{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:E4SHNPUA56WJC3LFT5XHI5IZ7N","short_pith_number":"pith:E4SHNPUA","schema_version":"1.0","canonical_sha256":"272476be80efac916d659f6e747519fb43a0fd87a61a573ed63712e24277957b","source":{"kind":"arxiv","id":"2412.09779","version":1},"attestation_state":"computed","paper":{"title":"A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Peter L. Bartlett, Saptarshi Chakraborty","submitted_at":"2024-12-13T01:15:17Z","abstract_excerpt":"Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this intrinsic dimension as the Minkowski dimension or the manifold dimension of the support of the underlying probability measures, which often results in sub-optimal rates and unrealistic assumptions. In this paper, we consider supervised deep learning when the response given the explanatory variable is distributed according to an exponential family with a $\\b"},"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":"2412.09779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-12-13T01:15:17Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"40178dda0a410dd535d3e61b77db47b11a37895ea9bfe36cb97c76e827cf7d9a","abstract_canon_sha256":"a7863ac725e0a94176f53a3d57974087c300bd91fabd905858806ff10d2afcde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:41.240585Z","signature_b64":"u9mQu0RkS58OUqcUNR2s/8COZwy8E8i4bkFFlTb3yPVrT64nW4yQJDOpdspPABToFoaiAmmiOdOApHZwntGVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"272476be80efac916d659f6e747519fb43a0fd87a61a573ed63712e24277957b","last_reissued_at":"2026-07-05T09:48:41.240171Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:41.240171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Peter L. Bartlett, Saptarshi Chakraborty","submitted_at":"2024-12-13T01:15:17Z","abstract_excerpt":"Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this intrinsic dimension as the Minkowski dimension or the manifold dimension of the support of the underlying probability measures, which often results in sub-optimal rates and unrealistic assumptions. In this paper, we consider supervised deep learning when the response given the explanatory variable is distributed according to an exponential family with a $\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.09779","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/2412.09779/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":"2412.09779","created_at":"2026-07-05T09:48:41.240229+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.09779v1","created_at":"2026-07-05T09:48:41.240229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.09779","created_at":"2026-07-05T09:48:41.240229+00:00"},{"alias_kind":"pith_short_12","alias_value":"E4SHNPUA56WJ","created_at":"2026-07-05T09:48:41.240229+00:00"},{"alias_kind":"pith_short_16","alias_value":"E4SHNPUA56WJC3LF","created_at":"2026-07-05T09:48:41.240229+00:00"},{"alias_kind":"pith_short_8","alias_value":"E4SHNPUA","created_at":"2026-07-05T09:48:41.240229+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/E4SHNPUA56WJC3LFT5XHI5IZ7N","json":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N.json","graph_json":"https://pith.science/api/pith-number/E4SHNPUA56WJC3LFT5XHI5IZ7N/graph.json","events_json":"https://pith.science/api/pith-number/E4SHNPUA56WJC3LFT5XHI5IZ7N/events.json","paper":"https://pith.science/paper/E4SHNPUA"},"agent_actions":{"view_html":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N","download_json":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N.json","view_paper":"https://pith.science/paper/E4SHNPUA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.09779&json=true","fetch_graph":"https://pith.science/api/pith-number/E4SHNPUA56WJC3LFT5XHI5IZ7N/graph.json","fetch_events":"https://pith.science/api/pith-number/E4SHNPUA56WJC3LFT5XHI5IZ7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N/action/storage_attestation","attest_author":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N/action/author_attestation","sign_citation":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N/action/citation_signature","submit_replication":"https://pith.science/pith/E4SHNPUA56WJC3LFT5XHI5IZ7N/action/replication_record"}},"created_at":"2026-07-05T09:48:41.240229+00:00","updated_at":"2026-07-05T09:48:41.240229+00:00"}