{"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/injecting-hamiltonian-architectural-bias-into","title":"Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks","arxiv_id":"2405.17163","date":"2024-05-27","proceeding":null,"authors":["Simon Heilig","Alessio Gravina","Alessandro Trenta","Claudio Gallicchio","Davide Bacciu"],"abstract":"The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.","url_abs":"https://arxiv.org/abs/2405.17163v2","url_pdf":"https://arxiv.org/pdf/2405.17163v2.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":[{"task_slug":"graph-representation-learning","task_name":"Graph Representation Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2405.17163","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2405.17163"}},"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/simonheilig/porthamiltonian-dgn","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran":6,"unverified":4},"by_repo_kind":{"found_in_text":{"samples":10,"ran":6,"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":"adcdf6d3cfdc929c","entry":"eval_ap","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_prop_pred/train_GraphProp.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_prop_pred/train_GraphProp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"adcdf6d3cfdc929c"}},{"code_sha256_prefix":"7cf0c0aa4c265cb4","entry":"line_graph","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_transfer_task/graph_transfer_data.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_transfer_task/graph_transfer_data.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7cf0c0aa4c265cb4"}},{"code_sha256_prefix":"57358b1aca0d6ae1","entry":"ring_transfer_graph","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_transfer_task/graph_transfer_data.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_transfer_task/graph_transfer_data.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"57358b1aca0d6ae1"}},{"code_sha256_prefix":"67cf67f9cfc213a8","entry":"split","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"minesweeper/model_selection.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/minesweeper/model_selection.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"67cf67f9cfc213a8"}},{"code_sha256_prefix":"ccdff96dde8c6510","entry":"train","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_prop_pred/train_GraphProp.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_prop_pred/train_GraphProp.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ccdff96dde8c6510"}},{"code_sha256_prefix":"51c5c74c2f169b4a","entry":"update_csv","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_transfer_task/utils.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_transfer_task/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"51c5c74c2f169b4a"}},{"code_sha256_prefix":"9e23c0bf026e8677","entry":"cliquepath_transfer_graph","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_transfer_task/graph_transfer_data.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_transfer_task/graph_transfer_data.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":"9e23c0bf026e8677"}},{"code_sha256_prefix":"4c8636912cd02526","entry":"is_uninitialized_parameter","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_prop_pred/models/phdgn_utils.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_prop_pred/models/phdgn_utils.py","link_basis":"harvester_set","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":"4c8636912cd02526"}},{"code_sha256_prefix":"171608f792ff5805","entry":"reset_bias_","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_prop_pred/models/phdgn_utils.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_prop_pred/models/phdgn_utils.py","link_basis":"harvester_set","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":"171608f792ff5805"}},{"code_sha256_prefix":"37dc8fcbfe178a3d","entry":"reset_weight_","repo":"simonheilig/porthamiltonian-dgn","repo_kind":"found_in_text","path":"graph_prop_pred/models/phdgn_utils.py","file_url":"https://github.com/simonheilig/porthamiltonian-dgn/blob/HEAD/graph_prop_pred/models/phdgn_utils.py","link_basis":"harvester_set","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":"37dc8fcbfe178a3d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}