{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZO2USPX4MZXRALAW6RAWC7U5SB","short_pith_number":"pith:ZO2USPX4","schema_version":"1.0","canonical_sha256":"cbb5493efc666f102c16f441617e9d90409befebd5681454ba9cdcd6a3c5b436","source":{"kind":"arxiv","id":"1911.09554","version":2},"attestation_state":"computed","paper":{"title":"Discrete and Continuous Deep Residual Learning Over Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Anderson R. Tavares, Luis C. Lamb, Marco Gori, Pedro H. C. Avelar","submitted_at":"2019-11-21T15:48:15Z","abstract_excerpt":"In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are those which are applied by integrating through an Ordinary Differential Equation (ODE) solver to produce their output. We experimentally show that these residuals achieve better results than the ones with non-residual modules when multiple layers are used, mitigating the low-pass filtering effect of GCN-based models. Finally, we apply and analyse the behaviou"},"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":"1911.09554","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-21T15:48:15Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b160bdb967ff80dae863c71d590c6d638147727509317b484b47d6bbdb472f68","abstract_canon_sha256":"87e203f81aaf9886caa4d040d9d8d0846119b13772bd81b64ad79b507e245ec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:06.636457Z","signature_b64":"ts7vkIoRFKqT9Tz1K9cpRbU7B8bNTrWDpEfW3Wn288Riemz6CCC6NxUVpOwgGqE9kmBTYxplhGVQgN4jf9ZFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbb5493efc666f102c16f441617e9d90409befebd5681454ba9cdcd6a3c5b436","last_reissued_at":"2026-07-05T00:22:06.636025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:06.636025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete and Continuous Deep Residual Learning Over Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Anderson R. Tavares, Luis C. Lamb, Marco Gori, Pedro H. C. Avelar","submitted_at":"2019-11-21T15:48:15Z","abstract_excerpt":"In this paper we propose the use of continuous residual modules for graph kernels in Graph Neural Networks. We show how both discrete and continuous residual layers allow for more robust training, being that continuous residual layers are those which are applied by integrating through an Ordinary Differential Equation (ODE) solver to produce their output. We experimentally show that these residuals achieve better results than the ones with non-residual modules when multiple layers are used, mitigating the low-pass filtering effect of GCN-based models. Finally, we apply and analyse the behaviou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09554","kind":"arxiv","version":2},"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/1911.09554/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":"1911.09554","created_at":"2026-07-05T00:22:06.636087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.09554v2","created_at":"2026-07-05T00:22:06.636087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09554","created_at":"2026-07-05T00:22:06.636087+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZO2USPX4MZXR","created_at":"2026-07-05T00:22:06.636087+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZO2USPX4MZXRALAW","created_at":"2026-07-05T00:22:06.636087+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZO2USPX4","created_at":"2026-07-05T00:22:06.636087+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.00190","citing_title":"On the Effectiveness of Random Weights in Graph Neural Networks","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB","json":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB.json","graph_json":"https://pith.science/api/pith-number/ZO2USPX4MZXRALAW6RAWC7U5SB/graph.json","events_json":"https://pith.science/api/pith-number/ZO2USPX4MZXRALAW6RAWC7U5SB/events.json","paper":"https://pith.science/paper/ZO2USPX4"},"agent_actions":{"view_html":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB","download_json":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB.json","view_paper":"https://pith.science/paper/ZO2USPX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.09554&json=true","fetch_graph":"https://pith.science/api/pith-number/ZO2USPX4MZXRALAW6RAWC7U5SB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZO2USPX4MZXRALAW6RAWC7U5SB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB/action/storage_attestation","attest_author":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB/action/author_attestation","sign_citation":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB/action/citation_signature","submit_replication":"https://pith.science/pith/ZO2USPX4MZXRALAW6RAWC7U5SB/action/replication_record"}},"created_at":"2026-07-05T00:22:06.636087+00:00","updated_at":"2026-07-05T00:22:06.636087+00:00"}