{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MZ2I4YLEG7HIJFPTREGGR2ATBF","short_pith_number":"pith:MZ2I4YLE","schema_version":"1.0","canonical_sha256":"66748e616437ce8495f3890c68e8130954da1af7d88306fc10454382952d8a5f","source":{"kind":"arxiv","id":"2606.19367","version":1},"attestation_state":"computed","paper":{"title":"Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Tiexin Ding","submitted_at":"2026-06-11T03:50:14Z","abstract_excerpt":"Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter $\\lambda$ grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the"},"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":"2606.19367","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"13f49c945e26e399eb4af14457a586432bb65991599bcfa9c1bb54f179a8d4d2","abstract_canon_sha256":"8e9321f4d7deec0a7a4de6913711d16f10ebc713837b5b2da42208c6cded9709"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:23.303200Z","signature_b64":"QhD6YmaIX6zNOnXtF9McM/p0K4hJIstgOswaMqAgLkKmXRB7JnBFYpwXGpn9UvFtnFKUlScVbQrHTiQshsCdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66748e616437ce8495f3890c68e8130954da1af7d88306fc10454382952d8a5f","last_reissued_at":"2026-06-19T16:12:23.302722Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:23.302722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Tiexin Ding","submitted_at":"2026-06-11T03:50:14Z","abstract_excerpt":"Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter $\\lambda$ grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19367","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/2606.19367/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":"2606.19367","created_at":"2026-06-19T16:12:23.302776+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19367v1","created_at":"2026-06-19T16:12:23.302776+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19367","created_at":"2026-06-19T16:12:23.302776+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZ2I4YLEG7HI","created_at":"2026-06-19T16:12:23.302776+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZ2I4YLEG7HIJFPT","created_at":"2026-06-19T16:12:23.302776+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZ2I4YLE","created_at":"2026-06-19T16:12:23.302776+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF","json":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF.json","graph_json":"https://pith.science/api/pith-number/MZ2I4YLEG7HIJFPTREGGR2ATBF/graph.json","events_json":"https://pith.science/api/pith-number/MZ2I4YLEG7HIJFPTREGGR2ATBF/events.json","paper":"https://pith.science/paper/MZ2I4YLE"},"agent_actions":{"view_html":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF","download_json":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF.json","view_paper":"https://pith.science/paper/MZ2I4YLE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19367&json=true","fetch_graph":"https://pith.science/api/pith-number/MZ2I4YLEG7HIJFPTREGGR2ATBF/graph.json","fetch_events":"https://pith.science/api/pith-number/MZ2I4YLEG7HIJFPTREGGR2ATBF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF/action/storage_attestation","attest_author":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF/action/author_attestation","sign_citation":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF/action/citation_signature","submit_replication":"https://pith.science/pith/MZ2I4YLEG7HIJFPTREGGR2ATBF/action/replication_record"}},"created_at":"2026-06-19T16:12:23.302776+00:00","updated_at":"2026-06-19T16:12:23.302776+00:00"}