{"as_of":"2026-08-14T15:17:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:48048265c5aa4b44e602354234a7306f9cdc4a7d955df58c5be0e5bbb95acad6","coverage":[{"denominator":57,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":57,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:23:25.414640Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2505.19537/citation-record","integrity":"/paper/2505.19537/integrity","json":"/paper/2505.19537/citation-record.json","paper":"/paper/2505.19537"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.110915Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.110915Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:02c934fbcf6c07251d60cb694738cbeab2db9bc98987a0a7e194990e54d303da","observation_id":"2db6a8c9-0637-4fdb-ac30-045de42972df","resolution":{"observed_at":"2026-08-07T14:23:25.110915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:33.389712Z","title":"Accelerating smooth games by manipulating spectral shapes","venue":null,"work_id":"5d8c5954-bcbe-4a88-82b6-410ef0a35987","year":2020},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.116747Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:31d028bad92365751afa3fa9fb588e2e0634fe01c1390c087d628dd4552c0461","observation_id":"8487cec3-e51b-41c0-afab-37de032a4eb8","resolution":{"observed_at":"2026-08-07T14:23:33.456832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:33.142214Z","title":"P., Gidel, G., and Piliouras, G","venue":null,"work_id":"baab09f6-5007-46cd-ae94-f784eba52f02","year":2020},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.120963Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:7260a9bad22d32e89e91e8a2b92a898cf92f200fc3002e4f637719be4c738ed8","observation_id":"8abc4a2d-f7e3-40cf-9109-d0eeb55bf719","resolution":{"observed_at":"2026-08-07T14:23:33.231941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.05001","last_updated":"2022-04-24T17:11:00Z","snapshot_observed_at":"2026-08-13T17:36:57.146226Z","submitted_at":"2020-02-11T14:51:31Z","title":"A Tutorial on Matrix Perturbation Theory (using compact matrix notation)","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.05001","snapshot_observed_at":"2026-08-07T14:23:25.124821Z","title":"A tutorial on matrix perturbation theory (using compact matrix notation)","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.124821Z"},"links":{"cited_paper":"/paper/2002.05001","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:6dbcf89ec4a4f804eed07c07767f0757522f3f3bbf4df1c9ae04577f69fe7b0b","observation_id":"12822aa1-a7c9-446c-8481-839721c0f479","resolution":{"observed_at":"2026-08-07T14:23:25.124821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:32.913748Z","title":null,"venue":null,"work_id":"29ad60eb-7381-4b4d-98ca-d54984a681db","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.129163Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:b567f71ab387a7a3fe4d84e0f166b3bb83f81a9a2739f16c29e4bbac9e9db548","observation_id":"90d7455d-fba4-49ab-acec-9d97be9bd112","resolution":{"observed_at":"2026-08-07T14:23:33.011198Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15958","last_updated":"2025-03-10T23:28:01Z","snapshot_observed_at":"2026-08-14T02:09:38.131183Z","submitted_at":"2024-11-24T19:07:31Z","title":"Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15958","snapshot_observed_at":"2026-08-07T14:23:25.132951Z","title":"M., Liu, T., Islamov, R., Proske, F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.132951Z"},"links":{"cited_paper":"/paper/2411.15958","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:eb256e5211fec3c1e49561d7252af3eaf65c0d76984a8db5912e90f306eb4dd5","observation_id":"c7fddd65-5c33-4514-87fa-c38da97a0d79","resolution":{"observed_at":"2026-08-07T14:23:25.132951Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:32.711522Z","title":"M., Orvieto, A., Kersting, H., Proske, F., and Lucchi, A","venue":null,"work_id":"7f4cad76-6d3c-4920-9b91-410940d35c54","year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.137055Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:c4782840b63354835905b0d3414ef93816949ad742db8c1acf9b55e1a154fcde","observation_id":"9697a326-f7a3-464f-a0a3-3b059b829c8c","resolution":{"observed_at":"2026-08-07T14:23:32.803261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1711.00141","last_updated":"2018-02-13T16:33:55Z","snapshot_observed_at":"2026-08-11T03:46:49.503188Z","submitted_at":"2017-10-31T23:09:08Z","title":"Training