{"as_of":"2026-08-05T06:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0480a1e2789fc0c953f92fa951a12415fd26f7d39fdc1912a7395c8018a95f7d","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T12:27:10.934480Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-05T06:32:48.257954+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T08:04:06.432613Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-04T18:40:02.584054Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"cited_work":{"arxiv_id":"2604.13870","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.13870","snapshot_observed_at":"2026-07-04T18:40:02.584054Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","venue":"math.OC","work_id":"2105309c-84a1-43b7-8703-b8d6deccc10c","year":2026},"citing_paper":{"arxiv_id":"2606.24879","last_updated":"2026-06-23T17:55:18Z","snapshot_observed_at":"2026-07-06T23:59:23.407216Z","submitted_at":"2026-06-23T17:55:18Z","title":"New Bounds for the Last Iterate of the Stochastic subGradient Method","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-25T22:43:06.513763Z"},"links":{"cited_paper":"/paper/2604.13870","citing_paper":"/paper/2606.24879"},"observation_digest":"sha256:b6a20435cfefda87d23b2f9efff74d0f4ff7e1935a66c2a985cb76c36968f015","observation_id":"e337a14d-a41b-47a1-b130-7f0223b7f36b","resolution":{"observed_at":"2026-07-04T18:40:02.585381Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"cited_work":{"arxiv_id":"2604.13870","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.13870","snapshot_observed_at":"2026-07-04T18:40:02.584054Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","venue":"math.OC","work_id":"2105309c-84a1-43b7-8703-b8d6deccc10c","year":2026},"citing_paper":{"arxiv_id":"2606.28123","last_updated":"2026-06-26T14:24:11Z","snapshot_observed_at":"2026-08-03T16:18:21.650544Z","submitted_at":"2026-06-26T14:24:11Z","title":"Dangerous Liaisons of Convex Learning and Non-Affine Aggregation","version":1},"reference_index":231,"source":"arxiv_source","source_observed_at":"2026-06-29T05:00:47.642665Z"},"links":{"cited_paper":"/paper/2604.13870","citing_paper":"/paper/2606.28123"},"observation_digest":"sha256:2cde097c3838b7c7898539f9b91da9667ea25844a25ebe8e8ec236628842f371","observation_id":"9e1462eb-f937-4532-a010-5810f11c25c9","resolution":{"observed_at":"2026-06-29T18:53:52.019759Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.13870","snapshot_observed_at":"2026-07-14T08:04:06.432613Z","title":"arXiv preprint arXiv:2604.13870 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10959","last_updated":"2026-07-12T23:24:42Z","snapshot_observed_at":"2026-08-03T13:16:14.672928Z","submitted_at":"2026-07-12T23:24:42Z","title":"WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-07-14T08:04:06.432613Z"},"links":{"cited_paper":"/paper/2604.13870","citing_paper":"/paper/2607.10959"},"observation_digest":"sha256:c4a81b75c27e3d3aaf0759cab4c68bfa84fa26c2a3097b2c53dac32d4bdc521e","observation_id":"4899f82c-5462-4ba3-8c4b-3f31964622b5","resolution":{"observed_at":"2026-07-14T08:04:06.432613Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2604.13870/citation-record","integrity":"/paper/2604.13870/integrity","json":"/paper/2604.13870/citation-record.json","paper":"/paper/2604.13870"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Acceleration by stepsize hedging: Silver stepsize schedule for smooth convex optimization","venue":null,"work_id":"51cf61dc-b7f8-4aec-8948-f37d8b8dc769","year":2024},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:676311216b66e6b9e93b23a39af08d29f41dee91c7865319b0058e013799234c","observation_id":"1646cc3f-e3e0-4919-86f6-3b5621937565","resolution":{"observed_at":"2026-05-19T09:13:04.749803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.11274","last_updated":"2025-07-28T11:03:24Z","snapshot_observed_at":"2026-07-06T21:57:32.181776Z","submitted_at":"2025-07-15T12:52:47Z","title":"Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime","version":2},"cited_work":{"arxiv_id":"2507.11274","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.11274","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fast last-iterate convergenceofsgdinthesmoothinterpolationregime","venue":null,"work_id":"cf146778-3eeb-415a-a75b-a8f57fe4355b","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"cited_paper":"/paper/2507.11274","citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:10b2ef2ce95582075aca3ad9be1c4a3ad2ad8229ccffaee41ad33dba73a9f41d","observation_id":"83288431-43cb-420e-a64a-c918a27ab892","resolution":{"observed_at":"2026-05-10T12:30:23.755228Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Large-scale machine learning with stochastic gradient