{"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/wilting-trees-interpreting-the-distance","title":"WILTing Trees: Interpreting the Distance Between MPNN Embeddings","arxiv_id":"2505.24642","date":"2025-05-30","proceeding":null,"authors":["Masahiro Negishi","Thomas Gärtner","Pascal Welke"],"abstract":"We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to structural distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.","url_abs":"https://arxiv.org/abs/2505.24642v1","url_pdf":"https://arxiv.org/pdf/2505.24642v1.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":[],"methods":[{"method_slug":"mpnn","method_name":"MPNN"},{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2505.24642","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2505.24642"}},"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/masahiro-negishi/wilt","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":1,"samples":[{"code_sha256_prefix":"13517f94de30d789","entry":"WeisfeilerLemanLabelingTree","repo":"masahiro-negishi/wilt","repo_kind":"found_in_text","path":"src/tree.py","file_url":"https://github.com/masahiro-negishi/wilt/blob/HEAD/src/tree.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":"13517f94de30d789"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}