{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BPPMH3A2PVS6RS7RXLD7U2TJME","short_pith_number":"pith:BPPMH3A2","canonical_record":{"source":{"id":"1808.01531","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-04T20:47:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3c93726d46085d2bc25710ad0382c9e7740fa6db246e1df6e576063efec5d393","abstract_canon_sha256":"a59fff18b40a34177b66787974fbb009b79183e5a0688fb4b10550af5c37998b"},"schema_version":"1.0"},"canonical_sha256":"0bdec3ec1a7d65e8cbf1bac7fa6a69612d6ad5d2d8ecdb8722e85f7ff6415c13","source":{"kind":"arxiv","id":"1808.01531","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01531","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01531v3","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01531","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"BPPMH3A2PVS6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BPPMH3A2PVS6RS7R","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BPPMH3A2","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BPPMH3A2PVS6RS7RXLD7U2TJME","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01531","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-04T20:47:44Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3c93726d46085d2bc25710ad0382c9e7740fa6db246e1df6e576063efec5d393","abstract_canon_sha256":"a59fff18b40a34177b66787974fbb009b79183e5a0688fb4b10550af5c37998b"},"schema_version":"1.0"},"canonical_sha256":"0bdec3ec1a7d65e8cbf1bac7fa6a69612d6ad5d2d8ecdb8722e85f7ff6415c13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:52.941179Z","signature_b64":"T/53ddebiLimQokXGu8HcwJ17iTYveRvtHPz6De1cZX7Tui4rhHkIohVYBeYjptCAhXmYZUt6B0vxXVqaO3kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bdec3ec1a7d65e8cbf1bac7fa6a69612d6ad5d2d8ecdb8722e85f7ff6415c13","last_reissued_at":"2026-05-17T23:45:52.940737Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:52.940737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01531","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D62lFGWpX8OHV+f56bSK/ii3++u7oGBJ54y6/LRxFyp1behoW7YpSjanrthMMODdeDaCRLh3h0WbUEze2bKwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:26:40.108016Z"},"content_sha256":"569758af0bf124b818dcaafe5b576422d60d3cbac7a6ac5b0b1aab4c3780e789","schema_version":"1.0","event_id":"sha256:569758af0bf124b818dcaafe5b576422d60d3cbac7a6ac5b0b1aab4c3780e789"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BPPMH3A2PVS6RS7RXLD7U2TJME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Convergence to the Equilibrium of GANs using Variational Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Ian Gemp, Sridhar Mahadevan","submitted_at":"2018-08-04T20:47:44Z","abstract_excerpt":"In optimization, the negative gradient of a function denotes the direction of steepest descent. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. In this work, we show that these orthogonal directions that are ignored by gradient descent can be critical in equilibrium problems. Equilibrium problems have drawn heightened attention in machine learning due to the emergence of the Generative Adversarial Network (GAN). We use the framework of Variational Inequalities to analyze popular training algorithms for a fundamental GAN variant: the Wasse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01531","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7YDEHBPH1r/vjb7XbYL8rKzOoD24CLAZPsJoY50U4+s7iistQynkMKqpuShE54hfyCvqgqNdfbC0RHhUNf0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:26:40.108607Z"},"content_sha256":"7919b7ea1108aa9bc88fd5e51b5bc60f7d0f1c0d52cbc8d011d0e72eb99783b1","schema_version":"1.0","event_id":"sha256:7919b7ea1108aa9bc88fd5e51b5bc60f7d0f1c0d52cbc8d011d0e72eb99783b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/bundle.json","state_url":"https://pith.science/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T02:26:40Z","links":{"resolver":"https://pith.science/pith/BPPMH3A2PVS6RS7RXLD7U2TJME","bundle":"https://pith.science/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/bundle.json","state":"https://pith.science/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPPMH3A2PVS6RS7RXLD7U2TJME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BPPMH3A2PVS6RS7RXLD7U2TJME","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":"a59fff18b40a34177b66787974fbb009b79183e5a0688fb4b10550af5c37998b","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-04T20:47:44Z","title_canon_sha256":"3c93726d46085d2bc25710ad0382c9e7740fa6db246e1df6e576063efec5d393"},"schema_version":"1.0","source":{"id":"1808.01531","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01531","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01531v3","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01531","created_at":"2026-05-17T23:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"BPPMH3A2PVS6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BPPMH3A2PVS6RS7R","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BPPMH3A2","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7919b7ea1108aa9bc88fd5e51b5bc60f7d0f1c0d52cbc8d011d0e72eb99783b1","target":"graph","created_at":"2026-05-17T23:45:52Z","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":"In optimization, the negative gradient of a function denotes the direction of steepest descent. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. In this work, we show that these orthogonal directions that are ignored by gradient descent can be critical in equilibrium problems. Equilibrium problems have drawn heightened attention in machine learning due to the emergence of the Generative Adversarial Network (GAN). We use the framework of Variational Inequalities to analyze popular training algorithms for a fundamental GAN variant: the Wasse","authors_text":"Ian Gemp, Sridhar Mahadevan","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-04T20:47:44Z","title":"Global Convergence to the Equilibrium of GANs using Variational Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01531","kind":"arxiv","version":3},"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":"sha256:569758af0bf124b818dcaafe5b576422d60d3cbac7a6ac5b0b1aab4c3780e789","target":"record","created_at":"2026-05-17T23:45:52Z","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":"a59fff18b40a34177b66787974fbb009b79183e5a0688fb4b10550af5c37998b","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-08-04T20:47:44Z","title_canon_sha256":"3c93726d46085d2bc25710ad0382c9e7740fa6db246e1df6e576063efec5d393"},"schema_version":"1.0","source":{"id":"1808.01531","kind":"arxiv","version":3}},"canonical_sha256":"0bdec3ec1a7d65e8cbf1bac7fa6a69612d6ad5d2d8ecdb8722e85f7ff6415c13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bdec3ec1a7d65e8cbf1bac7fa6a69612d6ad5d2d8ecdb8722e85f7ff6415c13","first_computed_at":"2026-05-17T23:45:52.940737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:52.940737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/53ddebiLimQokXGu8HcwJ17iTYveRvtHPz6De1cZX7Tui4rhHkIohVYBeYjptCAhXmYZUt6B0vxXVqaO3kCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:52.941179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01531","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:569758af0bf124b818dcaafe5b576422d60d3cbac7a6ac5b0b1aab4c3780e789","sha256:7919b7ea1108aa9bc88fd5e51b5bc60f7d0f1c0d52cbc8d011d0e72eb99783b1"],"state_sha256":"2e774b998bcc37ce45042a632d1e2dd5ee1d452a0a0ec54909617d19b455af6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ERVUkhAUcw6CxdvfDCBHYa4GOoJT84mTwY1/9Xngy0icOCw3or3M7H2+UVbdJQDfWxAXsolPToniix/izGdnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:26:40.111623Z","bundle_sha256":"fee672a0032c0b3041186deb4382ce0548c325ea9d723787e3818f2593b38217"}}