GANs with Optimism","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00141","snapshot_observed_at":"2026-08-07T14:23:25.140625Z","title":"Training GAN s with optimism","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.140625Z"},"links":{"cited_paper":"/paper/1711.00141","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:503394fa89db218874e4c0333677c4d3f2011538d4080b60fe549c5096419781","observation_id":"08a6b370-a4dd-412f-9f50-a5299d57f0de","resolution":{"observed_at":"2026-08-07T14:23:25.140625Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:32.441314Z","title":"H., Nguyen, D., Nguyen, D., Harikumar, H., Tran, T., Rana, S., and Venkatesh, S","venue":null,"work_id":"ffe0a8c6-0e85-46d5-9c07-8c27b1743586","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.144378Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:32242e857f74990490ee9111d53864cef7746c469cfa004201820d4b680926d8","observation_id":"6e84253f-e641-4b1f-80e4-8609d7b4a3e7","resolution":{"observed_at":"2026-08-07T14:23:32.593660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:32.277851Z","title":"Rapid learning in constrained minimax games with negative momentum","venue":null,"work_id":"519a6b8a-f013-4c31-a629-ff5b658ced87","year":2025},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.151817Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:468dcb9399221b8fdda3889c52252098c665af1c006c98556f1b395877580db1","observation_id":"acadbb35-b8fa-440c-8748-0a48319bac96","resolution":{"observed_at":"2026-08-07T14:23:32.333237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:32.157110Z","title":"Prediction accuracy of learning in games: Follow-the-regularized-leader meets heisenberg","venue":null,"work_id":"575511fe-2cfc-4c9b-be70-b0a13ff58f5c","year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.155755Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:5d1af509b07993274e0ad95ed36a8a3d143a8e27927427ecc9374b8f34fc5d85","observation_id":"dd7f38c4-9f7d-4856-8d86-d95e255264da","resolution":{"observed_at":"2026-08-07T14:23:32.214839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.159156Z","title":"Sharpness-aware minimization for efficiently improving generalization","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.159156Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:5cdedff8129b6ec3ec67aedfa250caea4c394b47b7c5b40e3847085772e5a422","observation_id":"fcc6a432-bb1b-4f58-9f08-7d7b7023f03d","resolution":{"observed_at":"2026-08-07T14:23:25.159156Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:31.975822Z","title":"Implicit regularization in heavy-ball momentum accelerated stochastic gradient descent","venue":null,"work_id":"cf597659-6339-4e55-b474-e6d1cdf56788","year":2023},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.163503Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:16f339709e42b42b4558de55b9764c0d246c7c6ed07165c2dd58183bc4ca5264","observation_id":"da54151d-efe0-4c44-8324-e5caf15f273f","resolution":{"observed_at":"2026-08-07T14:23:32.076555Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:31.764585Z","title":"A., Pezeshki, M., Le Priol, R., Huang, G., Lacoste-Julien, S., and Mitliagkas, I","venue":null,"work_id":"7b29d131-36a8-467c-a902-d7ad74406cd5","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.167776Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:d54fa9296474d8720acae08d7f829ebfef9854c333e5b5130cc471d82174aaa8","observation_id":"c07aa117-5742-4702-8ae8-5c83a8f95820","resolution":{"observed_at":"2026-08-07T14:23:31.854489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.171558Z","title":"Why momentum really