{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JRTLC55NYMKASDXGJUNXTHN7GC","short_pith_number":"pith:JRTLC55N","schema_version":"1.0","canonical_sha256":"4c66b177adc314090ee64d1b799dbf30a04733f0acbe847293b288dfd05570c8","source":{"kind":"arxiv","id":"2504.13558","version":1},"attestation_state":"computed","paper":{"title":"Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Bokai Yan, Yang Wang, Yanming Lai, Yuling Jiao","submitted_at":"2025-04-18T08:56:53Z","abstract_excerpt":"The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the H\\\"older continuous function class $\\mathcal{H}_{Q}^{\\beta}\\left([0,1]^{d\\times n},\\mathbb{R}^{d\\times n}\\right)$ by Transformers and constructs several Transformers that can overcome the curse of dimensionality. These Transformers consist of one self-attention layer with one head and the softmax function as the activation function, along with several feedforward layers. For example, to achieve an approximation accuracy of "},"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":"2504.13558","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-18T08:56:53Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"3d13061c6f52192f39ad108bdfb24e4cc2b4767bf6dafbdf1eb6b12552bd1daa","abstract_canon_sha256":"2a9c4cece60675622153094984aef9c6f531adbc5bb5a8b760aa3ee30d3d4672"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:57.794386Z","signature_b64":"y1GZVP2tbgy/U+J5s8hS70p2wsuBmLdV764HRelrPjji6o1ZiU7UjnUPwQe8M1SVozFXLe8iRL7pztXYV/+GAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c66b177adc314090ee64d1b799dbf30a04733f0acbe847293b288dfd05570c8","last_reissued_at":"2026-07-05T10:50:57.793923Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:57.793923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Bokai Yan, Yang Wang, Yanming Lai, Yuling Jiao","submitted_at":"2025-04-18T08:56:53Z","abstract_excerpt":"The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the H\\\"older continuous function class $\\mathcal{H}_{Q}^{\\beta}\\left([0,1]^{d\\times n},\\mathbb{R}^{d\\times n}\\right)$ by Transformers and constructs several Transformers that can overcome the curse of dimensionality. These Transformers consist of one self-attention layer with one head and the softmax function as the activation function, along with several feedforward layers. For example, to achieve an approximation accuracy of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.13558","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/2504.13558/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":"2504.13558","created_at":"2026-07-05T10:50:57.793981+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.13558v1","created_at":"2026-07-05T10:50:57.793981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.13558","created_at":"2026-07-05T10:50:57.793981+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRTLC55NYMKA","created_at":"2026-07-05T10:50:57.793981+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRTLC55NYMKASDXG","created_at":"2026-07-05T10:50:57.793981+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRTLC55N","created_at":"2026-07-05T10:50:57.793981+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/JRTLC55NYMKASDXGJUNXTHN7GC","json":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC.json","graph_json":"https://pith.science/api/pith-number/JRTLC55NYMKASDXGJUNXTHN7GC/graph.json","events_json":"https://pith.science/api/pith-number/JRTLC55NYMKASDXGJUNXTHN7GC/events.json","paper":"https://pith.science/paper/JRTLC55N"},"agent_actions":{"view_html":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC","download_json":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC.json","view_paper":"https://pith.science/paper/JRTLC55N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.13558&json=true","fetch_graph":"https://pith.science/api/pith-number/JRTLC55NYMKASDXGJUNXTHN7GC/graph.json","fetch_events":"https://pith.science/api/pith-number/JRTLC55NYMKASDXGJUNXTHN7GC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC/action/storage_attestation","attest_author":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC/action/author_attestation","sign_citation":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC/action/citation_signature","submit_replication":"https://pith.science/pith/JRTLC55NYMKASDXGJUNXTHN7GC/action/replication_record"}},"created_at":"2026-07-05T10:50:57.793981+00:00","updated_at":"2026-07-05T10:50:57.793981+00:00"}