{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MWOIJRFXEU4MZX6EUNANSWFFTK","short_pith_number":"pith:MWOIJRFX","schema_version":"1.0","canonical_sha256":"659c84c4b72538ccdfc4a340d958a59a81ae776b3a8c5cc61de1ea7ab12c6dc0","source":{"kind":"arxiv","id":"2506.05295","version":2},"attestation_state":"computed","paper":{"title":"Sample Complexity and Representation Ability of Test-time Scaling Paradigms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Ameet Talwalkar, Baihe Huang, Jiantao Jiao, Kannan Ramchandran, Michael I. Jordan, Shanda Li, Tianhao Wu, Yiming Yang","submitted_at":"2025-06-05T17:48:19Z","abstract_excerpt":"Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $\\Theta(1/\\Delta^2)$ samples to produce the correct answer, while best-of-$n$ only needs $\\Theta(1/\\Delta)$, where $\\Delta < 1$ denotes the probability gap be"},"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":"2506.05295","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-05T17:48:19Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"67dd75fc8b746ff6462bef387abc0b156516278b1ef244ec0b67f0dc6dac2e8e","abstract_canon_sha256":"f3d63ee606b2f7fb8e59bbe27d1380f14ae107bee6b49a6c7c02b0a4240d287a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:38.371844Z","signature_b64":"Namcw2OLJte2k/FrgL9dKj4SYlm3/ek1rI4qTGSAPD8TVyAUWWXT1o4jdDyKO47e9cPntNpbx1rldHUuGWMPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659c84c4b72538ccdfc4a340d958a59a81ae776b3a8c5cc61de1ea7ab12c6dc0","last_reissued_at":"2026-07-05T11:20:38.371395Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:38.371395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sample Complexity and Representation Ability of Test-time Scaling Paradigms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Ameet Talwalkar, Baihe Huang, Jiantao Jiao, Kannan Ramchandran, Michael I. Jordan, Shanda Li, Tianhao Wu, Yiming Yang","submitted_at":"2025-06-05T17:48:19Z","abstract_excerpt":"Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $\\Theta(1/\\Delta^2)$ samples to produce the correct answer, while best-of-$n$ only needs $\\Theta(1/\\Delta)$, where $\\Delta < 1$ denotes the probability gap be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05295","kind":"arxiv","version":2},"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/2506.05295/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":"2506.05295","created_at":"2026-07-05T11:20:38.371451+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05295v2","created_at":"2026-07-05T11:20:38.371451+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05295","created_at":"2026-07-05T11:20:38.371451+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWOIJRFXEU4M","created_at":"2026-07-05T11:20:38.371451+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWOIJRFXEU4MZX6E","created_at":"2026-07-05T11:20:38.371451+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWOIJRFX","created_at":"2026-07-05T11:20:38.371451+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/MWOIJRFXEU4MZX6EUNANSWFFTK","json":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK.json","graph_json":"https://pith.science/api/pith-number/MWOIJRFXEU4MZX6EUNANSWFFTK/graph.json","events_json":"https://pith.science/api/pith-number/MWOIJRFXEU4MZX6EUNANSWFFTK/events.json","paper":"https://pith.science/paper/MWOIJRFX"},"agent_actions":{"view_html":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK","download_json":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK.json","view_paper":"https://pith.science/paper/MWOIJRFX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05295&json=true","fetch_graph":"https://pith.science/api/pith-number/MWOIJRFXEU4MZX6EUNANSWFFTK/graph.json","fetch_events":"https://pith.science/api/pith-number/MWOIJRFXEU4MZX6EUNANSWFFTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK/action/storage_attestation","attest_author":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK/action/author_attestation","sign_citation":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK/action/citation_signature","submit_replication":"https://pith.science/pith/MWOIJRFXEU4MZX6EUNANSWFFTK/action/replication_record"}},"created_at":"2026-07-05T11:20:38.371451+00:00","updated_at":"2026-07-05T11:20:38.371451+00:00"}