works","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.171558Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:41364f34afb5bb208db97bd0e129969c35dc076d62e687a0998f0dde4ce0fc62","observation_id":"528622f4-1229-4add-becd-5213f7d08ea5","resolution":{"observed_at":"2026-08-07T14:23:25.171558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:31.501749Z","title":"J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y","venue":null,"work_id":"9c9411ed-6641-4697-ae95-d5dc6340b222","year":2014},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.175975Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:697f93afe61b4fd4debdbf34af6c0f30093171739092a6bd2874d345ef022d56","observation_id":"468b2ae9-eaed-4b41-8e60-1ecf22d27cf0","resolution":{"observed_at":"2026-08-07T14:23:31.629739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:31.306678Z","title":"Matrix Theory and Applications for Scientists and Engineers","venue":null,"work_id":"5e4476f2-7472-4b6d-9922-7d2a5a3982c5","year":2018},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.180138Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:6dfd58cf0f586df591c33459eef0e2f4753bf8d6f09d2aa810d1d8eeaeda6dea","observation_id":"c03501b8-a008-441a-b720-e516604809ba","resolution":{"observed_at":"2026-08-07T14:23:31.417465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:31.045550Z","title":null,"venue":null,"work_id":"3bc54a72-0cbc-4b04-8425-71683a04135e","year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.184285Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:a50222e886f1ec0268635b7309242f812cf4b36e8bd8ea1af44b22f4ec9ee3b9","observation_id":"1edcf77b-75a9-4649-901e-19facff81900","resolution":{"observed_at":"2026-08-07T14:23:31.163391Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.12529","last_updated":"2025-06-18T16:11:36Z","snapshot_observed_at":"2026-08-07T18:10:13.864971Z","submitted_at":"2025-02-18T04:32:52Z","title":"Alternating Regret for Online Convex Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.12529","snapshot_observed_at":"2026-08-07T14:23:25.188591Z","title":"Alternating regret for online convex optimization","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.188591Z"},"links":{"cited_paper":"/paper/2502.12529","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:03b79020bef5952b8ed57d20c5838dd1847a6daeafe5a37a6feecdcf3679a3de","observation_id":"c70c3e5d-9c9b-4b85-bad7-3ea827bb22cd","resolution":{"observed_at":"2026-08-07T14:23:25.188591Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.832635Z","title":"GAN s trained by a two time-scale update rule converge to a local N ash equilibrium","venue":null,"work_id":"a4ee4bdb-f890-4e53-b558-8211bc5a9f32","year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.192555Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:2a22c11a0b6b5caa4c96ff0765bde5f3b81047956101f3767d65a731c2061377","observation_id":"ed65c2bb-03d2-43d2-a591-afc3676191ea","resolution":{"observed_at":"2026-08-07T14:23:30.911907Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.651521Z","title":"The limits of min-max optimization algorithms: Convergence to spurious non-critical sets","venue":null,"work_id":"0123826a-5056-4643-903b-4239d8edc7d0","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.196258Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:c711d6abc9eacecdd34813a6f4e6c2aa1a766fd24ccca4c2a2ea660087c5de34","observation_id":"a54b86c3-e703-46d5-9337-18e0f7bab052","resolution":{"observed_at":"2026-08-07T14:23:30.699674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-07T14:23:25.199512Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.199512Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:9f98bd1d68cdee5bf06fbbcebbb2070d9d375a1eb1c606938ec5ad464e81ec74","observation_id":"ef9f2111-0adc-431b-9d03-c85949d57081","resolution":{"observed_at":"2026-08-07T14:23:25.199512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.510846Z","title":null,"venue":null,"work_id":"d89a434b-dff7-4353-8a5c-bc60807453a5","year":1976},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.203091Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:aa5e95218d1179edf933d484c9326be6d7aeb4f63a09726fd9aa3254d6570990","observation_id":"0e8522e9-e378-46ab-9e22-927db6397319","resolution":{"observed_at":"2026-08-07T14:23:30.588366Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.422242Z","title":null,"venue":null,"work_id":"4227dec8-9784-40c2-ac34-bffc49d2c78f","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.207183Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:780221323d4d94c1c0c4f6510c233db077200f991c33bc81ad05c56835d4fd11","observation_id":"e2ecdda5-04a6-44a8-b624-7e969e2f5928","resolution":{"observed_at":"2026-08-07T14:23:30.465391Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.302181Z","title":"Fundamental