{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SDSP2RBIFIXUQ3JDK2FRTCNOIL","short_pith_number":"pith:SDSP2RBI","schema_version":"1.0","canonical_sha256":"90e4fd44282a2f486d23568b1989ae42c08b89f200c299bb35dd4855cd7b59ae","source":{"kind":"arxiv","id":"2608.09558","version":1},"attestation_state":"computed","paper":{"title":"Training-Free Universal Approximation by Prompting Random Transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Alexander Hsu, Rongjie Lai","submitted_at":"2026-08-10T12:57:22Z","abstract_excerpt":"How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for determining whether task-specific behavior must be stored in model weights or can instead be induced at inference time through the prompt. We show, in an approximation-theoretic sense, that pretraining is optional: a single-layer softmax attention network with random, untrained weights can approximate any H\\\"older function on a compact manifold when steered by an appropriate soft prompt. Guided by the connection betw"},"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":"2608.09558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-10T12:57:22Z","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.TH"],"title_canon_sha256":"65f24dd7fc4267ac6d65b2e8a2b1779ecb9aae63ae07f35a17ceb7117b5d0385","abstract_canon_sha256":"ece0d879afd854db06ab8c73efe8c754d22a52dbac36f4f7b3f0ef88a97cee73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:24:30.229192Z","signature_b64":"NoqwdLoikUuRxkEd195+MoVao5RhabUv+MUZ/p97qxtWhyYOjJxJIpt8/XOFUIJrLSMjuZ2B9G5CMhR+ut9YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90e4fd44282a2f486d23568b1989ae42c08b89f200c299bb35dd4855cd7b59ae","last_reissued_at":"2026-08-11T02:24:30.227576Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:24:30.227576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Training-Free Universal Approximation by Prompting Random Transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Alexander Hsu, Rongjie Lai","submitted_at":"2026-08-10T12:57:22Z","abstract_excerpt":"How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for determining whether task-specific behavior must be stored in model weights or can instead be induced at inference time through the prompt. We show, in an approximation-theoretic sense, that pretraining is optional: a single-layer softmax attention network with random, untrained weights can approximate any H\\\"older function on a compact manifold when steered by an appropriate soft prompt. Guided by the connection betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09558","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/2608.09558/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":"2608.09558","created_at":"2026-08-11T02:24:30.228206+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.09558v1","created_at":"2026-08-11T02:24:30.228206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09558","created_at":"2026-08-11T02:24:30.228206+00:00"},{"alias_kind":"pith_short_12","alias_value":"SDSP2RBIFIXU","created_at":"2026-08-11T02:24:30.228206+00:00"},{"alias_kind":"pith_short_16","alias_value":"SDSP2RBIFIXUQ3JD","created_at":"2026-08-11T02:24:30.228206+00:00"},{"alias_kind":"pith_short_8","alias_value":"SDSP2RBI","created_at":"2026-08-11T02:24:30.228206+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/SDSP2RBIFIXUQ3JDK2FRTCNOIL","json":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL.json","graph_json":"https://pith.science/api/pith-number/SDSP2RBIFIXUQ3JDK2FRTCNOIL/graph.json","events_json":"https://pith.science/api/pith-number/SDSP2RBIFIXUQ3JDK2FRTCNOIL/events.json","paper":"https://pith.science/paper/SDSP2RBI"},"agent_actions":{"view_html":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL","download_json":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL.json","view_paper":"https://pith.science/paper/SDSP2RBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.09558&json=true","fetch_graph":"https://pith.science/api/pith-number/SDSP2RBIFIXUQ3JDK2FRTCNOIL/graph.json","fetch_events":"https://pith.science/api/pith-number/SDSP2RBIFIXUQ3JDK2FRTCNOIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL/action/storage_attestation","attest_author":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL/action/author_attestation","sign_citation":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL/action/citation_signature","submit_replication":"https://pith.science/pith/SDSP2RBIFIXUQ3JDK2FRTCNOIL/action/replication_record"}},"created_at":"2026-08-11T02:24:30.228206+00:00","updated_at":"2026-08-11T02:24:30.228206+00:00"}