{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:IJZMBOAG3EUN5RYLAE33OIJZ7D","short_pith_number":"pith:IJZMBOAG","canonical_record":{"source":{"id":"2202.08087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-16T14:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"bf8ee889f7800bd0cdec24440f852a8f3e516eb9184488302c7905198b2da968","abstract_canon_sha256":"3cb22ea1d479287ff3866010827abeb720f9b1688c9d08d1e7efcd9b087c1c8b"},"schema_version":"1.0"},"canonical_sha256":"4272c0b806d928dec70b0137b72139f8fff027d07175266456360b3b4f7d6ac2","source":{"kind":"arxiv","id":"2202.08087","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.08087","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2202.08087v3","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.08087","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"IJZMBOAG3EUN","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"IJZMBOAG3EUN5RYL","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"IJZMBOAG","created_at":"2026-07-05T05:05:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:IJZMBOAG3EUN5RYLAE33OIJZ7D","target":"record","payload":{"canonical_record":{"source":{"id":"2202.08087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-16T14:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"bf8ee889f7800bd0cdec24440f852a8f3e516eb9184488302c7905198b2da968","abstract_canon_sha256":"3cb22ea1d479287ff3866010827abeb720f9b1688c9d08d1e7efcd9b087c1c8b"},"schema_version":"1.0"},"canonical_sha256":"4272c0b806d928dec70b0137b72139f8fff027d07175266456360b3b4f7d6ac2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:05:45.564395Z","signature_b64":"q4YQC9HYvLgPtUqryYlinc+hPMFpRCAx5LoWjaPMOUbzQwth0coIMdl7lEMGRMDfRjXN5MECispmRVzlU9VdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4272c0b806d928dec70b0137b72139f8fff027d07175266456360b3b4f7d6ac2","last_reissued_at":"2026-07-05T05:05:45.562617Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:05:45.562617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.08087","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2HWYzUp8sZ+/8Yy2V4LFxZJB6tFecNNyD0tMXwiwcw6FOHc/oWnaOv1tTyViyvLfLarcuZdAfC9OPT0+2wwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:28:39.554922Z"},"content_sha256":"5eb02dd540bd875bc432678540434e97831fe1104a1a5c297c0a876b649a3e44","schema_version":"1.0","event_id":"sha256:5eb02dd540bd875bc432678540434e97831fe1104a1a5c297c0a876b649a3e44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:IJZMBOAG3EUN5RYLAE33OIJZ7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended Unconstrained Features Model for Exploring Deep Neural Collapse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Joan Bruna, Tom Tirer","submitted_at":"2022-02-16T14:17:37Z","abstract_excerpt":"The modern strategy for training deep neural networks for classification tasks includes optimizing the network's weights even after the training error vanishes to further push the training loss toward zero. Recently, a phenomenon termed \"neural collapse\" (NC) has been empirically observed in this training procedure. Specifically, it has been shown that the learned features (the output of the penultimate layer) of within-class samples converge to their mean, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's weights. Recent pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.08087","kind":"arxiv","version":3},"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/2202.08087/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":"2026-07-05T05:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejpCT/BWYjKOeKFqtAMYu5qX5yWtJP6IK+1LQvM8Bf1157cuedxx3YR2NjM4OD5xtbnsgjs49cqSmwPdp7o7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:28:39.555463Z"},"content_sha256":"a1715a5ca7777464f24abaef2032b1e9d72103118734e39fdeef0d8ff041d077","schema_version":"1.0","event_id":"sha256:a1715a5ca7777464f24abaef2032b1e9d72103118734e39fdeef0d8ff041d077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/bundle.json","state_url":"https://pith.science/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/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":"2026-08-18T02:28:39Z","links":{"resolver":"https://pith.science/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D","bundle":"https://pith.science/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/bundle.json","state":"https://pith.science/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJZMBOAG3EUN5RYLAE33OIJZ7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:IJZMBOAG3EUN5RYLAE33OIJZ7D","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":"3cb22ea1d479287ff3866010827abeb720f9b1688c9d08d1e7efcd9b087c1c8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-16T14:17:37Z","title_canon_sha256":"bf8ee889f7800bd0cdec24440f852a8f3e516eb9184488302c7905198b2da968"},"schema_version":"1.0","source":{"id":"2202.08087","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.08087","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2202.08087v3","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.08087","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"IJZMBOAG3EUN","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"IJZMBOAG3EUN5RYL","created_at":"2026-07-05T05:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"IJZMBOAG","created_at":"2026-07-05T05:05:45Z"}],"graph_snapshots":[{"event_id":"sha256:a1715a5ca7777464f24abaef2032b1e9d72103118734e39fdeef0d8ff041d077","target":"graph","created_at":"2026-07-05T05:05:45Z","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/2202.08087/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The modern strategy for training deep neural networks for classification tasks includes optimizing the network's weights even after the training error vanishes to further push the training loss toward zero. Recently, a phenomenon termed \"neural collapse\" (NC) has been empirically observed in this training procedure. Specifically, it has been shown that the learned features (the output of the penultimate layer) of within-class samples converge to their mean, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer's weights. Recent pa","authors_text":"Joan Bruna, Tom Tirer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-16T14:17:37Z","title":"Extended Unconstrained Features Model for Exploring Deep Neural Collapse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.08087","kind":"arxiv","version":3},"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":"sha256:5eb02dd540bd875bc432678540434e97831fe1104a1a5c297c0a876b649a3e44","target":"record","created_at":"2026-07-05T05:05:45Z","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":"3cb22ea1d479287ff3866010827abeb720f9b1688c9d08d1e7efcd9b087c1c8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-16T14:17:37Z","title_canon_sha256":"bf8ee889f7800bd0cdec24440f852a8f3e516eb9184488302c7905198b2da968"},"schema_version":"1.0","source":{"id":"2202.08087","kind":"arxiv","version":3}},"canonical_sha256":"4272c0b806d928dec70b0137b72139f8fff027d07175266456360b3b4f7d6ac2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4272c0b806d928dec70b0137b72139f8fff027d07175266456360b3b4f7d6ac2","first_computed_at":"2026-07-05T05:05:45.562617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:05:45.562617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4YQC9HYvLgPtUqryYlinc+hPMFpRCAx5LoWjaPMOUbzQwth0coIMdl7lEMGRMDfRjXN5MECispmRVzlU9VdDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:05:45.564395Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.08087","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5eb02dd540bd875bc432678540434e97831fe1104a1a5c297c0a876b649a3e44","sha256:a1715a5ca7777464f24abaef2032b1e9d72103118734e39fdeef0d8ff041d077"],"state_sha256":"09f4b748c1112a26228ffd48e4e32f66364c5047678901bbfe37e87f90a3aa8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9L4bZKpJLDiLg+fhKlQXOH7965K5DyhL0RTLIGGYqduiPsaJuYMBq1gzj4G1wyXQNnqF2tCsZZAfqPkNfUiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:28:39.561345Z","bundle_sha256":"ed80e76d7f3491231835f30b810718306b36e96dc89a5d98991d6f20ea6bde47"}}