{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:6EPYXWLOSMAGJ4KJNN7NEVJWEF","short_pith_number":"pith:6EPYXWLO","schema_version":"1.0","canonical_sha256":"f11f8bd96e930064f1496b7ed25536214f379f829b364c4d6c66821ac898bf5d","source":{"kind":"arxiv","id":"2206.10991","version":5},"attestation_state":"computed","paper":{"title":"Understanding convolution on graphs via energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Benjamin P. Chamberlain, Francesco Di Giovanni, James Rowbottom, Michael M. Bronstein, Thomas Markovich","submitted_at":"2022-06-22T11:45:36Z","abstract_excerpt":"Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed by a shared, linear transformation before being propagated over the edges. On node-classification tasks, graph convolutions have been shown to suffer from two limitations: poor performance on heterophilic graphs, and over-smoothing. It is common belief that both phenomena occur because such models behave as low-pass filters, meaning that the Dirichlet energy "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2206.10991","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-06-22T11:45:36Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"fd0eb87d7eed88e7832cd6affc8ddec963d0b8a558daeda91935a74fbe8337f9","abstract_canon_sha256":"57978f9deb9ce17de6fb239052184d268083939013343eed15f35909f1a66770"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:02.749998Z","signature_b64":"r72IDHlP6HgePe4Zk7ahYvlc9k/VHzXnErWL14w3xa7o+VDem5Qf9IEw2DD/na6lrN0jYar9zDJHGb5ChKbwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f11f8bd96e930064f1496b7ed25536214f379f829b364c4d6c66821ac898bf5d","last_reissued_at":"2026-07-05T06:48:02.749577Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:02.749577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Understanding convolution on graphs via energies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Benjamin P. Chamberlain, Francesco Di Giovanni, James Rowbottom, Michael M. Bronstein, Thomas Markovich","submitted_at":"2022-06-22T11:45:36Z","abstract_excerpt":"Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed by a shared, linear transformation before being propagated over the edges. On node-classification tasks, graph convolutions have been shown to suffer from two limitations: poor performance on heterophilic graphs, and over-smoothing. It is common belief that both phenomena occur because such models behave as low-pass filters, meaning that the Dirichlet energy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10991","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.10991/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2206.10991","created_at":"2026-07-05T06:48:02.749637+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.10991v5","created_at":"2026-07-05T06:48:02.749637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.10991","created_at":"2026-07-05T06:48:02.749637+00:00"},{"alias_kind":"pith_short_12","alias_value":"6EPYXWLOSMAG","created_at":"2026-07-05T06:48:02.749637+00:00"},{"alias_kind":"pith_short_16","alias_value":"6EPYXWLOSMAGJ4KJ","created_at":"2026-07-05T06:48:02.749637+00:00"},{"alias_kind":"pith_short_8","alias_value":"6EPYXWLO","created_at":"2026-07-05T06:48:02.749637+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.21247","citing_title":"Graph Navier Stokes Networks","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.23708","citing_title":"Learning Dynamic Stability Landscapes in Synchronization Networks","ref_index":160,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21247","citing_title":"Graph Navier Stokes Networks","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19028","citing_title":"Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors","ref_index":112,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF","json":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF.json","graph_json":"https://pith.science/api/pith-number/6EPYXWLOSMAGJ4KJNN7NEVJWEF/graph.json","events_json":"https://pith.science/api/pith-number/6EPYXWLOSMAGJ4KJNN7NEVJWEF/events.json","paper":"https://pith.science/paper/6EPYXWLO"},"agent_actions":{"view_html":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF","download_json":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF.json","view_paper":"https://pith.science/paper/6EPYXWLO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.10991&json=true","fetch_graph":"https://pith.science/api/pith-number/6EPYXWLOSMAGJ4KJNN7NEVJWEF/graph.json","fetch_events":"https://pith.science/api/pith-number/6EPYXWLOSMAGJ4KJNN7NEVJWEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF/action/storage_attestation","attest_author":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF/action/author_attestation","sign_citation":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF/action/citation_signature","submit_replication":"https://pith.science/pith/6EPYXWLOSMAGJ4KJNN7NEVJWEF/action/replication_record"}},"created_at":"2026-07-05T06:48:02.749637+00:00","updated_at":"2026-07-05T06:48:02.749637+00:00"}