{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CYEJQUMA4BWG3SRHBI45LBVPN6","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":"34516a65b5039ec1ab6f8f30869c76d39a9d0cd50c45e8b86b3b99158d8aa1c1","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-21T08:16:03Z","title_canon_sha256":"41fa679f943c97b1b1ba845537ad4424df889cd6bc273cd8fa571edafbfb6608"},"schema_version":"1.0","source":{"id":"2505.15239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.15239","created_at":"2026-07-05T11:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2505.15239v1","created_at":"2026-07-05T11:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.15239","created_at":"2026-07-05T11:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"CYEJQUMA4BWG","created_at":"2026-07-05T11:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"CYEJQUMA4BWG3SRH","created_at":"2026-07-05T11:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"CYEJQUMA","created_at":"2026-07-05T11:06:42Z"}],"graph_snapshots":[{"event_id":"sha256:ac9aa5c97107d709ec4f22bc9eac1817f2a8f4721ccb405025a013b143abd654","target":"graph","created_at":"2026-07-05T11:06:42Z","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/2505.15239/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The empirical emergence of neural collapse -- a surprising symmetry in the feature representations of the training data in the penultimate layer of deep neural networks -- has spurred a line of theoretical research aimed at its understanding. However, existing work focuses on data-agnostic models or, when data structure is taken into account, it remains limited to multi-layer perceptrons. Our paper fills both these gaps by analyzing modern architectures in a data-aware regime: we prove that global optima of deep regularized transformers and residual networks (ResNets) with LayerNorm trained wi","authors_text":"Christoph H. Lampert, Marco Mondelli, Peter S\\'uken\\'ik","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15239","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:b7a7cde30bceee5d0ece27985cfb0c412c70756fcfe05f582f13b087af6d1cfb","target":"record","created_at":"2026-07-05T11:06:42Z","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":"34516a65b5039ec1ab6f8f30869c76d39a9d0cd50c45e8b86b3b99158d8aa1c1","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-21T08:16:03Z","title_canon_sha256":"41fa679f943c97b1b1ba845537ad4424df889cd6bc273cd8fa571edafbfb6608"},"schema_version":"1.0","source":{"id":"2505.15239","kind":"arxiv","version":1}},"canonical_sha256":"1608985180e06c6dca270a39d586af6f97f3d182c0c97f0d0c546c059d4e165b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1608985180e06c6dca270a39d586af6f97f3d182c0c97f0d0c546c059d4e165b","first_computed_at":"2026-07-05T11:06:42.572828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:42.572828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MRaDrnBw5ygpOWN6rJBnSxRVGtskDFi6aIiKYF8pVnNjchl6Y6n4cS2Btlb8og9FXJoTzSD5iDZKmlAmx3FbDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:42.573291Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.15239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7a7cde30bceee5d0ece27985cfb0c412c70756fcfe05f582f13b087af6d1cfb","sha256:ac9aa5c97107d709ec4f22bc9eac1817f2a8f4721ccb405025a013b143abd654"],"state_sha256":"1a30ea544fa7d5ecb72fb0a8bbaba65a9d620f3090a71fdede7b1623c81cf21a"}