{"as_of":"2026-08-04T15:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5c40786cf9da434453a0a1ca2c52d3dd9a80dc68c01c3e2d02d2e847d9c1b0a7","coverage":[{"denominator":62,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":62,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T00:59:39.800662Z","state":"measured"},{"denominator":63,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":63,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T22:42:16.293180Z","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":"2026-07-02T16:27:09.258295Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"cited_work":{"arxiv_id":"2604.21016","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.21016","snapshot_observed_at":"2026-07-02T16:27:09.258295Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","venue":"cs.LG","work_id":"d169f9ae-a9c7-4ea9-bd64-404cbf3a1e17","year":2026},"citing_paper":{"arxiv_id":"2606.06412","last_updated":"2026-06-04T17:15:50Z","snapshot_observed_at":"2026-07-06T23:46:15.936608Z","submitted_at":"2026-06-04T17:15:50Z","title":"Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forces","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-27T22:42:16.293180Z"},"links":{"cited_paper":"/paper/2604.21016","citing_paper":"/paper/2606.06412"},"observation_digest":"sha256:6666ebfe03af6afb4198642ce778b93735c29dd30a4a804010b281bad7fad6b2","observation_id":"3b3d83fe-013e-49bc-8ac6-a4917fb8335a","resolution":{"observed_at":"2026-07-02T16:27:09.259494Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2604.21016/citation-record","integrity":"/paper/2604.21016/integrity","json":"/paper/2604.21016/citation-record.json","paper":"/paper/2604.21016"},"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":"Ahn and J","venue":null,"work_id":"fcebdd2b-c583-4b29-b613-640927295b45","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:f9949ed27d302ce49c96f6b25f0d19eb8998003ec41981f03a0b9c7c8bcd787f","observation_id":"d004b060-440d-497c-a4db-438db73b13de","resolution":{"observed_at":"2026-05-23T10:15:35.140324Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Andreyev and P","venue":null,"work_id":"fad09338-666e-4139-9b5d-9a0a5c10ffbe","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:348b79680b74b9c7f8ec0276f8fe3ca1ad6f2ba6542acd97415e7a7435c25141","observation_id":"efdbf777-ec95-45d5-ba60-59d9f94f89bf","resolution":{"observed_at":"2026-05-23T10:15:35.134042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Arora and Z","venue":null,"work_id":"12543900-8110-4831-8359-e98f57d630d3","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:c4a7fc6a0cac9f226490208e96eb088f798f71f632e71bb9ce22bb65ef4fdad9","observation_id":"8a84c150-db08-4ef4-839a-172d42842ca1","resolution":{"observed_at":"2026-05-23T10:15:35.033495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Blanc and N","venue":null,"work_id":"8cdcaf58-f4fc-4cfd-a273-2cf33c19b83f","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:163929a5fc1a9b763cc8221b189d4e727b49d0b5dc439ceae9321de3aa81bfeb","observation_id":"d4f9a245-605a-4562-b8d6-a6a3a7da23e6","resolution":{"observed_at":"2026-05-23T10:15:35.045082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.04172","last_updated":"2023-07-26T10:48:54Z","snapshot_observed_at":"2026-07-06T13:18:52.367719Z","submitted_at":"2022-06-08T21:32:50Z","title":"Beyond the Edge of Stability via Two-step Gradient Updates","version":3},"cited_work":{"arxiv_id":"2206.04172","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2206.04172","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Chen and J","venue":null,"work_id":"295f06b5-3e03-4439-9798-edcbe00c2554","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"cited_paper":"/paper/2206.04172","citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:13930c4fd6482a4c8112f0476a0ae561bb8fddefca4ee6c51bc89159b1b8d826","observation_id":"64261711-25a8-41c0-92fd-48c6eabfcf9b","resolution":{"observed_at":"2026-05-10T00:59:49.381861Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Damian and