{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BAU3CNHBF6VPCJDIGKYCUE52K6","short_pith_number":"pith:BAU3CNHB","schema_version":"1.0","canonical_sha256":"0829b134e12faaf1246832b02a13ba57af4182ead2742d3a3cac00b3a80c2272","source":{"kind":"arxiv","id":"2602.20555","version":2},"attestation_state":"computed","paper":{"title":"Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with $C^{s,\\lambda}$ Targets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Defeng Sun, Yanming Lai","submitted_at":"2026-02-24T05:14:01Z","abstract_excerpt":"The tremendous success of Transformer models in fields such as large language models and computer vision necessitates a rigorous theoretical investigation. To the best of our knowledge, this paper is the first work proving that standard Transformers can approximate H\\\"older functions $ C^{s,\\lambda}\\left([0,1]^{d\\times n}\\right) $$ (s\\in\\mathbb{N}_{\\geq0},0<\\lambda\\leq1) $ under the $L^t$ distance ($t \\in [1, \\infty]$) with arbitrary precision. Building upon this approximation result, we demonstrate that standard Transformers achieve the minimax optimal rate in nonparametric regression for H\\\""},"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":"2602.20555","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-02-24T05:14:01Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"5814e02ec2cfe8676a602bb2cdc67d147569a927b7c143fcc248fb9705a08658","abstract_canon_sha256":"86334b74dc1f24039a3624282521cf7ba60bddca143f8cb514e1aacc0afb6440"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:24:30.142703Z","signature_b64":"kRFRHhFAYzsK2BYZ7pR890qu2deR2om2kgHB6uSbRIzBPcdtHhAH0isIIWd+zZx1XxDBS+FbP2P3RoQMX/PuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0829b134e12faaf1246832b02a13ba57af4182ead2742d3a3cac00b3a80c2272","last_reissued_at":"2026-07-29T01:24:30.141217Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:24:30.141217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with $C^{s,\\lambda}$ Targets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Defeng Sun, Yanming Lai","submitted_at":"2026-02-24T05:14:01Z","abstract_excerpt":"The tremendous success of Transformer models in fields such as large language models and computer vision necessitates a rigorous theoretical investigation. To the best of our knowledge, this paper is the first work proving that standard Transformers can approximate H\\\"older functions $ C^{s,\\lambda}\\left([0,1]^{d\\times n}\\right) $$ (s\\in\\mathbb{N}_{\\geq0},0<\\lambda\\leq1) $ under the $L^t$ distance ($t \\in [1, \\infty]$) with arbitrary precision. Building upon this approximation result, we demonstrate that standard Transformers achieve the minimax optimal rate in nonparametric regression for H\\\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.20555","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/2602.20555/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":"2602.20555","created_at":"2026-07-29T01:24:30.141716+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.20555v2","created_at":"2026-07-29T01:24:30.141716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.20555","created_at":"2026-07-29T01:24:30.141716+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAU3CNHBF6VP","created_at":"2026-07-29T01:24:30.141716+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAU3CNHBF6VPCJDI","created_at":"2026-07-29T01:24:30.141716+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAU3CNHB","created_at":"2026-07-29T01:24:30.141716+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.13280","citing_title":"Generalization Bounds for Transformer-Based Next-Token Prediction in a Language Model","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6","json":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6.json","graph_json":"https://pith.science/api/pith-number/BAU3CNHBF6VPCJDIGKYCUE52K6/graph.json","events_json":"https://pith.science/api/pith-number/BAU3CNHBF6VPCJDIGKYCUE52K6/events.json","paper":"https://pith.science/paper/BAU3CNHB"},"agent_actions":{"view_html":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6","download_json":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6.json","view_paper":"https://pith.science/paper/BAU3CNHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.20555&json=true","fetch_graph":"https://pith.science/api/pith-number/BAU3CNHBF6VPCJDIGKYCUE52K6/graph.json","fetch_events":"https://pith.science/api/pith-number/BAU3CNHBF6VPCJDIGKYCUE52K6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6/action/storage_attestation","attest_author":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6/action/author_attestation","sign_citation":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6/action/citation_signature","submit_replication":"https://pith.science/pith/BAU3CNHBF6VPCJDIGKYCUE52K6/action/replication_record"}},"created_at":"2026-07-29T01:24:30.141716+00:00","updated_at":"2026-07-29T01:24:30.141716+00:00"}