{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FNQBSFQJGYOVQM7HAFFGH5SVGK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"169ba3382728b5b1841df268871dadfd36a37ee7c7c4b696c4eebfe7e09d48e2","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-06-26T17:13:31Z","title_canon_sha256":"80df394787933b10da33be96d226d0951b4d72a4658582d665de5306d8ea2baf"},"schema_version":"1.0","source":{"id":"2306.14859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.14859","created_at":"2026-07-05T06:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"2306.14859v1","created_at":"2026-07-05T06:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.14859","created_at":"2026-07-05T06:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"FNQBSFQJGYOV","created_at":"2026-07-05T06:24:41Z"},{"alias_kind":"pith_short_16","alias_value":"FNQBSFQJGYOVQM7H","created_at":"2026-07-05T06:24:41Z"},{"alias_kind":"pith_short_8","alias_value":"FNQBSFQJ","created_at":"2026-07-05T06:24:41Z"}],"graph_snapshots":[{"event_id":"sha256:ce46f1bfe6cce1eae5d624909080ccb41efcaea97b78de34c13354a185232089","target":"graph","created_at":"2026-07-05T06:24:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.14859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying exactly on a low dimensional manifold is stringent. This paper introduces a relaxed assumption that the input data are concentrated around a subset of $\\mathbb{R}^d$ denoted by $\\mathcal{S}$, and the intrinsic dimension of $\\mathcal{S}$ can be characterized by a new complexity notation -- effective Minkowski dimension. We prove that, the sample compl","authors_text":"Mengdi Wang, Minshuo Chen, Tuo Zhao, Wenjing Liao, Zixuan Zhang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-06-26T17:13:31Z","title":"Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.14859","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6e629bf5227cc699c77290ec395ee181ec9d6a4e831290f7f51885446d55405b","target":"record","created_at":"2026-07-05T06:24:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"169ba3382728b5b1841df268871dadfd36a37ee7c7c4b696c4eebfe7e09d48e2","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-06-26T17:13:31Z","title_canon_sha256":"80df394787933b10da33be96d226d0951b4d72a4658582d665de5306d8ea2baf"},"schema_version":"1.0","source":{"id":"2306.14859","kind":"arxiv","version":1}},"canonical_sha256":"2b60191609361d5833e7014a63f65532ad3c6d67a2be0c0c2223fbb9f7c432f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b60191609361d5833e7014a63f65532ad3c6d67a2be0c0c2223fbb9f7c432f8","first_computed_at":"2026-07-05T06:24:41.504581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:24:41.504581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fnp/5rGSDV0YlAuKPz21ZV5rA2nvlHmw/hoSYv25S/Bw6Zl+EBAe2wOCot/nB9KB5AZoPJHC0sndaVfXuBWpBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:24:41.504983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.14859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e629bf5227cc699c77290ec395ee181ec9d6a4e831290f7f51885446d55405b","sha256:ce46f1bfe6cce1eae5d624909080ccb41efcaea97b78de34c13354a185232089"],"state_sha256":"36c306bbb363539f58376795621717a2f9d32a1c46f65842bed281c57c80a4b2"}