benefit of alternating updates in minimax optimization","venue":null,"work_id":"ab804b9f-7aae-4aab-8fd6-9c9447c73309","year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.210535Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:749180d30ad42976e7082e31559ce33a747b0ff5e18e342a352ccb2f3b6cd8ea","observation_id":"f9e3a1c7-5bae-4647-a3b8-e8b08f8f07d8","resolution":{"observed_at":"2026-08-07T14:23:30.375208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.184073Z","title":"D., Panageas, I., Piliouras, G., Simchowitz, M., Jordan, M","venue":null,"work_id":"79a9c481-874f-4f2e-9219-bf953ac0a640","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.214106Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:514675d8d9024e1839591f99908bd08af4e9341b01f2ed6966f7c8d91c3c085f","observation_id":"8aa79232-ee88-4afd-8c23-3a98878d700e","resolution":{"observed_at":"2026-08-07T14:23:30.231692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:30.047914Z","title":"Analysis and design of optimization algorithms via integral quadratic constraints","venue":null,"work_id":"db46a05b-52f3-4e5a-afb0-15aff4b9553a","year":2016},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.218782Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:733243f686140cf7931f29e5805171a4d528fefda423310e4e37bb16f7f5a268","observation_id":"e1f88007-027b-441e-abdc-d2f4fc6c738f","resolution":{"observed_at":"2026-08-07T14:23:30.118411Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.907990Z","title":"Differentiable game mechanics","venue":null,"work_id":"2b6be2a8-39f5-43c3-8458-c615c554cd5f","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.222143Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:8c2fa7966f67899718215bb4577c17b5b66a59382264dfebafbd6cefdc495dc6","observation_id":"8f6b0cb8-46d5-4884-980b-ca4884f67787","resolution":{"observed_at":"2026-08-07T14:23:29.986404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.226143Z","title":"Stochastic modified equations and adaptive stochastic gradient algorithms","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.226143Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:7b6dbe90c13147ecd199373e1e39a01c880e22c05d55ac31f88de255e4c08c93","observation_id":"1ef0ad99-0b03-44ff-8713-d911bbb49d0c","resolution":{"observed_at":"2026-08-07T14:23:25.226143Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.774769Z","title":"Accelerated regularized learning in finite n-person games","venue":null,"work_id":"c58155c4-389b-4e0b-b652-cfcb96bf5340","year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.230246Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:6da4b50ff23b6ea3640ea5cc51f94fdc0da7809ab6fc0c3846d7781ca363c5ef","observation_id":"d17fa66b-c9a0-4936-aff1-dc7bd6275e66","resolution":{"observed_at":"2026-08-07T14:23:29.846145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.619009Z","title":"An o (sr)-resolution ode framework for understanding discrete-time algorithms and applications to the linear convergence of minimax problems","venue":null,"work_id":"b28dcede-c4f0-43b7-9177-63482a54ed8e","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.234110Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:750c655495a1eb80afaf1fe8fc0453ebe536c319aaf76dc2a3e30b02adf02cbe","observation_id":"f4bc2845-5b24-4af7-906f-a7952be7b09d","resolution":{"observed_at":"2026-08-07T14:23:29.686104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1706.06083","last_updated":"2019-09-04T18:53:10Z","snapshot_observed_at":"2026-08-07T14:27:46.872660Z","submitted_at":"2017-06-19T17:53:11Z","title":"Towards Deep Learning Models Resistant to Adversarial Attacks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1706.06083","snapshot_observed_at":"2026-08-07T14:23:25.237367Z","title":"Towards deep learning models resistant to adversarial attacks","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.237367Z"},"links":{"cited_paper":"/paper/1706.06083","citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:7235b5aaa006cf560d18d6fd06860e28f7a059ad3f70597b5c9b4e1a3f856b8d","observation_id":"45762b72-ac31-4745-ba99-9d65dbfd2433","resolution":{"observed_at":"2026-08-07T14:23:25.237367Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.491478Z","title":"Which training methods for GAN s do actually converge? In International Conference on Machine Learning, pp.