{"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/neural-message-passing-induced-by-energy","title":"Neural Message Passing Induced by Energy-Constrained Diffusion","arxiv_id":"2409.09111","date":"2024-09-13","proceeding":null,"authors":["Qitian Wu","David Wipf","Junchi Yan"],"abstract":"Learning representations for structured data with certain geometries (observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper, we propose an energy-constrained diffusion model as a principled interpretable framework for understanding the mechanism of MPNNs and navigating novel architectural designs. The model, inspired by physical systems, combines the inductive bias of diffusion on manifolds with layer-wise constraints of energy minimization. As shown by our analysis, the diffusion operators have a one-to-one correspondence with the energy functions implicitly descended by the diffusion process, and the finite-difference iteration for solving the energy-constrained diffusion system induces the propagation layers of various types of MPNNs operated on observed or latent structures. On top of these findings, we devise a new class of neural message passing models, dubbed as diffusion-inspired Transformers, whose global attention layers are induced by the principled energy-constrained diffusion. Across diverse datasets ranging from real-world networks to images and physical particles, we show that the new model can yield promising performance for cases where the data structures are observed (as a graph), partially observed or completely unobserved.","url_abs":"https://arxiv.org/abs/2409.09111v1","url_pdf":"https://arxiv.org/pdf/2409.09111v1.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":"neural-message-passing-induced-by-energy","repo_url":"https://github.com/qitianwu/difformer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"inductive-bias","task_name":"Inductive Bias"}],"methods":[{"method_slug":"attention","method_name":"Attention"},{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2409.09111","atlas_url":"https://app.syntology.ai/?focus=2409.09111","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2409.09111"}},"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/qitianwu/difformer","reach":{"status":"ok"}}],"summary":{"unverified":1},"by_repo_kind":{"listed":{"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":"086cc22e87a696a3","entry":"full_attention_conv","repo":"qitianwu/difformer","repo_kind":"listed","path":"spatial-temporal/difformer.py","file_url":"https://github.com/qitianwu/difformer/blob/HEAD/spatial-temporal/difformer.py","link_basis":"harvester_set","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":"086cc22e87a696a3"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}