{"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/on-asymptotic-behaviors-of-graph-cnns-from","title":"Graph Neural Networks Exponentially Lose Expressive Power for Node Classification","arxiv_id":"1905.10947","date":"2019-05-27","proceeding":"ICLR 2020 1","authors":["Kenta Oono","Taiji Suzuki"],"abstract":"Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of graph NNs via their asymptotic behaviors as the layer size tends to infinity. Our strategy is to generalize the forward propagation of a Graph Convolutional Network (GCN), which is a popular graph NN variant, as a specific dynamical system. In the case of a GCN, we show that when its weights satisfy the conditions determined by the spectra of the (augmented) normalized Laplacian, its output exponentially approaches the set of signals that carry information of the connected components and node degrees only for distinguishing nodes. Our theory enables us to relate the expressive power of GCNs with the topological information of the underlying graphs inherent in the graph spectra. To demonstrate this, we characterize the asymptotic behavior of GCNs on the Erd\\H{o}s -- R\\'{e}nyi graph. We show that when the Erd\\H{o}s -- R\\'{e}nyi graph is sufficiently dense and large, a broad range of GCNs on it suffers from the \"information loss\" in the limit of infinite layers with high probability. Based on the theory, we provide a principled guideline for weight normalization of graph NNs. We experimentally confirm that the proposed weight scaling enhances the predictive performance of GCNs in real data. Code is available at https://github.com/delta2323/gnn-asymptotics.","url_abs":"https://arxiv.org/abs/1905.10947v5","url_pdf":"https://arxiv.org/pdf/1905.10947v5.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":"on-asymptotic-behaviors-of-graph-cnns-from","repo_url":"https://github.com/delta2323/gnn-asymptotics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[{"method_slug":"gcn","method_name":"GCN"},{"method_slug":"weight-normalization","method_name":"Weight Normalization"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1905.10947","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.10947"}},"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/delta2323/gnn-asymptotics","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":"3a416a00dcff8c2d","entry":"make_dynamics","repo":"delta2323/gnn-asymptotics","repo_kind":"official","path":"gnn_dynamics/dynamics.py","file_url":"https://github.com/delta2323/gnn-asymptotics/blob/HEAD/gnn_dynamics/dynamics.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3a416a00dcff8c2d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}