\\ 3481--3490","venue":null,"work_id":"ff43d707-7513-4569-acb4-b364eb462829","year":2018},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.241402Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:9ccc0ed8a231682b1c36f3a1f42a2712274bfbd6769def8dbcd7b39cffe2b199","observation_id":"e688e79d-857d-4d72-9759-a3b1fd6cdd9b","resolution":{"observed_at":"2026-08-07T14:23:29.556938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.296153Z","title":"and Jordan, M","venue":null,"work_id":"69dd3442-d113-409f-ac82-a155e2241000","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.249688Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:07db34cfba4ceb11b27f6b97acb250d34d64df4dbffac3092982fb7b7face307","observation_id":"75be3433-9610-413d-ab53-67b9a5add9d0","resolution":{"observed_at":"2026-08-07T14:23:29.395340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:29.071968Z","title":"and Jordan, M","venue":null,"work_id":"a2803eb3-b8e7-418d-84e6-7088ffa36a36","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.253115Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:7d94531651989ad21329f91006f382c253c16eda0012759416b347e0871ab401","observation_id":"b00eb4bc-340b-4d4b-a356-8b6660272ad8","resolution":{"observed_at":"2026-08-07T14:23:29.189179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.888810Z","title":"Local convergence of the heavy-ball method and i P iano for non-convex optimization","venue":null,"work_id":"128ceffd-b867-48c1-a669-19936dad89cf","year":2018},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.257193Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:5348ded0eeb530da99f4cb072c9d713eaa4f26e1e52a26d156ebf57a454b8234","observation_id":"a244ac9a-cf66-4974-82a0-2f5a6129ef92","resolution":{"observed_at":"2026-08-07T14:23:28.992663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.727417Z","title":"and Candes, E","venue":null,"work_id":"4d77b43d-1272-462c-b3f3-4ab1483002f2","year":2015},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.261079Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:b7345df3d26dbef74ba73c042d08ed23d4e501227d5a01d2fa6f33bcb0869965","observation_id":"a995e61c-7f67-42fc-b216-7169fb0d0d04","resolution":{"observed_at":"2026-08-07T14:23:28.789087Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.577502Z","title":"Stable nonconvex-nonconcave training via linear interpolation","venue":null,"work_id":"2da84681-43ea-4ea9-94a0-e438e0f7f26f","year":2023},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.264755Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:17232fa9e0e500abb8231710e955656090ed4cc5cd053d87c25385f30e7db0ed","observation_id":"f5abd3c5-e028-4786-aba1-212c5001f099","resolution":{"observed_at":"2026-08-07T14:23:28.633310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.270742Z","title":null,"venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.270742Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:a8a3e7010339c7d2c77695176fa43b604c1998150f8ca9e4bb588be35aabe5dc","observation_id":"8b7bd377-2446-49b8-b4a7-30a2ad7d2f62","resolution":{"observed_at":"2026-08-07T14:23:25.270742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.425680Z","title":"On the momentum term in gradient descent learning algorithms","venue":null,"work_id":"f3249665-c649-4296-8a7d-e976da2db302","year":1999},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.279561Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:50c08b878a8c96b1da24e11c472bea71b3ad865ae2550508803c8c38c28788d1","observation_id":"869f9560-4da9-4778-a8d5-8606363a8a33","resolution":{"observed_at":"2026-08-07T14:23:28.502704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.239249Z","title":"J., Burden, S","venue":null,"work_id":"fcdca48f-9000-480d-b4b2-4ed87aa43331","year":2016},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.292181Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:283030603fd6455d6838bc14a6289178285e6371bbaa7dab2705b09721edc728","observation_id":"60a1c117-2f5b-47af-bdd8-867b6442566e","resolution":{"observed_at":"2026-08-07T14:23:28.345984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:28.077261Z","title":"C., Wu, Y., Dherin, B., and