{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2KJHMPACPBTPNOMMP6OCBSRAMA","short_pith_number":"pith:2KJHMPAC","schema_version":"1.0","canonical_sha256":"d292763c027866f6b98c7f9c20ca206017563a023d8d9c98d80326a8f468d5a9","source":{"kind":"arxiv","id":"1806.09235","version":2},"attestation_state":"computed","paper":{"title":"Towards a Better Understanding and Regularization of GAN Training Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ankit Patel, Weili Nie","submitted_at":"2018-06-24T23:19:23Z","abstract_excerpt":"Generative adversarial networks (GANs) are notoriously difficult to train and the reasons underlying their (non-)convergence behaviors are still not completely understood. By first considering a simple yet representative GAN example, we mathematically analyze its local convergence behavior in a non-asymptotic way. Furthermore, the analysis is extended to general GANs under certain assumptions. We find that in order to ensure a good convergence rate, two factors of the Jacobian in the GAN training dynamics should be simultaneously avoided, which are (i) the Phase Factor, i.e., the Jacobian has "},"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":"1806.09235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-24T23:19:23Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2bc22571a96af5a5cbd7299c94901cf9db606a608d9e503a24aa41d390557fd5","abstract_canon_sha256":"bbf651485c2733967401d960d99fcd0476b228434e2dbf514d028efa488220eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:53.981971Z","signature_b64":"uwJdpKJhw2yjElYewpsBTVo0thH51IcdkDBwJuFk1V0bS2H9jiA4rk+c1w5uCoQ/87/WKtnnkATk89dUjiu3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d292763c027866f6b98c7f9c20ca206017563a023d8d9c98d80326a8f468d5a9","last_reissued_at":"2026-05-17T23:41:53.981590Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:53.981590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a Better Understanding and Regularization of GAN Training Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ankit Patel, Weili Nie","submitted_at":"2018-06-24T23:19:23Z","abstract_excerpt":"Generative adversarial networks (GANs) are notoriously difficult to train and the reasons underlying their (non-)convergence behaviors are still not completely understood. By first considering a simple yet representative GAN example, we mathematically analyze its local convergence behavior in a non-asymptotic way. Furthermore, the analysis is extended to general GANs under certain assumptions. We find that in order to ensure a good convergence rate, two factors of the Jacobian in the GAN training dynamics should be simultaneously avoided, which are (i) the Phase Factor, i.e., the Jacobian has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09235","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1806.09235","created_at":"2026-05-17T23:41:53.981646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09235v2","created_at":"2026-05-17T23:41:53.981646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09235","created_at":"2026-05-17T23:41:53.981646+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KJHMPACPBTP","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KJHMPACPBTPNOMM","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KJHMPAC","created_at":"2026-05-18T12:32:02.567920+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/2KJHMPACPBTPNOMMP6OCBSRAMA","json":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA.json","graph_json":"https://pith.science/api/pith-number/2KJHMPACPBTPNOMMP6OCBSRAMA/graph.json","events_json":"https://pith.science/api/pith-number/2KJHMPACPBTPNOMMP6OCBSRAMA/events.json","paper":"https://pith.science/paper/2KJHMPAC"},"agent_actions":{"view_html":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA","download_json":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA.json","view_paper":"https://pith.science/paper/2KJHMPAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09235&json=true","fetch_graph":"https://pith.science/api/pith-number/2KJHMPACPBTPNOMMP6OCBSRAMA/graph.json","fetch_events":"https://pith.science/api/pith-number/2KJHMPACPBTPNOMMP6OCBSRAMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA/action/storage_attestation","attest_author":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA/action/author_attestation","sign_citation":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA/action/citation_signature","submit_replication":"https://pith.science/pith/2KJHMPACPBTPNOMMP6OCBSRAMA/action/replication_record"}},"created_at":"2026-05-17T23:41:53.981646+00:00","updated_at":"2026-05-17T23:41:53.981646+00:00"}