{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:76DN3ZRLVFJAURRLIBYTQ4JS4M","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":"ee0b5d2e60983fdc1eb1cef04aa4fc12e9ff54cee0bb6d82cea4d192216389ab","cross_cats_sorted":["cs.GT","cs.MA","cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-13T09:21:08Z","title_canon_sha256":"e1480e55809727756e4a3c327c8a7dcf94e1e3abb71c08c8289f3f6fd01e6d6c"},"schema_version":"1.0","source":{"id":"1905.04926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04926","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04926v1","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04926","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"76DN3ZRLVFJA","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"76DN3ZRLVFJAURRL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"76DN3ZRL","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9b2727f8b468aef3b57662bdb18b7630ee476863f00a58a7272e324c132adcf3","target":"graph","created_at":"2026-05-17T23:46:23Z","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"},"paper":{"abstract_excerpt":"Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. The behavior of gradient-based methods in games is not well understood -- and is becoming increasingly important as adversarial and multi-objective architectures proliferate. In this paper, we develop new tools to understand and control the dynamics in n-player differentiable games.\n  The key result is to decompose the game Jacobian into two c","authors_text":"Alistair Letcher, David Balduzzi, Jakob Foerster, James Martens, Karl Tuyls, Sebastien Racaniere, Thore Graepel","cross_cats":["cs.GT","cs.MA","cs.NE","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-13T09:21:08Z","title":"Differentiable Game Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04926","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:a2e071879ba2124d8adea6abc2f75659f10557f5d3accd47536fb9f0b03b2139","target":"record","created_at":"2026-05-17T23:46:23Z","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":"ee0b5d2e60983fdc1eb1cef04aa4fc12e9ff54cee0bb6d82cea4d192216389ab","cross_cats_sorted":["cs.GT","cs.MA","cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-13T09:21:08Z","title_canon_sha256":"e1480e55809727756e4a3c327c8a7dcf94e1e3abb71c08c8289f3f6fd01e6d6c"},"schema_version":"1.0","source":{"id":"1905.04926","kind":"arxiv","version":1}},"canonical_sha256":"ff86dde62ba9520a462b4071387132e3007b44e65612f454cd59bdfa69b897b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff86dde62ba9520a462b4071387132e3007b44e65612f454cd59bdfa69b897b3","first_computed_at":"2026-05-17T23:46:23.080785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:23.080785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4k9A6AlpIwpf3B+sjrK8E5i7RDroYcjnONHLEKzcErqxIHXBCvL+yldo70P/adZ2D1sQCQ1079G+iXUFFEzDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:23.081402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2e071879ba2124d8adea6abc2f75659f10557f5d3accd47536fb9f0b03b2139","sha256:9b2727f8b468aef3b57662bdb18b7630ee476863f00a58a7272e324c132adcf3"],"state_sha256":"d47984820cb7a58501d9c7b3be3f03ab50df543e590f6d552eca3b2498729051"}