T","venue":null,"work_id":"f57237e3-cdbb-4be1-8890-58e67e808f2c","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:7060054ad410b2f2ad646185b33d840a0dab427bb3199dfd665c38f02823ce96","observation_id":"30496f9b-dd94-4563-9f9c-fc4438fee185","resolution":{"observed_at":"2026-05-23T10:15:35.030480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Foret and A","venue":null,"work_id":"b1364876-c6e4-4661-994c-f4535639f3ae","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:740addbdf43c89e84555662e8839e330d0dfe3f27470d1a7c148c076d24cf736","observation_id":"4ae57921-aff7-48e3-9bb9-92e6375b8f29","resolution":{"observed_at":"2026-05-23T10:15:35.041586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Gilmer and B","venue":null,"work_id":"50c9bd71-f790-4876-b3a8-0c8012bb2ead","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:17ebb18aa850aaede259d0cefcdbd10cac1da81ba6f0c9659ea6d3f1c587f0bc","observation_id":"7bacc273-8362-4f80-9251-dd9379e6b27c","resolution":{"observed_at":"2026-05-23T10:15:35.051654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Jastrzebski and Z","venue":null,"work_id":"397ecccf-ae70-4521-89d5-d12238f68dd5","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:87a6d89403ae16694661bfa43925fee711466c06cb41c5d8f64a1506a2941c49","observation_id":"eb0d038d-154f-41d3-ab03-0dc50013845b","resolution":{"observed_at":"2026-05-23T10:15:35.064839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Jastrzebski and M","venue":null,"work_id":"acefa1e7-5ce9-42a6-90be-43a3028259cd","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:eaf36f0cd2efbc729c72280b62014bc5fc4c2cbb0e8944193dcd6caf27c1a7e9","observation_id":"4cff7b41-32d8-44ca-a52f-1d1701fac88d","resolution":{"observed_at":"2026-05-23T10:15:35.008540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Jiang and B","venue":null,"work_id":"746cb922-d336-4aca-b5c3-aff13884b7f9","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:861dab68d33d5a2c1a9589ec0dbc1db954c8d5ca36776c75aa0f58ef825de7e2","observation_id":"33945e7b-5f52-42b2-ad56-5cfab34121d6","resolution":{"observed_at":"2026-05-23T10:15:35.005547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":null,"venue":null,"work_id":"4fc7f9b8-3ff2-49ac-9b01-fa4e07e5597f","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:89c7855a2122b76cbee68b96b37a912522f002c88acb224bb89a9bd41f0b0cfb","observation_id":"954667dc-f153-4bea-bf49-4758cc7d4961","resolution":{"observed_at":"2026-05-23T10:15:35.018142Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Lee and C","venue":null,"work_id":"72152dbb-4e79-44c6-a6a0-0b5ba7cf1852","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:758af80c74ecf6591629006c6456d26da42f8bc1fbaec4ae80e1f0c3bb6a191c","observation_id":"93657e69-7aea-43e6-a590-305ff369fc34","resolution":{"observed_at":"2026-05-23T10:15:35.020956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Li and C","venue":null,"work_id":"b27efb43-6ae0-48f9-a9c7-01943498450c","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:c3d37993567530fb3356868e02a07ea1a458a51a463b328769ff5f09ffd65b19","observation_id":"d7a3f6ce-94f8-4769-95a8-443f6979bc10","resolution":{"observed_at":"2026-05-23T10:15:35.058492Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Li and T","venue":null,"work_id":"24363817-306d-443b-9967-ed7aeee9d2c3","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:519382b4b38f6761ad72cd128d1a80b3d7969cc400ddb3035704fb1b3039636a","observation_id":"893aff6a-f43a-4a51-9990-80e81ec4a9aa","resolution":{"observed_at":"2026-05-23T10:15:35.104736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Li and T","venue":null,"work_id":"39a88978-66e4-409e-ba85-3bb6d86a725f","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:9310fd3cd5cbd5b36fd24989ad11abc928c6ec64bf08faebd61068d1f7c0244f","observation_id":"59afe470-039c-4bb8-8f71-14057a454112","resolution":{"observed_at":"2026-05-23T10:15:35.107739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Lyu and Z","venue":null,"work_id":"ebda636e-ee10-4330-825f-091173dcdeed","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:89cc7edc213ca3e9cadc3cbfb8ff52cbfe6e4f01f49fbb8983bb59fe93c18cfd","observation_id":"66115fa8-ad5c-4773-a191-864a87b6b772","resolution":{"observed_at":"2026-05-23T10:15:35.161664Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Ma