{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ORG2DZ5OLIJ5KGWEJEOSQ6SFX4","short_pith_number":"pith:ORG2DZ5O","schema_version":"1.0","canonical_sha256":"744da1e7ae5a13d51ac4491d287a45bf0950dadfca8e1d130c00345f2ec3d4c7","source":{"kind":"arxiv","id":"2605.20105","version":1},"attestation_state":"computed","paper":{"title":"Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andrew Saxe, Cl\\'ementine Domin\\'e, Marco Mondelli, Rachel Swanson, Valentina Njaradi","submitted_at":"2026-05-19T16:56:56Z","abstract_excerpt":"Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelle"},"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":"2605.20105","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T16:56:56Z","cross_cats_sorted":[],"title_canon_sha256":"5c8f6335628d93922b09fc08ebe5b9b2a12386efe4e629fb7b889a4aaf54d6d6","abstract_canon_sha256":"c4e5a1838346ad3f0ba00cacfb5065786814ca395d78fdeb64b5e077c57160f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:06:02.264043Z","signature_b64":"FmG7SpvI+1VVXVC6eBjlar29S9ZL6Zx+UeWBrB1HzjLhTK84KxOZUNjqJVLRUOAe4LlrbVhQH5uukHyu36Q1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"744da1e7ae5a13d51ac4491d287a45bf0950dadfca8e1d130c00345f2ec3d4c7","last_reissued_at":"2026-05-20T02:06:02.263416Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:06:02.263416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Representation Size: High-Dimensional Analysis of Pretraining and Linear Probing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andrew Saxe, Cl\\'ementine Domin\\'e, Marco Mondelli, Rachel Swanson, Valentina Njaradi","submitted_at":"2026-05-19T16:56:56Z","abstract_excerpt":"Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20105","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/2605.20105/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":"2605.20105","created_at":"2026-05-20T02:06:02.263514+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20105v1","created_at":"2026-05-20T02:06:02.263514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20105","created_at":"2026-05-20T02:06:02.263514+00:00"},{"alias_kind":"pith_short_12","alias_value":"ORG2DZ5OLIJ5","created_at":"2026-05-20T02:06:02.263514+00:00"},{"alias_kind":"pith_short_16","alias_value":"ORG2DZ5OLIJ5KGWE","created_at":"2026-05-20T02:06:02.263514+00:00"},{"alias_kind":"pith_short_8","alias_value":"ORG2DZ5O","created_at":"2026-05-20T02:06:02.263514+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/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4","json":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4.json","graph_json":"https://pith.science/api/pith-number/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/graph.json","events_json":"https://pith.science/api/pith-number/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/events.json","paper":"https://pith.science/paper/ORG2DZ5O"},"agent_actions":{"view_html":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4","download_json":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4.json","view_paper":"https://pith.science/paper/ORG2DZ5O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20105&json=true","fetch_graph":"https://pith.science/api/pith-number/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/graph.json","fetch_events":"https://pith.science/api/pith-number/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/action/storage_attestation","attest_author":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/action/author_attestation","sign_citation":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/action/citation_signature","submit_replication":"https://pith.science/pith/ORG2DZ5OLIJ5KGWEJEOSQ6SFX4/action/replication_record"}},"created_at":"2026-05-20T02:06:02.263514+00:00","updated_at":"2026-05-20T02:06:02.263514+00:00"}