Barrett, D","venue":null,"work_id":"76c85bdb-8826-4267-885c-6b9c5790d37e","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.297531Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:dbcdbc5c2b2ff7442a10684f97a36466b721ddccda971562e164dd0ad683e266","observation_id":"1cf2a485-fd20-48c0-9038-3db49c02bf20","resolution":{"observed_at":"2026-08-07T14:23:28.161707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.304039Z","title":"Improved techniques for training gans","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.304039Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:13f45c1e6651a7684dcecc3785a47f0e5cb3f5cb15b866f5a0391a3957f12ea1","observation_id":"c3c73305-2d15-4bc2-9868-d3536ec38609","resolution":{"observed_at":"2026-08-07T14:23:25.304039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:27.907724Z","title":"S., Jordan, M","venue":null,"work_id":"7fa1026b-14fb-41e5-abbd-8cc452d166e4","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.311452Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:20c7bde692259cdb4599cd86163c0fbd7d1b81acf2901a23c81caceb02b7e029","observation_id":"2fff9162-875b-424e-9776-d5e48068f8b3","resolution":{"observed_at":"2026-08-07T14:23:27.982284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:27.706967Z","title":null,"venue":null,"work_id":"c0259c3d-6471-427b-b65d-e42f335bf9c4","year":2016},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.317258Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:f1ff297aec7c9cb73ba9a246ea7e3f638623fcb99b1d943cf40061cbda6e4671","observation_id":"82c40546-d05b-4003-b215-291064b880ef","resolution":{"observed_at":"2026-08-07T14:23:27.799786Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:27.519569Z","title":"On the importance of initialization and momentum in deep learning","venue":null,"work_id":"13cba413-c9a7-49db-8b05-30adf972039a","year":2013},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.325453Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:33e8d1b4d1876217bf676c22a5b5726e50d073bbe4ef35ea27a87f0a8a31b14f","observation_id":"cd8a4823-54ba-4e15-8a46-87c464d72f25","resolution":{"observed_at":"2026-08-07T14:23:27.600476Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:27.314747Z","title":"Improving generalization and stability of generative adversarial networks","venue":null,"work_id":"53ab32c9-5044-4d9d-8c8e-4b56a8a17dba","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.334381Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:0a6a14e7e317e5ca131f8fe73d7d4a5dc6885dc9da8b44349ed4e0362ba0078b","observation_id":"db7371ee-2dbe-422e-802e-cac3443cbb29","resolution":{"observed_at":"2026-08-07T14:23:27.394585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:27.082497Z","title":"and Chizat, L","venue":null,"work_id":"807a5a04-6041-4045-b516-e36d3de635c6","year":2024},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.342489Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:c0579f332ebad15d6cbe683989474de4953c6493ce06f666f5bc2b0ac0985f7d","observation_id":"35c0c7df-ceb4-481e-a128-d5c7fea568d0","resolution":{"observed_at":"2026-08-07T14:23:27.208938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.956308Z","title":"Provable acceleration of heavy ball beyond quadratics for a class of P olyak- L ojasiewicz functions when the non-convexity is averaged-out","venue":null,"work_id":"6f1d6bba-4bec-42a5-8678-8dc6ddc08c97","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.349855Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:ac80414e00b02d9bf7b3c7616056e4aada91920abb2a561f390a32597800e542","observation_id":"592602ab-d8c4-4cd0-af76-f6a1d5326936","resolution":{"observed_at":"2026-08-07T14:23:27.014310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.762734Z","title":"On the convergence and robustness of adversarial