{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6PV3XVEAF34O24TU5AVF32XYFC","short_pith_number":"pith:6PV3XVEA","canonical_record":{"source":{"id":"2403.07806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-12T16:43:55Z","cross_cats_sorted":[],"title_canon_sha256":"ef6ddf029beec39b12af93659ff6cf777ebd69f628df4d2802410223f09e494a","abstract_canon_sha256":"2170f5d0e63772307d58cb65886881f902fd4a5118b2bc3e048735ebbd5e70ba"},"schema_version":"1.0"},"canonical_sha256":"f3ebbbd4802ef8ed7274e82a5deaf8288e108713a86c59578b60216ba360955d","source":{"kind":"arxiv","id":"2403.07806","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.07806","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.07806v2","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.07806","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"6PV3XVEAF34O","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"6PV3XVEAF34O24TU","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"6PV3XVEA","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6PV3XVEAF34O24TU5AVF32XYFC","target":"record","payload":{"canonical_record":{"source":{"id":"2403.07806","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-12T16:43:55Z","cross_cats_sorted":[],"title_canon_sha256":"ef6ddf029beec39b12af93659ff6cf777ebd69f628df4d2802410223f09e494a","abstract_canon_sha256":"2170f5d0e63772307d58cb65886881f902fd4a5118b2bc3e048735ebbd5e70ba"},"schema_version":"1.0"},"canonical_sha256":"f3ebbbd4802ef8ed7274e82a5deaf8288e108713a86c59578b60216ba360955d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:15.141547Z","signature_b64":"f3XVLT+pa39/86x2PJEtZGdj6UyecWqGnW9IuQj97QmZKOjaLKWvwOIfV3JZHgrDwGcTa5s7m5xhrNXwoklMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3ebbbd4802ef8ed7274e82a5deaf8288e108713a86c59578b60216ba360955d","last_reissued_at":"2026-05-18T02:45:15.141045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:15.141045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.07806","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n3LKinEGwsDMcyIdmNJ78+RqViuOEjXltJlTcrXFt4wsKD72wuJN7e/IvwqVL+iDm0+RDFVMZ4SXjogo9s8HCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:51:35.900663Z"},"content_sha256":"041aa3055a4d453863821f97d3100280255870752ca90100f155d1ddd9f44175","schema_version":"1.0","event_id":"sha256:041aa3055a4d453863821f97d3100280255870752ca90100f155d1ddd9f44175"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6PV3XVEAF34O24TU5AVF32XYFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Stochastic GDA Method With Backtracking For Solving Nonconvex Concave Minimax Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mert G\\\"urb\\\"uzbalaban, Necdet Serhat Aybat, Qiushui Xu, Xuan Zhang","submitted_at":"2024-03-12T16:43:55Z","abstract_excerpt":"We propose a stochastic GDA (gradient descent ascent) method with backtracking (SGDA-B) to solve nonconvex-concave (NCC) minimax problems of the form: $\\min_{\\mathbf{x}} \\max_y \\sum_{i=1}^N g_i(x_i)+f(\\mathbf{x},y)-h(y)$, where $h$ and $g_i$ for $i=1,\\cdots,N$ are closed, convex functions, and for some $L,\\mu\\geq 0$, $f$ is $L$-smooth and $f(\\mathbf{x},\\cdot)$ is $\\mu$-strongly concave for all $\\mathbf{x}$ in the problem domain. We consider the stochastic setting where one only has an access to an unbiased stochastic oracle of $\\nabla f$ with a finite variance bound $\\sigma^2$. While most of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07806","kind":"arxiv","version":2},"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":"2026-05-18T02:45:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eOnZaBWKXWEKKZOa75DBSNlsCk9+w/kmUaQHf/7npOXrXBmzo8dBvMdKdiOpQTQjAd9grxLX4g7Md5hL96qGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T18:51:35.901033Z"},"content_sha256":"0f79ee25415c91ab898a8e1b14e88da0188e21e919af5ef94d6a30bcbdcf9642","schema_version":"1.0","event_id":"sha256:0f79ee25415c91ab898a8e1b14e88da0188e21e919af5ef94d6a30bcbdcf9642"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PV3XVEAF34O24TU5AVF32XYFC/bundle.json","state_url":"https://pith.science/pith/6PV3XVEAF34O24TU5AVF32XYFