},"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. 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/rpaolino/loopy","reach":null}],"summary":{"ran_fixture":1,"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":2,"ran":2,"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":"292508e17bb058d4","entry":"custom_propagate","repo":"rpaolino/loopy","repo_kind":"official","path":"src/nn/loopy.py","file_url":"https://github.com/rpaolino/loopy/blob/HEAD/src/nn/loopy.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"292508e17bb058d4"}},{"code_sha256_prefix":"7793d0b0e246afd9","entry":"get_nonlinearity","repo":"rpaolino/loopy","repo_kind":"official","path":"src/nn/loopy.py","file_url":"https://github.com/rpaolino/loopy/blob/HEAD/src/nn/loopy.py","link_basis":"first_harvest_node","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":"7793d0b0e246afd9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}