{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:263PGZLU6K2RQXKRNALP5KW4FA","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":"a35e54d5316ac6fdb1940e67e0d9b13de478fdbb03a9f059fe4f70a3fae97646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:59:46Z","title_canon_sha256":"5ca003089dd37f8e48727c7136131b1d7078e92daac5749e3a7991228ea7c51a"},"schema_version":"1.0","source":{"id":"2102.04448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.04448","created_at":"2026-07-05T02:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"2102.04448v1","created_at":"2026-07-05T02:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.04448","created_at":"2026-07-05T02:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"263PGZLU6K2R","created_at":"2026-07-05T02:13:33Z"},{"alias_kind":"pith_short_16","alias_value":"263PGZLU6K2RQXKR","created_at":"2026-07-05T02:13:33Z"},{"alias_kind":"pith_short_8","alias_value":"263PGZLU","created_at":"2026-07-05T02:13:33Z"}],"graph_snapshots":[{"event_id":"sha256:1184a0b48be8f5672bf9e9a4064ab681e4cab4ea37225ea7c497cebe8f76a959","target":"graph","created_at":"2026-07-05T02:13:33Z","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/2102.04448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent work demonstrated the benefits of studying continuous-time dynamics governing the GAN training. However, this dynamics is analyzed in the model parameter space, which results in finite-dimensional dynamical systems. We propose a novel perspective where we study the local dynamics of adversarial training in the general functional space and show how it can be represented as a system of partial differential equations. Thus, the convergence properties can be inferred from the eigenvalues of the resulting differential operator. We show that these eigenvalues can be efficiently estimated from","authors_text":"Artem Babenko, Ivan Oseledets, Valentin Khrulkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:59:46Z","title":"Functional Space Analysis of Local GAN Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.04448","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":"sha256:6d376999c5907cd806c6fedf787b0b18219a3e29e69f00d5cb09a10fd747206c","target":"record","created_at":"2026-07-05T02:13:33Z","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":"a35e54d5316ac6fdb1940e67e0d9b13de478fdbb03a9f059fe4f70a3fae97646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:59:46Z","title_canon_sha256":"5ca003089dd37f8e48727c7136131b1d7078e92daac5749e3a7991228ea7c51a"},"schema_version":"1.0","source":{"id":"2102.04448","kind":"arxiv","version":1}},"canonical_sha256":"d7b6f36574f2b5185d516816feaadc28218237087ec05704692808d0d49bd237","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7b6f36574f2b5185d516816feaadc28218237087ec05704692808d0d49bd237","first_computed_at":"2026-07-05T02:13:33.152734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:33.152734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qvud//E1cboTrNGY4LLHeqbt6J0SuaJWFgKYfHe0QutsFXRqjBPcdtaWPIqcJU+smo6L9ZUdhPRc6jIapfoSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:33.153109Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.04448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d376999c5907cd806c6fedf787b0b18219a3e29e69f00d5cb09a10fd747206c","sha256:1184a0b48be8f5672bf9e9a4064ab681e4cab4ea37225ea7c497cebe8f76a959"],"state_sha256":"0fa31e6dd9fcf64348c9a288de8f659e62e186a29d9bd0d2c870e3f42c0a48e2"}