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PV3XVEAF34O24TU5AVF32XYFC/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":"2026-05-21T18:51:35Z","links":{"resolver":"https://pith.science/pith/6PV3XVEAF34O24TU5AVF32XYFC","bundle":"https://pith.science/pith/6PV3XVEAF34O24TU5AVF32XYFC/bundle.json","state":"https://pith.science/pith/6PV3XVEAF34O24TU5AVF32XYFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PV3XVEAF34O24TU5AVF32XYFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6PV3XVEAF34O24TU5AVF32XYFC","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":"2170f5d0e63772307d58cb65886881f902fd4a5118b2bc3e048735ebbd5e70ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-12T16:43:55Z","title_canon_sha256":"ef6ddf029beec39b12af93659ff6cf777ebd69f628df4d2802410223f09e494a"},"schema_version":"1.0","source":{"id":"2403.07806","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.07806","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.07806v2","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.07806","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"6PV3XVEAF34O","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"6PV3XVEAF34O24TU","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"6PV3XVEA","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:0f79ee25415c91ab898a8e1b14e88da0188e21e919af5ef94d6a30bcbdcf9642","target":"graph","created_at":"2026-05-18T02:45:15Z","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 propose a stochastic GDA (gradient descent ascent) method with backtracking (SGDA-B) to solve nonconvex-concave (NCC) minimax problems of the form: $\\min_{\\mathbf{x}} \\max_y \\sum_{i=1}^N g_i(x_i)+f(\\mathbf{x},y)-h(y)$, where $h$ and $g_i$ for $i=1,\\cdots,N$ are closed, convex functions, and for some $L,\\mu\\geq 0$, $f$ is $L$-smooth and $f(\\mathbf{x},\\cdot)$ is $\\mu$-strongly concave for all $\\mathbf{x}$ in the problem domain. We consider the stochastic setting where one only has an access to an unbiased stochastic oracle of $\\nabla f$ with a finite variance bound $\\sigma^2$. While most of t","authors_text":"Mert G\\\"urb\\\"uzbalaban, Necdet Serhat Aybat, Qiushui Xu, Xuan Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-12T16:43:55Z","title":"A Stochastic GDA Method With Backtracking For Solving Nonconvex Concave Minimax Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07806","kind":"arxiv","version":2},"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":"sha256:041aa3055a4d453863821f97d3100280255870752ca90100f155d1ddd9f44175","target":"record","created_at":"2026-05-18T02:45:15Z","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":"2170f5d0e63772307d58cb65886881f902fd4a5118b2bc3e048735ebbd5e70ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-03-12T16:43:55Z","title_canon_sha256":"ef6ddf029beec39b12af93659ff6cf777ebd69f628df4d2802410223f09e494a"},"schema_version":"1.0","source":{"id":"2403.07806","kind":"arxiv","version":2}},"canonical_sha256":"f3ebbbd4802ef8ed7274e82a5deaf8288e108713a86c59578b60216ba360955d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3ebbbd4802ef8ed7274e82a5deaf8288e108713a86c59578b60216ba360955d","first_computed_at":"2026-05-18T02:45:15.141045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:15.141045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f3XVLT+pa39/86x2PJEtZGdj6UyecWqGnW9IuQj97QmZKOjaLKWvwOIfV3JZHgrDwGcTa5s7m5xhrNXwoklMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:15.141547Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.07806","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:041aa3055a4d453863821f97d3100280255870752ca90100f155d1ddd9f44175","sha256:0f79ee25415c91ab898a8e1b14e88da0188e21e919af5ef94d6a30bcbdcf9642"],"state_sha256":"a02286bfeaaf3e8f274a7dc41a71651ebad7076a6a39ddf25e237b857606d6c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HDZ7AeLIIEFiq//8VB2UVczIuQiQ4MQeSa1w5rbuITD57LnbesILpaEb9fdFCbJqkijrSPvctOUYcFDofhmlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T18:51:35.903266Z","bundle_sha256":"29d47660c54402e7866d6e4eb7cec72a46229a91eff8ccda1c330e876d387633"}}