and L","venue":null,"work_id":"440067e1-59e7-4ce6-94d7-d3842a6c111c","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:d132d4a067c055ae1f71c3ed1663242e1f779e4d3f9a8840fcc9a785c49b2579","observation_id":"0c2ca4cb-5310-4cb8-9305-a7bd6b5c660d","resolution":{"observed_at":"2026-05-23T10:15:35.158787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Mandt and M","venue":null,"work_id":"f6732b52-4d87-4a3e-a275-ee06b699bb23","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:201ad97ba1a080558997d31a867ba234f251b3a7b9f89e240e07e975b3f403eb","observation_id":"baca19a2-4cde-44d3-83f0-dcbd61df6f3d","resolution":{"observed_at":"2026-05-23T10:15:35.155875Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Wu and C","venue":null,"work_id":"8ce2f42a-e279-4d14-9693-eb620917a329","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:7a035679730454d5afb8450463732fdce610278ff11bab9123d598a983350c87","observation_id":"8e832eb1-69eb-4237-8ca9-a8a6542efd66","resolution":{"observed_at":"2026-05-23T10:15:35.167854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-07-07T07:33:30.537723Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":"3a2239d2-e4c2-4554-ab89-453d2ac0b66a","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:8ab73f7f55a02cfafe3fedf23b0b780500c9ce2b8605e4f2833e129b370420bb","observation_id":"c450f7b4-b980-42bf-8c65-282684cba723","resolution":{"observed_at":"2026-05-23T10:15:35.143545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"4453f5ef-5758-414a-8ac7-00ebacb5cf36","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:ba431212ec9b8d033b82a6bec424a2a091a848d22a80d5f85a77f5f30dc31714","observation_id":"f4171b93-3271-48fe-869c-596fbdff6f21","resolution":{"observed_at":"2026-05-23T10:15:35.149601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Machine Learning , year=","venue":null,"work_id":"d9fe4c18-c51b-4827-9989-e356a14b2c64","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:5b86ddfcb113e2d2b84f8bbd9a0f2e7faf676cffb7432fce57776b2976ed3b5c","observation_id":"a498c573-dc71-40ef-9dda-ce84dc24aa62","resolution":{"observed_at":"2026-05-23T10:15:35.146586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"231227a4-2b25-45ae-9ad7-005c03582753","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:97b46907122c203aee53363a7e83124832fa2805a92dc3e76a75e4340c834d1c","observation_id":"a3f48902-c3dd-40ac-b274-748e288fca69","resolution":{"observed_at":"2026-05-23T10:15:35.170822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Analyzing Sharpness along","venue":null,"work_id":"8501b01a-e901-489d-a7c9-92fd06f4ffa9","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:1e8ead6a8318b5b6108ec8a71b2293a7d39b019377bc0e9aa13f5a47c2b63dc2","observation_id":"d212cf0f-acef-4283-9f83-b7e1a216df11","resolution":{"observed_at":"2026-05-23T10:15:35.183321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Machine Learning , year=","venue":null,"work_id":"6fd80788-da91-4611-86e8-8c209f094f48","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:f6354dbf60e2b0fbfee87a693eb2e7894e0ae2380160548637ca515b4ddad0bc","observation_id":"81e635f4-83af-4251-b83e-5d8337a69e03","resolution":{"observed_at":"2026-05-23T10:15:35.128013Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Machine Learning , year=","venue":null,"work_id":"9e6d31e3-1b0e-413b-924a-e5bd91ba63de","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:37224f7e24eac764e2a0a38dcab9b5ac41be871a3eccead28df5905fe89dfab9","observation_id":"94980865-8863-4da9-8f4a-13370bc29ed2","resolution":{"observed_at":"2026-05-23T10:15:35.131169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Machine Learning , year=","venue":null,"work_id":"74a16112-2bc7-46f0-98fd-54c7598b7283","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:74733fd5d9080d28f5abcf83397638c2ddcacbb77bae5c97256c38ce6c3fa3f1","observation_id":"9fe93dd4-0363-4dda-b3ad-42e3cc254179","resolution":{"observed_at":"2026-05-23T10:15:35.137396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"875dbbb1-a3e7-4b87-b24b-1dcbf6118b4b","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:4944ca5adc604f70ec8d90a5962bcdf17515619a79ff092fd78f0a0f71f29570","observation_id":"5a6904fe-a0b4-4518-926a-eae343cdfe66","resolution":{"observed_at":"2026-05-23T10:15:35.164873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"d51c86e6-76b4-4335-a262-d8c8191b0703","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:2404811bbf5c2b1a487edc18f74153fe63883d1384fc1b8b523389747d287a66","observation_id":"1799fb6c-4c69-406f-b1fb-4ecbbb84451a","resolution":{"observed_at":"2026-05-23T10:15:35.117840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"e89f5cb6-3025-4937-b743-0a42d1cca32e","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:d470c24db6fb89be824d6fe7b39052e76c33ca5e449be8bc97722f168a7d7c3f","observation_id":"4548b092-ce36-4d26-b213-33c366d47726","resolution":{"observed_at":"2026-05-23T10:15:35.101860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"and Kindermans, Pieter-Jan and Ying, Chris and Le, Quoc V","venue":null,"work_id":"89b75cb3-6f02-443b-bc7c-b42194136a53","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:a4d9a25d38fd538421d7fde1de955cc916a5d12b133d1516df93be102f5f1809","observation_id":"653ba075-7f0f-47d4-b1b7-665cad87d501","resolution":{"observed_at":"2026-05-23T10:15:35.120963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":null,"venue":null,"work_id":"dfcf7b78-608a-4f5d-8a5f-d49038affbd1","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:aa1be32761551f0ebe9759e0f6cfc534be0f33d8f13f17e5d0f364ba81b87a4b","observation_id":"109b704d-5ee9-4ba5-b5d5-92b219032506","resolution":{"observed_at":"2026-05-23T10:15:35.089396Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"International Conference on Learning Representations , year=","venue":null,"work_id":"18a32160-2adf-4327-97bf-65d77e8996af","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:00d00a5823abe33ac7d56f7862889ba974dbe6043323cea0777d78a60046ac8e","observation_id":"801420e9-4156-4725-b6c5-5c10fea83aa5","resolution":{"observed_at":"2026-05-23T10:15:35.173940Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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 Alignment Property of","venue":null,"work_id":"795023ce-1ff6-48b4-bd61-e44cbce0eb65","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:d510c5069a76188f7ffdbc37355d683b98d731ac876c49ae60e21b610fc02583","observation_id":"e6088551-f5e2-4476-ac69-8567d38b3082","resolution":{"observed_at":"2026-05-23T10:15:35.177007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Conference on Learning Theory , year=","venue":null,"work_id":"93bd7688-efda-449e-af31-ac1ed9fd4f23","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:b249152f0cbb963c31666385ee317445dfde50a55aae6ff92487135338315ff2","observation_id":"9ceca384-b229-4473-910c-332a767f015c","resolution":{"observed_at":"2026-05-23T10:15:35.080889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"booktitle=","venue":null,"work_id":"f1de3606-e70b-4483-a5ff-47f1cb2dec58","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:c4c6cb8c15b409b31691d7424b50d4928b35bf28e9823c87b77639ea11b98190","observation_id":"eb1267ce-f8ce-4fed-b487-87126628db33","resolution":{"observed_at":"2026-05-23T10:15:35.086673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Conference on Learning Theory , year=","venue":null,"work_id":"f3215a89-5acf-4fd9-8757-e72379df420f","year":null},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:49997817ceca196692f5ab62e6a86e70859c65a0ce63c3fe4bc8269397ed327d","observation_id":"14b43559-cc02-4bb4-bb3a-25d791007329","resolution":{"observed_at":"2026-05-23T10:15:35.095521Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Second-order regression models exhibit progressive sharpening to the edge of stability","venue":null,"work_id":"12dfb878-2df9-4406-b7a0-bc8741a8fc3c","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:f0e8c238f8204fd2e32604797871ad6dfb73dd1e09dcbd60ec45120c7628cf2c","observation_id":"a821f550-4380-4fc1-aa9d-a6c9d5afcd75","resolution":{"observed_at":"2026-05-23T10:15:35.092550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Andreyev