{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:VIL2A6NLG2VT66QZEMMTXXK4LR","short_pith_number":"pith:VIL2A6NL","schema_version":"1.0","canonical_sha256":"aa17a079ab36ab3f7a1923193bdd5c5c6ef4a303842d75c98ab5ea06e54e915e","source":{"kind":"arxiv","id":"2307.01951","version":2},"attestation_state":"computed","paper":{"title":"A Neural Collapse Perspective on Feature Evolution in Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.IT","math.IT","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Joan Bruna, Tom Tirer, Vignesh Kothapalli","submitted_at":"2023-07-04T23:03:21Z","abstract_excerpt":"Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block model graphs, and explore the feature evolution through the lens of the \"Neural Collapse\" (NC) phenomenon. When training instance-wise deep classifiers (e.g. for image classification) beyond the zero training error point, NC demonstrates a reduction in the deepest features' within"},"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":"2307.01951","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-07-04T23:03:21Z","cross_cats_sorted":["cs.AI","cs.IT","math.IT","math.OC","stat.ML"],"title_canon_sha256":"5ee519c853ffd5098d2ca5dd3fa8f0804c29aa0f81cb1c4c0b15618c11ec1f3f","abstract_canon_sha256":"a0ff81bbc540644d311e34debf83eed2cb05cff8c49e3270608338556d8f3705"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:05:10.277859Z","signature_b64":"px7rj/gh0MaOiOfP/AzAgCdEx2cVTjp92pHDlAAojeJbrNXCCX7D6wVseJFWAg9tJQ5y2PTc1OQBV7xOW+hsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa17a079ab36ab3f7a1923193bdd5c5c6ef4a303842d75c98ab5ea06e54e915e","last_reissued_at":"2026-07-05T07:05:10.277369Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:05:10.277369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Neural Collapse Perspective on Feature Evolution in Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.IT","math.IT","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Joan Bruna, Tom Tirer, Vignesh Kothapalli","submitted_at":"2023-07-04T23:03:21Z","abstract_excerpt":"Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block model graphs, and explore the feature evolution through the lens of the \"Neural Collapse\" (NC) phenomenon. When training instance-wise deep classifiers (e.g. for image classification) beyond the zero training error point, NC demonstrates a reduction in the deepest features' within"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.01951","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/2307.01951/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":"2307.01951","created_at":"2026-07-05T07:05:10.277425+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.01951v2","created_at":"2026-07-05T07:05:10.277425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.01951","created_at":"2026-07-05T07:05:10.277425+00:00"},{"alias_kind":"pith_short_12","alias_value":"VIL2A6NLG2VT","created_at":"2026-07-05T07:05:10.277425+00:00"},{"alias_kind":"pith_short_16","alias_value":"VIL2A6NLG2VT66QZ","created_at":"2026-07-05T07:05:10.277425+00:00"},{"alias_kind":"pith_short_8","alias_value":"VIL2A6NL","created_at":"2026-07-05T07:05:10.277425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.25978","citing_title":"Mini-Batch Class Composition Bias in Link Prediction","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR","json":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR.json","graph_json":"https://pith.science/api/pith-number/VIL2A6NLG2VT66QZEMMTXXK4LR/graph.json","events_json":"https://pith.science/api/pith-number/VIL2A6NLG2VT66QZEMMTXXK4LR/events.json","paper":"https://pith.science/paper/VIL2A6NL"},"agent_actions":{"view_html":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR","download_json":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR.json","view_paper":"https://pith.science/paper/VIL2A6NL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.01951&json=true","fetch_graph":"https://pith.science/api/pith-number/VIL2A6NLG2VT66QZEMMTXXK4LR/graph.json","fetch_events":"https://pith.science/api/pith-number/VIL2A6NLG2VT66QZEMMTXXK4LR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR/action/storage_attestation","attest_author":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR/action/author_attestation","sign_citation":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR/action/citation_signature","submit_replication":"https://pith.science/pith/VIL2A6NLG2VT66QZEMMTXXK4LR/action/replication_record"}},"created_at":"2026-07-05T07:05:10.277425+00:00","updated_at":"2026-07-05T07:05:10.277425+00:00"}