{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OSGEFRICWILD2SUNJQNTC42GYN","short_pith_number":"pith:OSGEFRIC","canonical_record":{"source":{"id":"2402.06751","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-09T19:28:02Z","cross_cats_sorted":[],"title_canon_sha256":"a7e83bfa7842763c2dc5b4e7a97e040ae47d5ee8992421fbaf64d39de17bc9ff","abstract_canon_sha256":"8cfd56088ccb6a09d0a6fc6b750ec400d275fc45b39c031a6d323501525fceb4"},"schema_version":"1.0"},"canonical_sha256":"748c42c502b2163d4a8d4c1b317346c368ae8075fd428e607ace8dd81d6460d4","source":{"kind":"arxiv","id":"2402.06751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06751","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06751v1","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06751","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"OSGEFRICWILD","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"OSGEFRICWILD2SUN","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"OSGEFRIC","created_at":"2026-07-05T07:43:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OSGEFRICWILD2SUNJQNTC42GYN","target":"record","payload":{"canonical_record":{"source":{"id":"2402.06751","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-09T19:28:02Z","cross_cats_sorted":[],"title_canon_sha256":"a7e83bfa7842763c2dc5b4e7a97e040ae47d5ee8992421fbaf64d39de17bc9ff","abstract_canon_sha256":"8cfd56088ccb6a09d0a6fc6b750ec400d275fc45b39c031a6d323501525fceb4"},"schema_version":"1.0"},"canonical_sha256":"748c42c502b2163d4a8d4c1b317346c368ae8075fd428e607ace8dd81d6460d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:43:37.947780Z","signature_b64":"EgdrJWofyoh9vdZqzTCOOrbr8lzbS+mD/VVoq1ZRxfEE8gU3E2J4ff0uCqrv6bXMhAxWMYiLp6638I94M9UdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"748c42c502b2163d4a8d4c1b317346c368ae8075fd428e607ace8dd81d6460d4","last_reissued_at":"2026-07-05T07:43:37.946755Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:43:37.946755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.06751","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmPwHxHhlvWyNldt4Jn64jivhDUylARUWbIW9I6EXXFpMcnHWvHeOsLkCebMMRaHj5zVPBZI/zFxtmRcKsxyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:28:11.508807Z"},"content_sha256":"1a1f1d395e8efcbb55ea55e67994c9a0d1b5ed9894f59766d813157b04868fbe","schema_version":"1.0","event_id":"sha256:1a1f1d395e8efcbb55ea55e67994c9a0d1b5ed9894f59766d813157b04868fbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OSGEFRICWILD2SUNJQNTC42GYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-Rank Learning by Design: the Role of Network Architecture and Activation Linearity in Gradient Rank Collapse","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Barak A. Pearlmutter, Bradley T. Baker, Robyn Miller, Sergey M. Plis, Vince D. Calhoun","submitted_at":"2024-02-09T19:28:02Z","abstract_excerpt":"Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of \"Neural Collapse\", where linear classifiers within DNNs converge to specific geometrical structures during late-stage training. However, the role of geometric constraints in learning extends beyond this terminal phase. For instance, gradients in fully-connected layers naturally develop a low-rank structure due to the accumulation of rank-one outer products over a training batch. Despite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06751","kind":"arxiv","version":1},"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/2402.06751/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfObPuRLauZVvCH6Mp0HKAAbY1z/1AnBvFbXe8g3S60I9HysXz75lWqXPQB9NX2HiBxdPFccM3xoPzIuO6jYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:28:11.509826Z"},"content_sha256":"8e545896251f9cac3242c4cf784ee87d755dc5c94cbe3e2b1a114d8bbe19c9b9","schema_version":"1.0","event_id":"sha256:8e545896251f9cac3242c4cf784ee87d755dc5c94cbe3e2b1a114d8bbe19c9b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSGEFRICWILD2SUNJQNTC42GYN/bundle.json","state_url":"https://pith.science/pith/OSGEFRICWILD2SUNJQNTC42GYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSGEFRICWILD2SUNJQNTC42GYN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T14:28:11Z","links":{"resolver":"https://pith.science/pith/OSGEFRICWILD2SUNJQNTC42GYN","bundle":"https://pith.science/pith/OSGEFRICWILD2SUNJQNTC42GYN/bundle.json","state":"https://pith.science/pith/OSGEFRICWILD2SUNJQNTC42GYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSGEFRICWILD2SUNJQNTC42GYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OSGEFRICWILD2SUNJQNTC42GYN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8cfd56088ccb6a09d0a6fc6b750ec400d275fc45b39c031a6d323501525fceb4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-09T19:28:02Z","title_canon_sha256":"a7e83bfa7842763c2dc5b4e7a97e040ae47d5ee8992421fbaf64d39de17bc9ff"},"schema_version":"1.0","source":{"id":"2402.06751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06751","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06751v1","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06751","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"OSGEFRICWILD","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"OSGEFRICWILD2SUN","created_at":"2026-07-05T07:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"OSGEFRIC","created_at":"2026-07-05T07:43:37Z"}],"graph_snapshots":[{"event_id":"sha256:8e545896251f9cac3242c4cf784ee87d755dc5c94cbe3e2b1a114d8bbe19c9b9","target":"graph","created_at":"2026-07-05T07:43:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.06751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of \"Neural Collapse\", where linear classifiers within DNNs converge to specific geometrical structures during late-stage training. However, the role of geometric constraints in learning extends beyond this terminal phase. For instance, gradients in fully-connected layers naturally develop a low-rank structure due to the accumulation of rank-one outer products over a training batch. Despite ","authors_text":"Barak A. Pearlmutter, Bradley T. Baker, Robyn Miller, Sergey M. Plis, Vince D. Calhoun","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-09T19:28:02Z","title":"Low-Rank Learning by Design: the Role of Network Architecture and Activation Linearity in Gradient Rank Collapse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06751","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1a1f1d395e8efcbb55ea55e67994c9a0d1b5ed9894f59766d813157b04868fbe","target":"record","created_at":"2026-07-05T07:43:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8cfd56088ccb6a09d0a6fc6b750ec400d275fc45b39c031a6d323501525fceb4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-09T19:28:02Z","title_canon_sha256":"a7e83bfa7842763c2dc5b4e7a97e040ae47d5ee8992421fbaf64d39de17bc9ff"},"schema_version":"1.0","source":{"id":"2402.06751","kind":"arxiv","version":1}},"canonical_sha256":"748c42c502b2163d4a8d4c1b317346c368ae8075fd428e607ace8dd81d6460d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"748c42c502b2163d4a8d4c1b317346c368ae8075fd428e607ace8dd81d6460d4","first_computed_at":"2026-07-05T07:43:37.946755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:43:37.946755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EgdrJWofyoh9vdZqzTCOOrbr8lzbS+mD/VVoq1ZRxfEE8gU3E2J4ff0uCqrv6bXMhAxWMYiLp6638I94M9UdCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:43:37.947780Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.06751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1f1d395e8efcbb55ea55e67994c9a0d1b5ed9894f59766d813157b04868fbe","sha256:8e545896251f9cac3242c4cf784ee87d755dc5c94cbe3e2b1a114d8bbe19c9b9"],"state_sha256":"8c7f084cd48e2bf767ccfc0115eb17718b6f15171be49bbd642c3a75c31a080c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLYqYBurCbrvgcuaKFiC7c0O9VvQ/z8N4jZkC6MBajIxz+vttbnwqa/Ku7hAXK+4cegLCrBJ4BXpBu7roC53Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T14:28:11.550107Z","bundle_sha256":"107ec40e81db9fa56139a20f123494d37a9e4bd660904684a1904fe0f401bb99"}}