and P","venue":null,"work_id":"af7ed644-7e86-4e01-a74f-e242f870a134","year":2025},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:d1481e5762e8d73181635ba4a0837cbf94447ff7551a84602ba1520c856aa69a","observation_id":"58bd7b13-7180-4238-967c-449948770604","resolution":{"observed_at":"2026-05-23T10:15:35.071101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Understanding gradient descent on the edge of stability in deep learning","venue":null,"work_id":"5134fd7a-4627-4ec4-8cf5-b76533e3d9e0","year":2022},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:576fcb7f216bd69edab6003470aa17c307a9213b6ff4bb1c62aa8e0923f9df96","observation_id":"b564e747-4112-4647-aa42-2f014099cc46","resolution":{"observed_at":"2026-05-23T10:15:35.074295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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 edge of stability via two-step gradient updates","venue":null,"work_id":"890daa51-895f-4c1a-af31-bd9ec23af799","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:1e8fa2b18d0487858b0c145c5a1d41b6d32f14ba0135c8327f40087bf9e7981b","observation_id":"63ac7944-1a52-4c11-ad6f-fc1bb886b089","resolution":{"observed_at":"2026-05-23T10:15:35.068209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Cohen, Simran Kaur, Yuanzhi Li, J","venue":null,"work_id":"7431cba0-f5d5-45f7-804f-f2a4ea62bf32","year":2021},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:9a5445799b28e7d4801969026468b518be21f286c858491987fb19de43c0241a","observation_id":"be9fb18d-25ef-4692-8da8-2e933847dc00","resolution":{"observed_at":"2026-05-23T10:15:35.077561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":null,"venue":null,"work_id":"27bbebc3-b71d-46e5-9a76-78885adcf19a","year":2021},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:a90d2f05b33689a9142c98076f9d8727a040288bc8ec3f78c697468441750ba5","observation_id":"bd2aee80-71cd-4918-a189-10fefb970181","resolution":{"observed_at":"2026-05-23T10:15:35.083802Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Lee, and Mahdi Soltanolkotabi","venue":null,"work_id":"749dd0e6-9e8c-42d2-8e42-40a2155b6c19","year":2022},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:9d69e8ff195ebcb35d7bd0f9237f50876dc96889118fe685fdb497df03a5c7c4","observation_id":"f2de42b8-6cff-43d2-9535-5d5ae4af7a16","resolution":{"observed_at":"2026-05-23T10:15:35.110842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":null,"venue":null,"work_id":"11120db2-2fe6-44ce-b2bd-16a835671a40","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:19c73fa89921587fa3c8e5fd49c829254b514f702dea6443e90d3a0a80c373a4","observation_id":"1de146f3-1456-41ba-901e-109082e5c128","resolution":{"observed_at":"2026-05-23T10:15:35.014893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"HaoChen, Colin Wei, Jason D","venue":null,"work_id":"78340352-dc99-4f52-84bb-1554fb78be4c","year":2021},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:b05fd4df55728c050ba0d73832ac34424ff8e733553daba02e6c6b75970534f9","observation_id":"d5d993b4-891e-4c8e-8d09-2fa28189de52","resolution":{"observed_at":"2026-05-23T10:15:35.152553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Jastrzebski, Z","venue":null,"work_id":"d5cd0b7c-9a0b-4a6c-bf34-f78c9f1dcc78","year":2019},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:45ba07f10a6ccd4044b221a28b8978ce16d204496fc007a0e6dd4b7ba0cb1ac2","observation_id":"1b859ee3-eada-4f76-9919-45ff1f0d1955","resolution":{"observed_at":"2026-05-23T10:15:35.114008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Jastrzebski, M","venue":null,"work_id":"030c58da-2203-48ec-b61b-f2918ec1d776","year":2020},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:ef85d6e7151f0c95bf52705ff01fd24f9542d2014e41204bd3f08e666ca18de6","observation_id":"e1179f28-8816-4949-a50f-4582765e82d3","resolution":{"observed_at":"2026-05-23T10:15:35.186177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Universal sharpness dynamics in neural network training: Fixed point analysis, edge of