{"as_of":"2026-08-13T06:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1597197c62f9472f0f6d1b0eae7582b7f60ebac8de59c4e23d013806fc38e949","coverage":[{"denominator":127,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:16:51.615837Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.00640/citation-record","integrity":"/paper/2412.00640/integrity","json":"/paper/2412.00640/citation-record.json","paper":"/paper/2412.00640"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.204216Z","title":"Deep residual learning for image recognition,","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.204216Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:df38bb625f28468a492edcdd3f62e6bac826d7c0f2f79aed88859bbb7fe0a361","observation_id":"19036b5b-88f1-437f-b84f-444520c83231","resolution":{"observed_at":"2026-08-12T05:16:51.204216Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.11929","last_updated":"2021-06-03T13:08:56Z","snapshot_observed_at":"2026-08-13T02:40:23.887636Z","submitted_at":"2020-10-22T17:55:59Z","title":"An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.11929","snapshot_observed_at":"2026-08-12T05:16:51.209208Z","title":"An image is worth 16x16 words: Transformers for image recogni- tion at scale,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.209208Z"},"links":{"cited_paper":"/paper/2010.11929","citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:15ac0bb56d6ae1cd94f7290bb168d201d70a5058886e07d0b9f1cdeaf1e3ab68","observation_id":"a5b88654-b3d4-4418-aa93-562a9f5f1484","resolution":{"observed_at":"2026-08-12T05:16:51.209208Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.213917Z","title":"Attention is all you need,","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.213917Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:c131860ed382aa3e3b9b6d6f7a39a4b088fa1649697f5e19b977e877ce70f6a9","observation_id":"4e1744ad-40cc-4c72-b7a2-027899f04278","resolution":{"observed_at":"2026-08-12T05:16:51.213917Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.04805","last_updated":"2019-05-24T20:37:26Z","snapshot_observed_at":"2026-07-30T09:12:38.100527Z","submitted_at":"2018-10-11T00:50:01Z","title":"BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.04805","snapshot_observed_at":"2026-08-12T05:16:51.218715Z","title":"Bert: Pre-training of deep bidirec- tional transformers for language understanding,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.218715Z"},"links":{"cited_paper":"/paper/1810.04805","citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:a10f700b51b3476a93582fa40283db25137a4a7554230ddbb5773fcd430f005a","observation_id":"9ee2c497-c09d-46ef-80f9-ced8b8efafd4","resolution":{"observed_at":"2026-08-12T05:16:51.218715Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.223431Z","title":"Language models are few-shot learners,","venue":null,"work_id":null,"year":1901},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.223431Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:72138396925c7e4ef16738e9e352475697ffa65e571d8892f563a2c9ef2367c5","observation_id":"c52ee23f-1e4b-4c71-9d8e-3bae752951b6","resolution":{"observed_at":"2026-08-12T05:16:51.223431Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.227715Z","title":"High-resolution image synthesis with latent diffusion models,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.227715Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:af09540a18d9d6fa97393bd18afb9f637d290ceb57a8f51ebf40ec8dadb68f25","observation_id":"9ee684cf-b140-48f4-8e29-1ec0b6e7b883","resolution":{"observed_at":"2026-08-12T05:16:51.227715Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.232365Z","title":"A stochastic approximation method,","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.232365Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:ec68833096032bf46ba312ca77adbb4611ab1440edecfb125619e09f66394d12","observation_id":"71d64fba-6860-40c1-a6c8-93ed29e62348","resolution":{"observed_at":"2026-08-12T05:16:51.232365Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-12T05:16:51.236425Z","title":"Adam: A method for stochastic optimization,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.236425Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d64cc70675508bedc451db406d0a317658b29e12b84b329ad6a30fcd1043554a","observation_id":"3a5bd3a2-781e-403c-881d-a381c593348c","resolution":{"observed_at":"2026-08-12T05:16:51.236425Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.04747","last_updated":"2017-06-15T13:21:04Z","snapshot_observed_at":"2026-08-04T02:05:40.539691Z","submitted_at":"2016-09-15T17:32:34Z","title":"An overview of gradient descent optimization algorithms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.04747","snapshot_observed_at":"2026-08-12T05:16:51.241496Z","title":"An overview of gradient descent optimization