{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:RFIDBTZSBDWMFWTNQY4RO67WOS","short_pith_number":"pith:RFIDBTZS","schema_version":"1.0","canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","source":{"kind":"arxiv","id":"2008.02545","version":3},"attestation_state":"computed","paper":{"title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Alexander Cloninger, Timo Klock","submitted_at":"2020-08-06T09:50:29Z","abstract_excerpt":"We study the approximation of two-layer compositions $f(x) = g(\\phi(x))$ via deep networks with ReLU activation, where $\\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically relevant choices for $\\phi$: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets. We achieve near optimal approximation rates, which depend only on the complexity of the dimensionality reducing map $\\phi$ rather than the ambient dimension. Since $\\phi$ encapsulates all nonlinear features that are mater"},"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":"2008.02545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-08-06T09:50:29Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"cb3f6cb1a5c8aa52d146b7b39795a1d6efa4a0f5fb59986d48192ebe16995d27","abstract_canon_sha256":"551a0d1b8f81ec9a2e09e73b1f35f34bef25e737e6cd8b3aa7ff140f1e30adf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:34:41.637879Z","signature_b64":"/eqBX4bZ6hohC4QO9DhI2Jk1AI3YNl3ZLyUHRYfnY28VVep1HS0wm9LSCok3gIage23+Exl3b5UZjLlpED07Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"895030cf3208ecc2da6d8639177bf6749157e52106b49443f658ffeeac572a5c","last_reissued_at":"2026-07-05T02:34:41.637408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:34:41.637408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Alexander Cloninger, Timo Klock","submitted_at":"2020-08-06T09:50:29Z","abstract_excerpt":"We study the approximation of two-layer compositions $f(x) = g(\\phi(x))$ via deep networks with ReLU activation, where $\\phi$ is a geometrically intuitive, dimensionality reducing feature map. We focus on two intuitive and practically relevant choices for $\\phi$: the projection onto a low-dimensional embedded submanifold and a distance to a collection of low-dimensional sets. We achieve near optimal approximation rates, which depend only on the complexity of the dimensionality reducing map $\\phi$ rather than the ambient dimension. Since $\\phi$ encapsulates all nonlinear features that are mater"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02545","kind":"arxiv","version":3},"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/2008.02545/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":"2008.02545","created_at":"2026-07-05T02:34:41.637461+00:00"},{"alias_kind":"arxiv_version","alias_value":"2008.02545v3","created_at":"2026-07-05T02:34:41.637461+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02545","created_at":"2026-07-05T02:34:41.637461+00:00"},{"alias_kind":"pith_short_12","alias_value":"RFIDBTZSBDWM","created_at":"2026-07-05T02:34:41.637461+00:00"},{"alias_kind":"pith_short_16","alias_value":"RFIDBTZSBDWMFWTN","created_at":"2026-07-05T02:34:41.637461+00:00"},{"alias_kind":"pith_short_8","alias_value":"RFIDBTZS","created_at":"2026-07-05T02:34:41.637461+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.20853","citing_title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS","json":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS.json","graph_json":"https://pith.science/api/pith-number/RFIDBTZSBDWMFWTNQY4RO67WOS/graph.json","events_json":"https://pith.science/api/pith-number/RFIDBTZSBDWMFWTNQY4RO67WOS/events.json","paper":"https://pith.science/paper/RFIDBTZS"},"agent_actions":{"view_html":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS","download_json":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS.json","view_paper":"https://pith.science/paper/RFIDBTZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2008.02545&json=true","fetch_graph":"https://pith.science/api/pith-number/RFIDBTZSBDWMFWTNQY4RO67WOS/graph.json","fetch_events":"https://pith.science/api/pith-number/RFIDBTZSBDWMFWTNQY4RO67WOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/action/storage_attestation","attest_author":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/action/author_attestation","sign_citation":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/action/citation_signature","submit_replication":"https://pith.science/pith/RFIDBTZSBDWMFWTNQY4RO67WOS/action/replication_record"}},"created_at":"2026-07-05T02:34:41.637461+00:00","updated_at":"2026-07-05T02:34:41.637461+00:00"}