{"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/understanding-the-relationship-between-over","title":"On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks","arxiv_id":"2212.02374","date":"2022-12-05","proceeding":null,"authors":["Jhony H. Giraldo","Konstantinos Skianis","Thierry Bouwmans","Fragkiskos D. Malliaros"],"abstract":"Graph Neural Networks (GNNs) have succeeded in various computer science applications, yet deep GNNs underperform their shallow counterparts despite deep learning's success in other domains. Over-smoothing and over-squashing are key challenges when stacking graph convolutional layers, hindering deep representation learning and information propagation from distant nodes. Our work reveals that over-smoothing and over-squashing are intrinsically related to the spectral gap of the graph Laplacian, resulting in an inevitable trade-off between these two issues, as they cannot be alleviated simultaneously. To achieve a suitable compromise, we propose adding and removing edges as a viable approach. We introduce the Stochastic Jost and Liu Curvature Rewiring (SJLR) algorithm, which is computationally efficient and preserves fundamental properties compared to previous curvature-based methods. Unlike existing approaches, SJLR performs edge addition and removal during GNN training while maintaining the graph unchanged during testing. Comprehensive comparisons demonstrate SJLR's competitive performance in addressing over-smoothing and over-squashing.","url_abs":"https://arxiv.org/abs/2212.02374v2","url_pdf":"https://arxiv.org/pdf/2212.02374v2.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":"understanding-the-relationship-between-over","repo_url":"https://github.com/jhonygiraldo/sjlr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2212.02374","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2212.02374"}},"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":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/jhonygiraldo/sjlr","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":9},"by_repo_kind":{"official":{"samples":9,"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":0,"samples":[{"code_sha256_prefix":"dc6573716bd3389f","entry":"balanced_forman_curvature","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/BFC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/BFC_curvature.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":"dc6573716bd3389f"}},{"code_sha256_prefix":"589c9df78f56f0af","entry":"compute_JLC_matrices","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/JLC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/JLC_curvature.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":"589c9df78f56f0af"}},{"code_sha256_prefix":"2697497d87010a62","entry":"compute_balaced_forman_curvature","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/BFC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/BFC_curvature.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":"2697497d87010a62"}},{"code_sha256_prefix":"962cbf0cde3c7b42","entry":"compute_jost_liu_curvature","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/JLC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/JLC_curvature.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":"962cbf0cde3c7b42"}},{"code_sha256_prefix":"c68140584cc0e991","entry":"get_component","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"load_data/data.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/load_data/data.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":"c68140584cc0e991"}},{"code_sha256_prefix":"d2845200b34fc758","entry":"get_dataset","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"load_data/data.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/load_data/data.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":"d2845200b34fc758"}},{"code_sha256_prefix":"b36878b25e3455a3","entry":"get_largest_connected_component","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"load_data/data.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/load_data/data.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":"b36878b25e3455a3"}},{"code_sha256_prefix":"006b8162ce0068b8","entry":"jost_liu_curvature","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/JLC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/JLC_curvature.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":"006b8162ce0068b8"}},{"code_sha256_prefix":"423f80b3cce420e7","entry":"stochastic_discrete_ricci_flow_rewiring","repo":"jhonygiraldo/sjlr","repo_kind":"official","path":"models/BFC_curvature.py","file_url":"https://github.com/jhonygiraldo/sjlr/blob/HEAD/models/BFC_curvature.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":"423f80b3cce420e7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}