descent","venue":null,"work_id":"5e4c8a5a-cf23-4272-86e8-edcf4ffc4d4a","year":2010},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:acb13ec6d7ce90b2e0587db65858c1b27bfc9aaa19c36a8e80633691e31693c9","observation_id":"78fc1514-2f93-44ff-9650-aa743fc22a8e","resolution":{"observed_at":"2026-05-19T09:13:04.745804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Last iterate convergence of incremental methods and applications in continual learning","venue":null,"work_id":"2c1a9aea-247a-4657-bd99-c4d7a2ab660e","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:7eaab1d7c993d90270880b6c819f4fb19a95124a9f6651169ed1de72ce938253","observation_id":"e3afec09-2a2f-42b1-8f6d-d88873b3fca0","resolution":{"observed_at":"2026-05-19T09:13:04.727885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"From continual learning to sgd and back: Better rates for continual linear models","venue":null,"work_id":"a8408a68-9df4-4c91-bdcb-312d67bbdc84","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:b440d5c650f589398e0d6e0f6e5f6e51fa841a1493c6f30440efebb310cb0fa1","observation_id":"e47af917-3ffd-459b-8fbf-3c188a7fe3f6","resolution":{"observed_at":"2026-05-19T09:13:04.694306Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.14122","last_updated":"2025-07-18T17:53:12Z","snapshot_observed_at":"2026-07-06T21:59:20.041999Z","submitted_at":"2025-07-18T17:53:12Z","title":"Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems","version":1},"cited_work":{"arxiv_id":"2507.14122","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.14122","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Garrigos, D","venue":null,"work_id":"1933487e-fb63-45aa-9c7f-2a8355446b40","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"cited_paper":"/paper/2507.14122","citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:13a548d2969499963f770198ae66f7aa2c430accf08205b6f0994d89b5bba3b5","observation_id":"391611ee-09ef-45c3-9222-b6a2be1738eb","resolution":{"observed_at":"2026-05-10T12:30:23.751347Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Deep learning, volume 1","venue":null,"work_id":"0b84da57-de4e-4b3c-bcbf-7a1212a1bbe4","year":2016},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:06c999ac1ebd87fc6d775094630b8f93fd5a0c3ccdc6fdc787fb489cd0f2d12e","observation_id":"f3f59019-e9c8-4dfe-8b99-776c5c10c9d4","resolution":{"observed_at":"2026-05-19T09:13:04.686371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-07-07T21:14:09.062374Z","title":"Sgd: General analysis and improved rates","venue":null,"work_id":"794f70fc-bb6f-4b76-ad48-44b9c5bf80e5","year":2019},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:c783b6d47ef470163d9971f240aea39e834d11f65e4b793e5263bf7789674922","observation_id":"016108b7-568b-47e3-990c-3df7428cbbe5","resolution":{"observed_at":"2026-05-19T09:13:04.690532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Accelerated objective gap and gradient norm convergence for gradient descent via long steps","venue":null,"work_id":"760cc4ab-4b1e-4b2c-8d3a-cd7372e3b84e","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:6ba8b40139dd07ecbbcca99cc07b236dd6a5dc946670982fbfbe411d83dc0ca5","observation_id":"2f306735-9496-4208-8b5c-c8baa68f2a56","resolution":{"observed_at":"2026-05-19T09:13:04.698033Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Tight analyses for non-smooth stochastic gradient descent","venue":null,"work_id":"30409b52-d450-4ef0-a1ea-e86baeffffb3","year":2019},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:533447ae8cf1b9f502b989ed5bb56f2a11be413ad91a6db0225a12634f97db46","observation_id":"77d71d06-cd3a-4775-8b4c-f509c36ab0db","resolution":{"observed_at":"2026-05-19T09:13:04.705726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Introduction to online convex optimization","venue":null,"work_id":"aee089a7-7344-47e6-8b87-a4e6b694a672","year":2016},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:2256c497e7eb7d876419576b93205a6a877d3eff274b9e4c21af0fceadd342a0","observation_id":"778408c6-7e05-44d8-8c3b-f8ff0cca68a6","resolution":{"observed_at":"2026-05-19T09:13:04.682461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Beyond the regret minimization barrier: optimal algorithms for stochastic strongly-convex optimization","venue":null,"work_id":"40c8bbc5-dcb4-437c-92de-11f0756c996f","year":2014},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:561c3cdc3da7aa9f80dc61a01ea52547721041b5bab3769527c2dcdcbbefc6de","observation_id":"f4c96784-25c1-4ca9-9b63-400fb3a0a277","resolution":{"observed_at":"2026-05-19T09:13:04.678602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Making the last iterate of sgd information theoretically optimal","venue":null,"work_id":"f7874d74-5f18-4439-8d2a-0d6d2cb8ab0a","year":2019},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:ee1e6043b5eee816beef4d81981d8795b192c1965f0047dc62da2b0af8431c9f","observation_id":"9ee75dda-e1c3-4918-91c8-c2c5b025ee1b","resolution":{"observed_at":"2026-05-19T09:13:04.701888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Open