stability, and route to chaos","venue":null,"work_id":"cf7716fe-1aeb-4010-adf6-1e2b8b9d82f6","year":2025},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:b169f7181383682294d1896272d1178c5e165ed4fefa8266986354b17a2c650d","observation_id":"88cfc3a3-dea4-4925-8284-11843791eaef","resolution":{"observed_at":"2026-05-23T10:15:35.180329Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"On large-batch training for deep learning: Generalization gap and sharp minima","venue":null,"work_id":"f491dfb4-2c7e-41f0-8abd-be92f9f60259","year":2017},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:4c2ec548be6d5d8772d3ea1c6db8a16414c2ab17d7a9ea586bc0d33c9a1464d6","observation_id":"83aa0659-97f4-41b2-9066-6fa0d1212646","resolution":{"observed_at":"2026-05-23T10:15:35.098764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Gradient descent monotonically decreases the sharpness of gradient flow solutions in scalar networks and beyond","venue":null,"work_id":"7f37b293-5e65-4391-8a85-7212f5082b79","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:ab465e3892a5938f2a7663e98a8d474d63e4c8e76a6f1219d516e4c92f2a5743","observation_id":"e986661e-6ff0-4307-84d6-e49d20e77b3f","resolution":{"observed_at":"2026-05-23T10:15:35.124619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Lee and C","venue":null,"work_id":"014573b9-d9a0-4e44-9646-c032d3ae8121","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:f7120d829269acbf34355f70a8f76d02e337d963fef224107069a7da93b434ca","observation_id":"26f31801-a862-496d-96c2-204a5054a8ef","resolution":{"observed_at":"2026-05-23T10:15:35.023676Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.02218","last_updated":"2020-03-04T17:52:48Z","snapshot_observed_at":"2026-07-06T09:02:13.895931Z","submitted_at":"2020-03-04T17:52:48Z","title":"The large learning rate phase of deep learning: the catapult mechanism","version":1},"cited_work":{"arxiv_id":"2003.02218","doi":"10.48550/arxiv.2003.02218","metadata_source":"arxiv_reference","pith_arxiv_id":"2003.02218","snapshot_observed_at":"2026-07-10T06:15:00.866473Z","title":"The large learning rate phase of deep learning: the catapult mechanism","venue":null,"work_id":"fdbcc7a5-2170-42dd-8424-9e228495e447","year":2003},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"cited_paper":"/paper/2003.02218","citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:11f22687d1dae9194150235db325662aa5c29b410adbb23b621e1670fe32409e","observation_id":"9602fa3f-807d-4725-8944-0d29c099e53f","resolution":{"observed_at":"2026-05-10T00:59:49.391917Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-07-12T15:49:36.486557+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-12T15:49:36.486557+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Analyzing sharpness along GD trajectory: Progressive sharpening and edge of stability","venue":null,"work_id":"198b6eb4-4b63-494f-84a1-ad590bec3563","year":2022},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:afcddb77960780b4483eb9fdc177f6a0bf79e13f5718cf430fea9b6080bea890","observation_id":"95ffec57-bff2-4431-b369-3720767ecc73","resolution":{"observed_at":"2026-05-23T10:15:35.026790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1711.04623","last_updated":"2018-09-13T09:29:55Z","snapshot_observed_at":"2026-07-06T06:09:11.794595Z","submitted_at":"2017-11-13T15:11:56Z","title":"Three Factors Influencing Minima in SGD","version":3},"cited_work":{"arxiv_id":"1711.04623","doi":"10.48550/arxiv.1711.04623","metadata_source":"pith","pith_arxiv_id":"1711.04623","snapshot_observed_at":"2026-07-10T16:57:24.468717Z","title":"Three Factors Influencing Minima in SGD","venue":"cs.LG","work_id":"bcb52129-9115-4696-8926-64f96214f2d7","year":2017},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"cited_paper":"/paper/1711.04623","citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:a5793516f680b3b06d53c7e9b2bcd275428456b8515b63d9b8490957cd50f1c3","observation_id":"1f026e50-cb93-46d8-8429-b78e026193e7","resolution":{"observed_at":"2026-05-10T00:59:49.389404Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Smith, Benoit