{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UE37JQ35FFJRN3PQHOBT4SIE2N","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":"7d342f4797e1750d5a92acbcfe8fc4fb56ac5ec167367f19a95496628e774f66","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-07T23:14:45Z","title_canon_sha256":"511c857cdcac98e9b0a6fe0a98055a6391280cab19b5dbd2ec9e7599225dbce5"},"schema_version":"1.0","source":{"id":"1811.03179","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03179","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03179v4","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03179","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"UE37JQ35FFJR","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"UE37JQ35FFJRN3PQ","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"UE37JQ35","created_at":"2026-07-05T03:21:03Z"}],"graph_snapshots":[{"event_id":"sha256:f27ded946973cc9003af943b5170ee3d9761a2d4972a65662920e4aaba55de84","target":"graph","created_at":"2026-07-05T03:21:03Z","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/1811.03179/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric target distributions under a host of objective evaluation metrics. We investigate how to obtain valid statistical guarantees for GANs through the lens of regularization. On the nonparametric end, we derive the optimal minimax rates for distribution estimation under the ad","authors_text":"Tengyuan Liang","cross_cats":["cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-07T23:14:45Z","title":"How Well Generative Adversarial Networks Learn Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03179","kind":"arxiv","version":4},"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":"sha256:152f54c262edf23dd80dd86fb0547f13944ccc9b2a2029329b73de34e29549b3","target":"record","created_at":"2026-07-05T03:21:03Z","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":"7d342f4797e1750d5a92acbcfe8fc4fb56ac5ec167367f19a95496628e774f66","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-11-07T23:14:45Z","title_canon_sha256":"511c857cdcac98e9b0a6fe0a98055a6391280cab19b5dbd2ec9e7599225dbce5"},"schema_version":"1.0","source":{"id":"1811.03179","kind":"arxiv","version":4}},"canonical_sha256":"a137f4c37d295316edf03b833e4904d34e7703b6f9996257a30cedf5d89694b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a137f4c37d295316edf03b833e4904d34e7703b6f9996257a30cedf5d89694b6","first_computed_at":"2026-07-05T03:21:03.661883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:21:03.661883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vf32TEFSlU1iMCB4BMGr3EYKWD8ODgtcuVAp3Sg2Bd0I24+6NucCrk2rZKpmgSSmAGwdp6zoujIkHWenuJu7Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:21:03.662439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03179","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:152f54c262edf23dd80dd86fb0547f13944ccc9b2a2029329b73de34e29549b3","sha256:f27ded946973cc9003af943b5170ee3d9761a2d4972a65662920e4aaba55de84"],"state_sha256":"238b23d11faa3125452112b6b55e3062a2fe870bf191ce43cb7484607c5de9cf"}