problem: Anytime convergence rate of gradient descent","venue":null,"work_id":"abe238b9-216c-428a-8879-856d92189b26","year":2024},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:5dbffe0ba138e9b73c4f932e941016a7ec57c1fcd837e690118c1914fccbfb89","observation_id":"70db4058-cdf6-4103-b02b-5cb974803b05","resolution":{"observed_at":"2026-05-19T09:13:04.741722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1212.2002","last_updated":"2012-12-20T20:55:23Z","snapshot_observed_at":"2026-07-06T03:01:36.476155Z","submitted_at":"2012-12-10T09:22:06Z","title":"A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method","version":2},"cited_work":{"arxiv_id":"1212.2002","doi":null,"metadata_source":"pith","pith_arxiv_id":"1212.2002","snapshot_observed_at":"2026-07-04T02:59:25.773753Z","title":"A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method","venue":"cs.LG","work_id":"1af20ac1-da90-4841-82b2-cf03c0148efc","year":2012},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"cited_paper":"/paper/1212.2002","citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:6e03655d456b20ee2fda1171bc1f61d307bf855a472eb80581f21556fea87b1e","observation_id":"0a357be5-d9a2-49dd-8558-668390df0f61","resolution":{"observed_at":"2026-05-10T12:30:23.740706Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.07723","last_updated":"2024-06-06T01:52:22Z","snapshot_observed_at":"2026-07-06T17:43:22.965126Z","submitted_at":"2024-03-12T15:01:17Z","title":"On the Last-Iterate Convergence of Shuffling Gradient Methods","version":3},"cited_work":{"arxiv_id":"2403.07723","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2403.07723","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the last-iterate convergence of shuffling gradient methods","venue":null,"work_id":"707ad85e-7e79-4b7b-951d-9fa5c3b35cbc","year":2024},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"cited_paper":"/paper/2403.07723","citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:584057876811c826526565baeb44583f0941b62711d8d0e4c83f03e2064a45a4","observation_id":"86faa8ba-363c-4dcb-a989-089fad399139","resolution":{"observed_at":"2026-05-10T12:30:23.744216Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Revisiting the last-iterate convergence of stochastic gradient methods","venue":null,"work_id":"3929a629-0cad-47ae-b60a-b6bc909c6a99","year":2024},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:6facbe58def2e893adf01c5fdbd647ab6171f7ea36bd23041b549731e79ef38a","observation_id":"61ffd648-4fbf-4db2-8d23-132d890b040d","resolution":{"observed_at":"2026-05-19T09:13:04.731011Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-07-07T21:14:09.038331Z","title":"Non-asymptotic analysis of stochastic approximation algorithms for machine learning","venue":null,"work_id":"582059aa-afa8-4b79-a939-8c7d86fbc435","year":2011},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:c18aa630733d207b10b71cfd6bc9b557f8ddc6fa66a7e6cbf770999f4a23bc64","observation_id":"e19c3644-f96d-47f9-a86a-fac7c120ad3a","resolution":{"observed_at":"2026-05-19T09:13:04.737979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Robust stochastic approximation approach to stochastic programming","venue":null,"work_id":"164d4bc0-59b5-4c5a-903e-2370c1d09031","year":2009},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:01e581e9dd41ab081b9e426a3d64f2deadc1b9498097d8d9bff14cb474e8e750","observation_id":"2c01f2ea-8f90-41b3-a970-8725063b6b61","resolution":{"observed_at":"2026-05-19T09:13:04.723136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Problem complexity and method efficiency in optimization","venue":null,"work_id":"661d3e2e-72e9-4ccf-8ad1-f244e42ea1af","year":1983},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:3b10052708a6c938d8348bd9f44e44c00ae30a39620997193549c779c549cea1","observation_id":"2d61c199-1f46-4708-8e77-f18333834d71","resolution":{"observed_at":"2026-05-19T09:13:04.709678Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"The asymptotic density of sequences","venue":null,"work_id":"48dc45c6-4657-4ec8-a96e-a43c538dfa35","year":1951},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:b9ef15d7ab2afb604e540d8d554fe5f847c4506c1f51667efc46e7d55e38ceb2","observation_id":"286c8b73-8bf1-492b-a902-f0fb7a374bc1","resolution":{"observed_at":"2026-05-19T09:13:04.719535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Acceleration of stochastic approximation by averaging","venue":null,"work_id":"36bdc44b-3ef4-4828-a785-cdc3fd01b626","year":1992},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:438c867229181b7078e959bec9e81e8629578435e67e4e8905b43a11afcdaff8","observation_id":"7d4d6dc1-ac57-450c-be31-c570bd34928c","resolution":{"observed_at":"2026-05-19T09:13:04.734334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Making gradient descent optimal for strongly convex stochastic