training","venue":null,"work_id":"beb92d39-e811-41bd-86ea-101ad040e0ae","year":2019},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.357628Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:cd81e2d4f64133375a31efa8e6419a335efb072446c3a24ab4c0c7b00b482ef2","observation_id":"218a2344-a3d9-481d-be71-594fe86d6f88","resolution":{"observed_at":"2026-08-07T14:23:26.855252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.576291Z","title":"C., and Jordan, M","venue":null,"work_id":"53474ee0-6aa3-4461-965b-12ff4eeae3a5","year":2016},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.364719Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:720c72753b28f4b8bd3e936c2a6f6b0fc4c8c29475dd13334ffa3866358de1e6","observation_id":"8fe68b5a-6246-47e0-968e-90a099ad47ea","resolution":{"observed_at":"2026-08-07T14:23:26.681665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.402980Z","title":"Alternating mirror descent for constrained min-max games","venue":null,"work_id":"600c0c11-22a3-4bdc-8476-f6b33ad1641a","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.372586Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:47cd0839fb545bfc2f46e60b23d2d35b7e7c0dc93b62404c060b8af71441885d","observation_id":"e85e4265-db70-447f-a0f6-d90fa9ae1e73","resolution":{"observed_at":"2026-08-07T14:23:26.488975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.222653Z","title":"Gradient normalization for generative adversarial networks","venue":null,"work_id":"c2c9bba4-1fd1-46e8-a879-8bbe02d2f5e2","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.380483Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:1c866ea70e8da4bf964bf4c4c20ed4fd8c0b96657acb6b1395743735951524a0","observation_id":"ca8e73e1-93db-41ba-9dd4-1e3ff17e0fdb","resolution":{"observed_at":"2026-08-07T14:23:26.314366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:26.072988Z","title":"Faster single-loop algorithms for minimax optimization without strong concavity","venue":null,"work_id":"c954a316-7cc8-4811-9fe3-455c4e7471bc","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.388248Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:dd27bf52dda4fdc1e7e5594562e284377267a413de4a32548d224601bafbafdc","observation_id":"1dd07469-0926-4e44-8182-32aedb6bb5c0","resolution":{"observed_at":"2026-08-07T14:23:26.139376Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.885704Z","title":"and Wang, Y","venue":null,"work_id":"8afca3c6-9a07-482b-8a00-476a471dbdde","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.398845Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:f91e706387df2a33ab5611f4ddb5bff633c4500173dfc16a2a322d756d71ec31","observation_id":"553ff183-081f-49aa-8e7d-63b4622136aa","resolution":{"observed_at":"2026-08-07T14:23:25.995982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.741947Z","title":"A unified analysis of first-order methods for smooth games via integral quadratic constraints","venue":null,"work_id":"b0835aaa-3972-4c89-bfad-5ac40a8bdfb7","year":2021},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.407610Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:319c8602161f026b61eaff0915fb6ae5ecf3bba26fbfec97a1d7a17e394830b1","observation_id":"6837e270-f101-4ff7-a600-037bfdab7e16","resolution":{"observed_at":"2026-08-07T14:23:25.782684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:23:25.554164Z","title":null,"venue":null,"work_id":"4a789466-b699-4c5a-8ae4-99e51e29d091","year":2022},"citing_paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-07T14:23:25.414640Z"},"links":{"citing_paper":"/paper/2505.19537"},"observation_digest":"sha256:4b12006f5202b135cfa6176ceb62ccdb7525cad065f86ab0275e1ca533ce44d9","observation_id":"57d64d32-052d-42b3-9971-d0988c0b79b7","resolution":{"observed_at":"2026-08-07T14:23:25.635941Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.19537","last_updated":"2025-05-26T05:55:16Z","latest_version":1,"primary_category":"cs.GT","snapshot_observed_at":"2026-08-11T01:38:27.846531Z","submitted_at":"2025-05-26T05:55:16Z","title":"Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games"},"reference_resolution":{"displayed":57,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":0,"verified_fuzzy":39},"total_outbound_references":57},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 0 inbound Pith citation observations for arXiv:2505.19537."}