{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DZW2CLWLQVYCN6WKA5AUPPIM2Q","short_pith_number":"pith:DZW2CLWL","schema_version":"1.0","canonical_sha256":"1e6da12ecb857026faca074147bd0cd40969239283c1b84879fae3a29b539870","source":{"kind":"arxiv","id":"2605.21292","version":1},"attestation_state":"computed","paper":{"title":"Large-Step Training Dynamics of a Two-Factor Linear Transformer Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.DS"],"primary_cat":"stat.ML","authors_text":"Krishnakumar Balasubramanian","submitted_at":"2026-05-20T15:25:13Z","abstract_excerpt":"Gradient-flow analyses show that simplified linear transformers can learn the in-context linear-regression algorithm, but they do not explain the finite-step behavior of gradient descent at large learning rates. Motivated by empirical work on high-learning-rate transformer instabilities and by the cubic-map phase diagram for quadratic regression, we study an exactly reducible one-prompt linear-transformer training problem. After normalization, the dynamics reduce to a two-factor product map with an effective step-size parameter \\(\\mu\\). On the balanced slice, this map recovers the known scalar"},"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":"2605.21292","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-20T15:25:13Z","cross_cats_sorted":["cs.AI","cs.LG","math.DS"],"title_canon_sha256":"d0d77273e936fd8b70015905af6f2f77620a9fad1b927c2cc5a4dfcc490e2e3c","abstract_canon_sha256":"6c640cedfce0f2cf08a82547b097da70c8e0a7524208999ecbd33342e7f9e374"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:27.444893Z","signature_b64":"pwZ7TEidojMxWcNQeAh2Qek/2HAt0BcYCi0XdrnxP5pnyGluMQyzmiUFS0HE35nC3IDSaJ4feO2gVk2BWl28DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e6da12ecb857026faca074147bd0cd40969239283c1b84879fae3a29b539870","last_reissued_at":"2026-05-21T02:05:27.444198Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:27.444198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large-Step Training Dynamics of a Two-Factor Linear Transformer Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.DS"],"primary_cat":"stat.ML","authors_text":"Krishnakumar Balasubramanian","submitted_at":"2026-05-20T15:25:13Z","abstract_excerpt":"Gradient-flow analyses show that simplified linear transformers can learn the in-context linear-regression algorithm, but they do not explain the finite-step behavior of gradient descent at large learning rates. Motivated by empirical work on high-learning-rate transformer instabilities and by the cubic-map phase diagram for quadratic regression, we study an exactly reducible one-prompt linear-transformer training problem. After normalization, the dynamics reduce to a two-factor product map with an effective step-size parameter \\(\\mu\\). On the balanced slice, this map recovers the known scalar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21292","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/2605.21292/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":"2605.21292","created_at":"2026-05-21T02:05:27.444348+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21292v1","created_at":"2026-05-21T02:05:27.444348+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21292","created_at":"2026-05-21T02:05:27.444348+00:00"},{"alias_kind":"pith_short_12","alias_value":"DZW2CLWLQVYC","created_at":"2026-05-21T02:05:27.444348+00:00"},{"alias_kind":"pith_short_16","alias_value":"DZW2CLWLQVYCN6WK","created_at":"2026-05-21T02:05:27.444348+00:00"},{"alias_kind":"pith_short_8","alias_value":"DZW2CLWL","created_at":"2026-05-21T02:05:27.444348+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/DZW2CLWLQVYCN6WKA5AUPPIM2Q","json":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q.json","graph_json":"https://pith.science/api/pith-number/DZW2CLWLQVYCN6WKA5AUPPIM2Q/graph.json","events_json":"https://pith.science/api/pith-number/DZW2CLWLQVYCN6WKA5AUPPIM2Q/events.json","paper":"https://pith.science/paper/DZW2CLWL"},"agent_actions":{"view_html":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q","download_json":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q.json","view_paper":"https://pith.science/paper/DZW2CLWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21292&json=true","fetch_graph":"https://pith.science/api/pith-number/DZW2CLWLQVYCN6WKA5AUPPIM2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/DZW2CLWLQVYCN6WKA5AUPPIM2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q/action/storage_attestation","attest_author":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q/action/author_attestation","sign_citation":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q/action/citation_signature","submit_replication":"https://pith.science/pith/DZW2CLWLQVYCN6WKA5AUPPIM2Q/action/replication_record"}},"created_at":"2026-05-21T02:05:27.444348+00:00","updated_at":"2026-05-21T02:05:27.444348+00:00"}