optimization","venue":null,"work_id":"3d44626d-60df-42d1-8c8f-aa5a76718c02","year":2012},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:69fc337b1346fa827c688d7f82f5b5fc6363e10545ea6585d69749883d09fc4b","observation_id":"ad5164eb-b86f-4806-9b02-7166038271d4","resolution":{"observed_at":"2026-05-19T09:13:04.713829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-07-07T21:14:09.041693Z","title":"A stochastic approximation method","venue":null,"work_id":"406974f3-4198-456a-b270-e507235b1a0d","year":1951},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:2463904f34623e991262170288dfb7f782b43b8b3c980afd394a8f320ac2c429","observation_id":"358f4fdb-14da-45d8-a4d8-d7a495ee0af0","resolution":{"observed_at":"2026-05-19T09:13:04.753565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Open problem: Is averaging needed for strongly convex stochastic gradient descent? In Conference on Learning Theory, pages 47--1","venue":null,"work_id":"d2c02752-3f3b-467f-b257-42c2820ba6b3","year":2012},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:07a89289e8a0db252dc045cb57c69b3f94603089b0e8cf368bb78203f69fe972","observation_id":"52438777-6c11-4529-a4a3-fd804b42c83d","resolution":{"observed_at":"2026-05-19T09:13:04.674483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Stochastic gradient descent for non-smooth optimization: Convergence results and optimal averaging schemes","venue":null,"work_id":"0a2f138d-b6d6-4fec-99de-54876a149187","year":2013},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:8464ba0928741d2e908ac8baef0e1c5b62547376e868630a92199419685a492f","observation_id":"5c6a6564-73a7-483c-b91d-792af65e0f19","resolution":{"observed_at":"2026-05-19T09:13:04.594693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions","venue":null,"work_id":"1e362e3b-7c23-4da8-8eeb-ebda2701bb39","year":2019},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:037f909d76b37b5aa32c776e5e2edfc11a5b4d75d8dc0a3804e161bed39dd169","observation_id":"1b851b89-0d2f-42bd-a121-9a1d2b6ab3c8","resolution":{"observed_at":"2026-05-19T09:13:04.665090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Last iterate convergence of sgd for least-squares in the interpolation regime","venue":null,"work_id":"c0bfaa21-4ec1-4cf2-b89a-537f63293fb9","year":2021},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:fc6cde8e8a4aad597e46658da4588a95d1b6d124bd4416228d532d5621641376","observation_id":"077b539b-34c8-4316-b5d1-ce1013ff897e","resolution":{"observed_at":"2026-05-19T09:13:04.669833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11134","last_updated":"2023-07-20T16:27:12Z","snapshot_observed_at":"2026-07-06T15:56:38.019661Z","submitted_at":"2023-07-20T16:27:12Z","title":"Exact convergence rate of the last iterate in subgradient methods","version":1},"cited_work":{"arxiv_id":"2307.11134","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2307.11134","snapshot_observed_at":"2026-07-03T04:37:36.542213Z","title":"and Glineur, F","venue":null,"work_id":"6e98478d-87d9-41ce-a069-82b09bdfe185","year":2023},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"cited_paper":"/paper/2307.11134","citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:a2e070217b42584aeefd7f675fcdfa7f6645eba30e5ed4b085274f0e1b2384a0","observation_id":"90df7d6c-f675-451f-a912-b49bbdbd2f20","resolution":{"observed_at":"2026-05-10T12:30:23.747778Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Solving large scale linear prediction problems using stochastic gradient descent algorithms","venue":null,"work_id":"d53b7e0b-10c3-494f-b9bd-828308c76cb8","year":2004},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:0d9c024310330a0f8cc11352ffbc16d82d75612aeb59b84b04724235b1e3d637","observation_id":"f9082fea-c936-4b01-b52f-04802ebea0d4","resolution":{"observed_at":"2026-05-19T09:13:04.571861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Anytime acceleration of gradient descent","venue":null,"work_id":"abc4f432-ac3c-4978-a327-24710282dbf8","year":2025},"citing_paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-05-10T12:27:10.934480Z"},"links":{"citing_paper":"/paper/2604.13870"},"observation_digest":"sha256:63b77f82666572eab3a2ba1ef044dc67d8a4b9f4170b58ce0b133aa18ccf69db","observation_id":"0e1f624e-113c-4f4e-bcb2-8790175b5b4b","resolution":{"observed_at":"2026-05-19T09:13:04.567951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.13870","last_updated":"2026-04-15T13:33:08Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-07-06T23:01:46.092000Z","submitted_at":"2026-04-15T13:33:08Z","title":"Gradient Descent's Last Iterate is Often (slightly) Suboptimal"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":0,"verified_exact":3,"verified_fuzzy":26},"total_outbound_references":31},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 3 inbound Pith citation observations for arXiv:2604.13870."}