{"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/graph-coupled-oscillator-networks","title":"Graph-Coupled Oscillator Networks","arxiv_id":"2202.02296","date":"2022-02-04","proceeding":null,"authors":["T. Konstantin Rusch","Benjamin P. Chamberlain","James Rowbottom","Siddhartha Mishra","Michael M. Bronstein"],"abstract":"We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear controlled and damped oscillators, coupled via the adjacency structure of the underlying graph. The flexibility of our framework permits any basic GNN layer (e.g. convolutional or attentional) as the coupling function, from which a multi-layer deep neural network is built up via the dynamics of the proposed ODEs. We relate the oversmoothing problem, commonly encountered in GNNs, to the stability of steady states of the underlying ODE and show that zero-Dirichlet energy steady states are not stable for our proposed ODEs. This demonstrates that the proposed framework mitigates the oversmoothing problem. Moreover, we prove that GraphCON mitigates the exploding and vanishing gradients problem to facilitate training of deep multi-layer GNNs. Finally, we show that our approach offers competitive performance with respect to the state-of-the-art on a variety of graph-based learning tasks.","url_abs":"https://arxiv.org/abs/2202.02296v2","url_pdf":"https://arxiv.org/pdf/2202.02296v2.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":"graph-coupled-oscillator-networks","repo_url":"https://github.com/tk-rusch/graphcon","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2202.02296","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2202.02296"}},"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/tk-rusch/GraphCON","reach":{"status":"ok"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/tk-rusch/graphcon","reach":{"status":"ok"}}],"summary":{"ran_draft_wrong":4},"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":4,"samples":[{"code_sha256_prefix":"1511f7031d44eafb","entry":"SymplecticEuler_step_func","repo":"tk-rusch/graphcon","repo_kind":"official","path":"src/homophilic_graphs/geometric_integrators.py","file_url":"https://github.com/tk-rusch/graphcon/blob/HEAD/src/homophilic_graphs/geometric_integrators.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"1511f7031d44eafb"}},{"code_sha256_prefix":"2ca430b1c5874d57","entry":"add_labels","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"2ca430b1c5874d57"}},{"code_sha256_prefix":"5198723f26aa8e49","entry":"get_label_masks","repo":"tk-rusch/graphcon","repo_kind":"official","path":"src/homophilic_graphs/run_GNN.py","file_url":"https://github.com/tk-rusch/graphcon/blob/HEAD/src/homophilic_graphs/run_GNN.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":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5198723f26aa8e49"}},{"code_sha256_prefix":"dab3444777a2e6c7","entry":"get_optimizer","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"dab3444777a2e6c7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}