{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OC4RRL3NR6MVJ2WSCVYWVCC6VC","short_pith_number":"pith:OC4RRL3N","schema_version":"1.0","canonical_sha256":"70b918af6d8f9954ead215716a885ea88ae512c3512410746d10da75fac35813","source":{"kind":"arxiv","id":"2311.07444","version":2},"attestation_state":"computed","paper":{"title":"On the Robustness of Neural Collapse and the Neural Collapse of Robustness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jingtong Su, Julia Kempe, Nikolaos Tsilivis, Ya Shi Zhang","submitted_at":"2023-11-13T16:18:58Z","abstract_excerpt":"Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex). While it has been observed empirically in various cases and has been theoretically motivated, its connection with crucial properties of neural networks, like their generalization and robustness, remains unclear. In this work, we study the stability properties of these simplices. We find that the simplex structure disappears under small adversarial attacks, and that perturbed examples \"leap\" b"},"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":"2311.07444","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-11-13T16:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"fabe89d043e6ec230f1bd987b9fa9ee10b07c93c4afe206dcefd91b741aa41f0","abstract_canon_sha256":"d0cce070e3eaca92333a61cbb307cd8d733c16cc2edfca6bc345a4d5c84c8cbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:34:55.239534Z","signature_b64":"idY0UHLVPcNH4yRfkUKf5w+J+GXFeHlZTNJioQVvLS18Mg6XWho+TSh/aI5Y1+lEuecdByyKumkvvktjww5LDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70b918af6d8f9954ead215716a885ea88ae512c3512410746d10da75fac35813","last_reissued_at":"2026-07-05T09:34:55.239005Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:34:55.239005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Robustness of Neural Collapse and the Neural Collapse of Robustness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jingtong Su, Julia Kempe, Nikolaos Tsilivis, Ya Shi Zhang","submitted_at":"2023-11-13T16:18:58Z","abstract_excerpt":"Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex). While it has been observed empirically in various cases and has been theoretically motivated, its connection with crucial properties of neural networks, like their generalization and robustness, remains unclear. In this work, we study the stability properties of these simplices. We find that the simplex structure disappears under small adversarial attacks, and that perturbed examples \"leap\" b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.07444","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/2311.07444/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":"2311.07444","created_at":"2026-07-05T09:34:55.239070+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.07444v2","created_at":"2026-07-05T09:34:55.239070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.07444","created_at":"2026-07-05T09:34:55.239070+00:00"},{"alias_kind":"pith_short_12","alias_value":"OC4RRL3NR6MV","created_at":"2026-07-05T09:34:55.239070+00:00"},{"alias_kind":"pith_short_16","alias_value":"OC4RRL3NR6MVJ2WS","created_at":"2026-07-05T09:34:55.239070+00:00"},{"alias_kind":"pith_short_8","alias_value":"OC4RRL3N","created_at":"2026-07-05T09:34:55.239070+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.23087","citing_title":"The Implicit Bias of Depth: From Neural Collapse to Softmax Codes","ref_index":126,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC","json":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC.json","graph_json":"https://pith.science/api/pith-number/OC4RRL3NR6MVJ2WSCVYWVCC6VC/graph.json","events_json":"https://pith.science/api/pith-number/OC4RRL3NR6MVJ2WSCVYWVCC6VC/events.json","paper":"https://pith.science/paper/OC4RRL3N"},"agent_actions":{"view_html":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC","download_json":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC.json","view_paper":"https://pith.science/paper/OC4RRL3N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.07444&json=true","fetch_graph":"https://pith.science/api/pith-number/OC4RRL3NR6MVJ2WSCVYWVCC6VC/graph.json","fetch_events":"https://pith.science/api/pith-number/OC4RRL3NR6MVJ2WSCVYWVCC6VC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC/action/storage_attestation","attest_author":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC/action/author_attestation","sign_citation":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC/action/citation_signature","submit_replication":"https://pith.science/pith/OC4RRL3NR6MVJ2WSCVYWVCC6VC/action/replication_record"}},"created_at":"2026-07-05T09:34:55.239070+00:00","updated_at":"2026-07-05T09:34:55.239070+00:00"}