algorithms,","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.241496Z"},"links":{"cited_paper":"/paper/1609.04747","citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1629b6d5cb81cc426b376afcfcb93b1c228acc95c4ea0ee9e867da88cb525cce","observation_id":"c7a540bb-bf7b-435a-b265-b2d8bc99425c","resolution":{"observed_at":"2026-08-12T05:16:51.241496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.246398Z","title":"Large scale distributed deep networks,","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.246398Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:eeac92d594300d34a8d0b77e4a5f96bd2ced923c1fe2dbd5d23f565afd11c0a3","observation_id":"11fed02a-cc62-40c9-a390-d56d7425ea04","resolution":{"observed_at":"2026-08-12T05:16:51.246398Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.250264Z","title":"Problème général de la stabilité du mouvement,","venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.250264Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:69ee32bbd958d3f558ab480072fa0283323e430ac1a194242bdf8c60b249ce74","observation_id":"135f1662-ed9d-420d-aab6-17725ec68544","resolution":{"observed_at":"2026-08-12T05:16:51.250264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.254493Z","title":"Sastry, Nonlinear systems: analysis, stability, and control","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.254493Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:b7c492bafda91680aa9ab8d049711bd0d009993413a64fec7b4589c9f2e2b1f2","observation_id":"6f377155-eb90-433c-82b0-fff0de3ea398","resolution":{"observed_at":"2026-08-12T05:16:51.254493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.258660Z","title":"van den Dries, Tame topology and o-minimal structures","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.258660Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f5e401458d35bedb0a1fd251b97a009a479f510505ff3c7db384869e9547da37","observation_id":"88b54bc1-066c-4595-8178-5f6e730c50ff","resolution":{"observed_at":"2026-08-12T05:16:51.258660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.263132Z","title":"An invitation to tame optimization,","venue":null,"work_id":null,"year":1917},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.263132Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:4c43ca277213fedaeb7fcd4d589f7c730ec8bcaa7a2abf84df57b752a1db134f","observation_id":"59f497b6-a15c-4cb6-97c6-cab0ee5fe558","resolution":{"observed_at":"2026-08-12T05:16:51.263132Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.267480Z","title":"Subdifferentiability of real functions,","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.267480Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:5331a76b4967166bd59e9dd0bdb4bc7625716e5077aacda752b67da2b0a6714a","observation_id":"ece95287-38b6-40b3-b775-a9089d7fca31","resolution":{"observed_at":"2026-08-12T05:16:51.267480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.272377Z","title":"Friedman, T","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.272377Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:234834bc8d593d1a736fcea15fd8f2e0b9927a38a0e60aa0752f7d02ddf177c3","observation_id":"7d7c9330-3a56-4a34-94b0-080d9194e737","resolution":{"observed_at":"2026-08-12T05:16:51.272377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.277095Z","title":"Generalized gradients and applications,","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.277095Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:3afef053ea6f4b13233fd5035c4f11715ea2747705f70424becc33834f703ff7","observation_id":"f6297abd-f57f-4abd-9b11-a2fd99b0e07c","resolution":{"observed_at":"2026-08-12T05:16:51.277095Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.280937Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.280937Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:e9a9629d8c4a9e0682f9fba016869f266123568f5d04053c4f0ec31946daee6d","observation_id":"628442dd-8629-4f4d-b863-30ae7a371514","resolution":{"observed_at":"2026-08-12T05:16:51.280937Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.285002Z","title":"Aubin and A","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.285002Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:dd84c46c985b5ca22829b7f85d6e7388ef70adcaee8992c45a4f9549f8dfca13","observation_id":"4b078cea-09af-49bc-bc4c-bad8364039b0","resolution":{"observed_at":"2026-08-12T05:16:51.285002Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.289092Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.289092Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:9618328d3330f8bf80f03fbe5047baa32c6201fb5a4c3f0ee57a4333679b3fc6","observation_id":"6afe91ac-92e0-4106-b7a0-ea99504911fa","resolution":{"observed_at":"2026-08-12T05:16:51.289092Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.293034Z","title":"Remarks on Tarski’s problem concerning ( R,+,∗, exp),","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.293034Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:520239ac847af8221378704ff80ca4f51e87c45bfbe8ab12178b63029c5b0bea","observation_id":"9c5d8914-aacf-4af3-87b9-e424448ea161","resolution":{"observed_at":"2026-08-12T05:16:51.293034Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.296675Z","title":"Definable sets in ordered structures. i,","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.296675Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:cd2ec76628e0d92c35c17734ba73c8de96bb445710b221b73e30cb8126470b8a","observation_id":"5e6b472e-31f7-43da-a3b8-4024ed23e3ea","resolution":{"observed_at":"2026-08-12T05:16:51.296675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.300804Z","title":"Bochnak, M","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.300804Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:04cb88aeb7f48d0256126b517a1ca262e270d04db5209e370578335a6e4d150f","observation_id":"03832b93-4e37-4ffd-8d7b-b5e11fa7ae1c","resolution":{"observed_at":"2026-08-12T05:16:51.300804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.304585Z","title":"Geometric categories and o-minimal structures,","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.304585Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:993b24b38428ef1ee74f95b449b26e2611ebedc18f3d75d04e4177efa277303f","observation_id":"6fa5d605-a8b6-4e15-a70d-fab7b4883b6f","resolution":{"observed_at":"2026-08-12T05:16:51.304585Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.308346Z","title":"Division d’une distribution par une fonction analytique de variables réelles,","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.308346Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:19ca14bb9032558eb8b786b862d56c4cad0cdf5218c871895befc9f378a585cd","observation_id":"8cc7df9f-67c9-493a-b2c4-a419980eacfc","resolution":{"observed_at":"2026-08-12T05:16:51.308346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.312083Z","title":"Sur le problème de la division,","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.312083Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f5181d6ce5951b710e1cb28cc10bf5b1b72d0dd25a627b045eb0e52d3609eb8b","observation_id":"1055d010-da91-42ff-8f9d-d9abec382680","resolution":{"observed_at":"2026-08-12T05:16:51.312083Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.315770Z","title":"On the division of distributions by polynomials,","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.315770Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:47bafc2541a4491dd508a640f43ba200d2f9e8ec6afdbe1535498b8fb2060763","observation_id":"cd46f27d-25d6-4402-9c7a-2e6c042cb24a","resolution":{"observed_at":"2026-08-12T05:16:51.315770Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.320098Z","title":"On gradients of functions definable in o-minimal structures,","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.320098Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:e29ffd7d2afc1cf0446580d2362ab1812b9628475a5b68541e3d5112494021ed","observation_id":"dc4b9d73-287c-4af2-a600-9a0466b31f97","resolution":{"observed_at":"2026-08-12T05:16:51.320098Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.324022Z","title":"Clarke subgradients of stratifiable func- tions,","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.324022Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1108333117601899bece38bd896dd9247cf389f39a0a153e1785c083b392e433","observation_id":"0e8d202e-fdd8-46d6-a33f-7a68c6bd621c","resolution":{"observed_at":"2026-08-12T05:16:51.324022Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.328191Z","title":"Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka- Łojasiewicz inequality,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.328191Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:e2b9f2bd8087b27248517665825f30834cb32bcf927187e3ad4e20623c062310","observation_id":"37d06759-92c3-41ba-a156-6aa1659d1457","resolution":{"observed_at":"2026-08-12T05:16:51.328191Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.332194Z","title":"Global convergence of the gradient method for functions definable in o-minimal structures,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.332194Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d8e5058a4a94b30f4b8ce3562b8fb76dd978f68c09d2de43e0d4f463627e2ac6","observation_id":"697c654a-dd46-4ab4-9f85-51148f4c24d4","resolution":{"observed_at":"2026-08-12T05:16:51.332194Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.336104Z","title":"Curves of descent,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.336104Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:6c0a225a44325ad8aab9934f4efa318ac5c03e96b9c991446cdf902ba4f7393d","observation_id":"d667e5ce-180f-4aff-a2bd-7804d1f3dfbc","resolution":{"observed_at":"2026-08-12T05:16:51.336104Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.340235Z","title":"Stochastic subgradient method converges on tame