{"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/homomorphism-counts-as-structural-encodings","title":"Homomorphism Counts as Structural Encodings for Graph Learning","arxiv_id":"2410.18676","date":"2024-10-24","proceeding":null,"authors":["Linus Bao","Emily Jin","Michael Bronstein","İsmail İlkan Ceylan","Matthias Lanzinger"],"abstract":"Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use of positional encodings (e.g., Laplacian positional encoding) or structural encodings (e.g., random-walk structural encoding). The quality of such encodings is critical, since they provide the necessary $\\textit{graph inductive biases}$ to condition the model on graph structure. In this work, we propose $\\textit{motif structural encoding}$ (MoSE) as a flexible and powerful structural encoding framework based on counting graph homomorphisms. Theoretically, we compare the expressive power of MoSE to random-walk structural encoding and relate both encodings to the expressive power of standard message passing neural networks. Empirically, we observe that MoSE outperforms other well-known positional and structural encodings across a range of architectures, and it achieves state-of-the-art performance on a widely studied molecular property prediction dataset.","url_abs":"https://arxiv.org/abs/2410.18676v2","url_pdf":"https://arxiv.org/pdf/2410.18676v2.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":"homomorphism-counts-as-structural-encodings","repo_url":"https://github.com/linusbao/MoSE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":"molecular-property-prediction","task_name":"Molecular Property Prediction"},{"task_slug":"property-prediction","task_name":"Property Prediction"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2410.18676","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.18676"}},"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/linusbao/MoSE","reach":null}],"summary":{"ran_honours":1,"ran":1,"unverified":1},"by_repo_kind":{"official":{"samples":3,"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":"1205ba1ddf655d66","entry":"compute_gradual_width","repo":"linusbao/MoSE","repo_kind":"official","path":"GRIT/grit/encoder/MLP_count_encoder.py","file_url":"https://github.com/linusbao/MoSE/blob/HEAD/GRIT/grit/encoder/MLP_count_encoder.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1205ba1ddf655d66"}},{"code_sha256_prefix":"4de9478be10770ce","entry":"trig_encoder","repo":"linusbao/MoSE","repo_kind":"official","path":"GRIT/grit/encoder/MLP_count_encoder.py","file_url":"https://github.com/linusbao/MoSE/blob/HEAD/GRIT/grit/encoder/MLP_count_encoder.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"4de9478be10770ce"}},{"code_sha256_prefix":"695228f7d3e1bc23","entry":"MLPNodeCountEncoder","repo":"linusbao/MoSE","repo_kind":"official","path":"GRIT/grit/encoder/MLP_count_encoder.py","file_url":"https://github.com/linusbao/MoSE/blob/HEAD/GRIT/grit/encoder/MLP_count_encoder.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":"695228f7d3e1bc23"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}