{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4BLFA27E3JW36UVKM6YU5EWEJC","short_pith_number":"pith:4BLFA27E","canonical_record":{"source":{"id":"1810.10207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-24T06:25:01Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c017b8dba0aafbcbb72373f7b78e5490da228e21243020fb9e28b8aadfc13ea2","abstract_canon_sha256":"39ffffefdbc5e9a345c8734a5dc502fb3d573381b854259a8b784285d17a5018"},"schema_version":"1.0"},"canonical_sha256":"e056506be4da6dbf52aa67b14e92c448815c7127375a5c1d5f4ed12d1ff4749d","source":{"kind":"arxiv","id":"1810.10207","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10207","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10207v4","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10207","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"4BLFA27E3JW3","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_16","alias_value":"4BLFA27E3JW36UVK","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_8","alias_value":"4BLFA27E","created_at":"2026-07-05T02:55:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4BLFA27E3JW36UVKM6YU5EWEJC","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-24T06:25:01Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c017b8dba0aafbcbb72373f7b78e5490da228e21243020fb9e28b8aadfc13ea2","abstract_canon_sha256":"39ffffefdbc5e9a345c8734a5dc502fb3d573381b854259a8b784285d17a5018"},"schema_version":"1.0"},"canonical_sha256":"e056506be4da6dbf52aa67b14e92c448815c7127375a5c1d5f4ed12d1ff4749d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:55:51.063769Z","signature_b64":"FAiFcGqAtsjAiF3VUKdgwikhGNSF1dcx/SKya9kOoN6H/xgKXEXubYFxElkNo2kaWtx1C7Tj2qHXAA6d3JIZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e056506be4da6dbf52aa67b14e92c448815c7127375a5c1d5f4ed12d1ff4749d","last_reissued_at":"2026-07-05T02:55:51.063352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:55:51.063352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10207","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRi0aPwhIbpdJUXXEQ1SzcRnfbSytY3CNQtjayOFjRyUd7gBL1tgLRduvFgLnpim21O+94yoG4vuKMRalfVtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:13:21.579784Z"},"content_sha256":"b37bfd3d443bfdac830e42f2bd79cc32a768364271cb2aa241b17e035cfae283","schema_version":"1.0","event_id":"sha256:b37bfd3d443bfdac830e42f2bd79cc32a768364271cb2aa241b17e035cfae283"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4BLFA27E3JW36UVKM6YU5EWEJC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Hassan Rafique, Mingrui Liu, Qihang Lin, Tianbao Yang","submitted_at":"2018-10-24T06:25:01Z","abstract_excerpt":"In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in machine learning including training Generative Adversarial Nets (GANs). We propose an algorithmic framework motivated by the inexact proximal point method, where the weakly monotone variational inequality (VI) corresponding to the original min-max problem is solved through approximat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10207","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.10207/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpIaZc6jS6VGftFPqnyYefP5f94jZpx/vE8DCqj9P/kOdSSiE2smw+ex6OqSX6Tzpitq2iL7CBfcmJf4daHbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:13:21.580307Z"},"content_sha256":"055d946af0da00f30d97e9a0b60cc65166ab6b1d712a3848b32d861622e02892","schema_version":"1.0","event_id":"sha256:055d946af0da00f30d97e9a0b60cc65166ab6b1d712a3848b32d861622e02892"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BLFA27E3JW36UVKM6YU5EWEJC/bundle.json","state_url":"https://pith.science/pith/4BLFA27E3JW36UVKM6YU5EWEJC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BLFA27E3JW36UVKM6YU5EWEJC/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":"2026-08-15T07:13:21Z","links":{"resolver":"https://pith.science/pith/4BLFA27E3JW36UVKM6YU5EWEJC","bundle":"https://pith.science/pith/4BLFA27E3JW36UVKM6YU5EWEJC/bundle.json","state":"https://pith.science/pith/4BLFA27E3JW36UVKM6YU5EWEJC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BLFA27E3JW36UVKM6YU5EWEJC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4BLFA27E3JW36UVKM6YU5EWEJC","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":"39ffffefdbc5e9a345c8734a5dc502fb3d573381b854259a8b784285d17a5018","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-24T06:25:01Z","title_canon_sha256":"c017b8dba0aafbcbb72373f7b78e5490da228e21243020fb9e28b8aadfc13ea2"},"schema_version":"1.0","source":{"id":"1810.10207","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10207","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10207v4","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10207","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"4BLFA27E3JW3","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_16","alias_value":"4BLFA27E3JW36UVK","created_at":"2026-07-05T02:55:51Z"},{"alias_kind":"pith_short_8","alias_value":"4BLFA27E","created_at":"2026-07-05T02:55:51Z"}],"graph_snapshots":[{"event_id":"sha256:055d946af0da00f30d97e9a0b60cc65166ab6b1d712a3848b32d861622e02892","target":"graph","created_at":"2026-07-05T02:55:51Z","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/1810.10207/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly concave in the variables of maximization. It has many important applications in machine learning including training Generative Adversarial Nets (GANs). We propose an algorithmic framework motivated by the inexact proximal point method, where the weakly monotone variational inequality (VI) corresponding to the original min-max problem is solved through approximat","authors_text":"Hassan Rafique, Mingrui Liu, Qihang Lin, Tianbao Yang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-24T06:25:01Z","title":"First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10207","kind":"arxiv","version":4},"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:b37bfd3d443bfdac830e42f2bd79cc32a768364271cb2aa241b17e035cfae283","target":"record","created_at":"2026-07-05T02:55:51Z","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":"39ffffefdbc5e9a345c8734a5dc502fb3d573381b854259a8b784285d17a5018","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-24T06:25:01Z","title_canon_sha256":"c017b8dba0aafbcbb72373f7b78e5490da228e21243020fb9e28b8aadfc13ea2"},"schema_version":"1.0","source":{"id":"1810.10207","kind":"arxiv","version":4}},"canonical_sha256":"e056506be4da6dbf52aa67b14e92c448815c7127375a5c1d5f4ed12d1ff4749d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e056506be4da6dbf52aa67b14e92c448815c7127375a5c1d5f4ed12d1ff4749d","first_computed_at":"2026-07-05T02:55:51.063352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:55:51.063352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAiFcGqAtsjAiF3VUKdgwikhGNSF1dcx/SKya9kOoN6H/xgKXEXubYFxElkNo2kaWtx1C7Tj2qHXAA6d3JIZDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:55:51.063769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10207","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b37bfd3d443bfdac830e42f2bd79cc32a768364271cb2aa241b17e035cfae283","sha256:055d946af0da00f30d97e9a0b60cc65166ab6b1d712a3848b32d861622e02892"],"state_sha256":"c6d4b7b3ac51984c69f39f97ae10cd6ffbfba297ca4c474bb470f49cba0dbefb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fo58Uodbf+cuuSA97u8cxTzaS/hUhLLcPwQRf4AU5F0/3rk2ERzC1I1UV1kkK0bxqGDXLXgQtZnGuMtv4+XoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T07:13:21.584287Z","bundle_sha256":"0ed26c6ece7f7558ea8834f20b3a59b7052a1d7db39259c843ae6e5473525624"}}