{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TPVCVXPE2ADHS2BYBGNGFHUE3I","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":"22d61da14adb3a88480770c7129bbdec0982d4fb170e8682ec8e8cef2f019751","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-06-08T00:05:39Z","title_canon_sha256":"3662194abfa0004b999d40c4e66371901bc0488e03db583816c34b772ec57a65"},"schema_version":"1.0","source":{"id":"2106.04018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04018","created_at":"2026-07-05T04:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04018v2","created_at":"2026-07-05T04:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04018","created_at":"2026-07-05T04:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"TPVCVXPE2ADH","created_at":"2026-07-05T04:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"TPVCVXPE2ADHS2BY","created_at":"2026-07-05T04:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"TPVCVXPE","created_at":"2026-07-05T04:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e3f3bdeea8bc78ef058cc8080a96b39b83f786444c2e4cf9e0ac1e31a77a7142","target":"graph","created_at":"2026-07-05T04:27:43Z","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/2106.04018/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension of a given population distribution from a finite sample. We introduce a new estimator of the intrinsic dimension and provide finite sample, non-asymptotic guarantees. We then apply our techniques to get new sample complexity bounds for Generative Adversarial Networks (GANs) depending only on the intrinsic dimension of the data.","authors_text":"Adam Block, Alexander Rakhlin, Yury Polyanskiy, Zeyu Jia","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-06-08T00:05:39Z","title":"Intrinsic Dimension Estimation Using Wasserstein Distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04018","kind":"arxiv","version":2},"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:c057636d927a2ffb609a3b7f76c3da84289098514b6975ba313b5a4e57b049db","target":"record","created_at":"2026-07-05T04:27:43Z","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":"22d61da14adb3a88480770c7129bbdec0982d4fb170e8682ec8e8cef2f019751","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-06-08T00:05:39Z","title_canon_sha256":"3662194abfa0004b999d40c4e66371901bc0488e03db583816c34b772ec57a65"},"schema_version":"1.0","source":{"id":"2106.04018","kind":"arxiv","version":2}},"canonical_sha256":"9bea2adde4d006796838099a629e84da1ae6ad766199a3a562f90e7f016dd60a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bea2adde4d006796838099a629e84da1ae6ad766199a3a562f90e7f016dd60a","first_computed_at":"2026-07-05T04:27:43.094550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:43.094550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Js1QPSlDhIZ7TeSq7l2e5I0sImbi5ovIiuIE3IHZLD4lo5BACz+UcYL8sBeLT+DlvGvF7iyT6Uyy3Ymz0qQDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:43.094916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.04018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c057636d927a2ffb609a3b7f76c3da84289098514b6975ba313b5a4e57b049db","sha256:e3f3bdeea8bc78ef058cc8080a96b39b83f786444c2e4cf9e0ac1e31a77a7142"],"state_sha256":"ba85fb49f8be10da7536233b46e50142f22a64299b8b1b7bb54256bb0e8fb61e"}