Dherin, David G","venue":null,"work_id":"059b5f2c-70b0-4804-bfb4-ada6e7fbd3e3","year":2021},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:e6440f9f7a7d108662d7bdbdc7f23124a82591604d2718b76816efb971880fce","observation_id":"09dc5c1f-f1f0-4f20-a5cd-eead84560c02","resolution":{"observed_at":"2026-05-23T10:15:35.048469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.17087","last_updated":"2023-12-12T04:06:02Z","snapshot_observed_at":"2026-07-06T16:38:40.508335Z","submitted_at":"2023-10-26T01:11:17Z","title":"Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult","version":2},"cited_work":{"arxiv_id":"2310.17087","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2310.17087","snapshot_observed_at":"2026-07-04T10:29:44.310723Z","title":"Good regularity creates large learning rate implicit biases: Edge of stability, balancing, and catapult","venue":null,"work_id":"1ea835e1-042f-42b1-acd6-8993e1039c6d","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"cited_paper":"/paper/2310.17087","citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:87531d7d4827e2a64cca0647fce22021ecadf86a2b0463365b69bdfdf2b1c2c8","observation_id":"760370c7-c22e-4d3b-a6eb-91ffca46d8d3","resolution":{"observed_at":"2026-05-10T00:59:49.384394Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"How SGD selects the global minima in over-parameterized learning: A dynamical stability perspective","venue":null,"work_id":"c50586e0-8f0b-4b10-a3f4-aba4c280652f","year":2018},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:b531986947b9a5e98fc2915cb2dbb1de90fe16cae315cf7f1363b528fa0494dd","observation_id":"47d59210-4e14-4d25-9076-735073415b9f","resolution":{"observed_at":"2026-05-23T10:15:35.055479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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 alignment property of SGD noise and how it helps select flat minima: A stability analysis","venue":null,"work_id":"caacbb3b-57d2-4fb6-a3c4-1ecfdf2958db","year":2022},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:d5dadb743bb70b5a5d9021c5bdd60e48c7fff87a7ca4a32acebb34dca1a82e0b","observation_id":"ce3a09dd-b434-4bc0-87ee-c7f800a65a4c","resolution":{"observed_at":"2026-05-23T10:15:35.061870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.08770","last_updated":"2018-05-30T01:15:02Z","snapshot_observed_at":"2026-07-06T06:25:07.039294Z","submitted_at":"2018-02-24T00:21:10Z","title":"A Walk with SGD","version":4},"cited_work":{"arxiv_id":"1802.08770","doi":"10.48550/arxiv.1802.08770","metadata_source":"pith","pith_arxiv_id":"1802.08770","snapshot_observed_at":"2026-07-10T06:15:00.866473Z","title":"A Walk with SGD","venue":"stat.ML","work_id":"77c1a49f-6cfe-422a-89dc-9367d48e9815","year":2018},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"cited_paper":"/paper/1802.08770","citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:1731d5d1c7144d44a278b1afdd9e37fb844deb052d5df3eec34596f979909f5b","observation_id":"cd6791f9-7f3d-40cf-a996-be2b876c1f3a","resolution":{"observed_at":"2026-05-10T00:59:49.386911Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"Understanding edge-of-stability training dynamics with a minimalist example","venue":null,"work_id":"293e47e7-429a-4dcf-88d5-8110db240304","year":2023},"citing_paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-05-10T00:59:39.800662Z"},"links":{"citing_paper":"/paper/2604.21016"},"observation_digest":"sha256:28282b1aedcbc187231f626f02c8f98b993544f22b247e4df4b65a82daae7a41","observation_id":"726548bc-f875-4514-822f-4a8d8789a653","resolution":{"observed_at":"2026-05-23T10:15:35.011864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.21016","last_updated":"2026-04-22T19:02:52Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-22T19:02:52Z","title":"SGD at the Edge of Stability: The Stochastic Sharpness Gap"},"reference_resolution":{"displayed":62,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":5,"verified_fuzzy":53},"total_outbound_references":62},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 1 inbound Pith citation observation for arXiv:2604.21016."}