{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OVJUM7RENCJ52HZBDSUOLDYISW","short_pith_number":"pith:OVJUM7RE","canonical_record":{"source":{"id":"1703.00573","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-03-02T01:14:03Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"3b5672a95b7acba93422adaf5982577b8a72d406f2d95f20b98c1742e4724ed4","abstract_canon_sha256":"aa24e77e27e57c8ade648fc51fa53534e4bac04286827fa080ed573bc6df97d4"},"schema_version":"1.0"},"canonical_sha256":"7553467e246893dd1f211ca8e58f08959447a56237d837d3a818e1a8fa5b544c","source":{"kind":"arxiv","id":"1703.00573","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00573","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00573v5","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00573","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"OVJUM7RENCJ5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OVJUM7RENCJ52HZB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OVJUM7RE","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OVJUM7RENCJ52HZBDSUOLDYISW","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00573","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-03-02T01:14:03Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"3b5672a95b7acba93422adaf5982577b8a72d406f2d95f20b98c1742e4724ed4","abstract_canon_sha256":"aa24e77e27e57c8ade648fc51fa53534e4bac04286827fa080ed573bc6df97d4"},"schema_version":"1.0"},"canonical_sha256":"7553467e246893dd1f211ca8e58f08959447a56237d837d3a818e1a8fa5b544c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:46.188899Z","signature_b64":"/uoTPL9nn/eeSD97CcwS79yRsJEtQh5ahtySCXwLGxLJ3fgJHN8p54HULcIpW96vGguJyl3SdaQrYGQs2yo4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7553467e246893dd1f211ca8e58f08959447a56237d837d3a818e1a8fa5b544c","last_reissued_at":"2026-05-18T00:38:46.188261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:46.188261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00573","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUG5SgcnwPLcJyzbsskcDz1y6NS86G/XGg9mJ0E6piHBNltwaKHJYeywnWEJQOZsC8t9g58kCIkNxCOWCVo8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:36:22.095805Z"},"content_sha256":"ae1c5ad3dfb917c05827be890981d6c362a681204cbe6d84b786ff07c39a68a8","schema_version":"1.0","event_id":"sha256:ae1c5ad3dfb917c05827be890981d6c362a681204cbe6d84b786ff07c39a68a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OVJUM7RENCJ52HZBDSUOLDYISW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalization and Equilibrium in Generative Adversarial Nets (GANs)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Rong Ge, Sanjeev Arora, Tengyu Ma, Yingyu Liang, Yi Zhang","submitted_at":"2017-03-02T01:14:03Z","abstract_excerpt":"We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate.\n  This existence of equilibrium inspires MIX+GAN protocol, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00573","kind":"arxiv","version":5},"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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2VLdEMxT0HF7GgmTN9pAg6q65ZXbRVWKZNBKNzxiGNo9OHzc3kz1f7X0T+hMJqQZkQHRRVf3/sF9s3Mgt+ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:36:22.096507Z"},"content_sha256":"7e62548e7e3d68ae22e7a3075dd39fab382ed10276eea3778eca372681f197ec","schema_version":"1.0","event_id":"sha256:7e62548e7e3d68ae22e7a3075dd39fab382ed10276eea3778eca372681f197ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVJUM7RENCJ52HZBDSUOLDYISW/bundle.json","state_url":"https://pith.science/pith/OVJUM7RENCJ52HZBDSUOLDYISW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVJUM7RENCJ52HZBDSUOLDYISW/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":"2026-05-29T14:36:22Z","links":{"resolver":"https://pith.science/pith/OVJUM7RENCJ52HZBDSUOLDYISW","bundle":"https://pith.science/pith/OVJUM7RENCJ52HZBDSUOLDYISW/bundle.json","state":"https://pith.science/pith/OVJUM7RENCJ52HZBDSUOLDYISW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVJUM7RENCJ52HZBDSUOLDYISW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OVJUM7RENCJ52HZBDSUOLDYISW","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":"aa24e77e27e57c8ade648fc51fa53534e4bac04286827fa080ed573bc6df97d4","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-03-02T01:14:03Z","title_canon_sha256":"3b5672a95b7acba93422adaf5982577b8a72d406f2d95f20b98c1742e4724ed4"},"schema_version":"1.0","source":{"id":"1703.00573","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00573","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00573v5","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00573","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"OVJUM7RENCJ5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OVJUM7RENCJ52HZB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OVJUM7RE","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:7e62548e7e3d68ae22e7a3075dd39fab382ed10276eea3778eca372681f197ec","target":"graph","created_at":"2026-05-18T00:38:46Z","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":"We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate.\n  This existence of equilibrium inspires MIX+GAN protocol, whi","authors_text":"Rong Ge, Sanjeev Arora, Tengyu Ma, Yingyu Liang, Yi Zhang","cross_cats":["cs.NE","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-03-02T01:14:03Z","title":"Generalization and Equilibrium in Generative Adversarial Nets (GANs)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00573","kind":"arxiv","version":5},"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:ae1c5ad3dfb917c05827be890981d6c362a681204cbe6d84b786ff07c39a68a8","target":"record","created_at":"2026-05-18T00:38:46Z","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":"aa24e77e27e57c8ade648fc51fa53534e4bac04286827fa080ed573bc6df97d4","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-03-02T01:14:03Z","title_canon_sha256":"3b5672a95b7acba93422adaf5982577b8a72d406f2d95f20b98c1742e4724ed4"},"schema_version":"1.0","source":{"id":"1703.00573","kind":"arxiv","version":5}},"canonical_sha256":"7553467e246893dd1f211ca8e58f08959447a56237d837d3a818e1a8fa5b544c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7553467e246893dd1f211ca8e58f08959447a56237d837d3a818e1a8fa5b544c","first_computed_at":"2026-05-18T00:38:46.188261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:46.188261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uoTPL9nn/eeSD97CcwS79yRsJEtQh5ahtySCXwLGxLJ3fgJHN8p54HULcIpW96vGguJyl3SdaQrYGQs2yo4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:46.188899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00573","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1c5ad3dfb917c05827be890981d6c362a681204cbe6d84b786ff07c39a68a8","sha256:7e62548e7e3d68ae22e7a3075dd39fab382ed10276eea3778eca372681f197ec"],"state_sha256":"44cc17675466e623050e34dc6085ae809a3bb942ce2ee6c705abcb79b6cde312"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k67vXxhVSETNxlZiMYlFnz11h/nAioC+fGbqMjXc80VlrklKGzpHg10Idzp5T35H5xKD//RJ7b5pMZopqiiIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:36:22.100377Z","bundle_sha256":"807347c8b68361d1052fc503da92179a932048658110e6c2ec4790064c800a7a"}}