functions,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.340235Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:46c15188bfcc8ade84074d901bd5685fdb1ffc900b6d03084162c19ea130d8c2","observation_id":"778f5260-7ed1-4982-a40f-5935467e61cb","resolution":{"observed_at":"2026-08-12T05:16:51.340235Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.344320Z","title":"Optimization methods for large-scale machine learning,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.344320Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:7af327f695d2b9a934c7fcdcfd475bd261601b6a713e9abf7cfcbdbae05a88ef","observation_id":"3182ff22-64b8-4215-9856-c8155e8bf5fd","resolution":{"observed_at":"2026-08-12T05:16:51.344320Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.348233Z","title":"Nonconvex Robust Low-Rank Matrix Recov- ery,","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.348233Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:8d8fa5778a9667ec69c4f6ce62da7e94ae181b9d7eac87a814aba2c0da0fe24d","observation_id":"4230129d-424e-4ac6-b199-69ac9246f672","resolution":{"observed_at":"2026-08-12T05:16:51.348233Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.352732Z","title":"Global convergence of sub-gradient method for robust matrix re- covery: Small initialization, noisy measurements, and over-parameterization,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.352732Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:c1dd80f786ec9ec528ba5852a60b3f61522f6b9e65de8d601a393ec3501c5e98","observation_id":"1e80e234-3ee9-419d-8d1e-c8465ce40ce6","resolution":{"observed_at":"2026-08-12T05:16:51.352732Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.356432Z","title":"Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.356432Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:bf93da88cc6476fef9e886698364affebcaac2089ea10c523bce1c0244ddf437","observation_id":"a30bb061-1dd6-4754-8d0f-5a6feba7491c","resolution":{"observed_at":"2026-08-12T05:16:51.356432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.360376Z","title":"Deep learning,","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.360376Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:09724a00f1e8c038a3fd974b5a30b208535c7a046cd1c06b231e923e5734b860","observation_id":"b830bace-8b40-41e8-8f9e-01b2289c3b1c","resolution":{"observed_at":"2026-08-12T05:16:51.360376Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.364142Z","title":"Sur l’Equation à l’Aide de Laquelle on Détermine les Inégalités Sécu- laires,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.364142Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1a07e17f9eff128cc7838d0b765737e662127d81bf15eb06e6f4fec66ae0c3fc","observation_id":"1483b8ef-053c-4973-94b6-ae4b9bb012c7","resolution":{"observed_at":"2026-08-12T05:16:51.364142Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.368029Z","title":"Continuous time analysis of momentum methods,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.368029Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:925559c4fbc044244f9701dcbc713dc3b00601d73beb5af8c600affe015e4cab","observation_id":"b5a55893-8d6b-48c9-98d3-1290ff43e7ed","resolution":{"observed_at":"2026-08-12T05:16:51.368029Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.371779Z","title":"Some methods of speeding up the convergence of iteration methods,","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.371779Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:bb2b041a33a0e08bf456dae45088be882b16686551ddb877161cfcc6bbd96471","observation_id":"fefa8cc5-9c9b-422e-8c57-50ed28b0721f","resolution":{"observed_at":"2026-08-12T05:16:51.371779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.375887Z","title":"Nesterov, Lectures on Convex Optimization","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.375887Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:fe261095bce73c271e9830f310062a125d8186c5674e166c85919962ef712c15","observation_id":"05fe9f29-8e1b-47d9-bb09-9b0a3189dd0f","resolution":{"observed_at":"2026-08-12T05:16:51.375887Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.380428Z","title":"Shor, “Application of the gradient method for the solution of network transportation problems","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.380428Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:40a8c588226ed35e4e8d03fc46eb588155f2ca3a9e5f5152cd828597007125b0","observation_id":"46c16fe8-8847-4399-8824-07bc42e09435","resolution":{"observed_at":"2026-08-12T05:16:51.380428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.385183Z","title":"On the structure of algorithms for numerical solution of problems of optimal planning and design,","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.385183Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f27087b085660bbbbae4d97dcbd2f6f398b7f2d72ec694a9fb2f6d27385bdb32","observation_id":"6e97949e-7543-4ac0-9366-956e877e680f","resolution":{"observed_at":"2026-08-12T05:16:51.385183Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.388986Z","title":"Bertsekas, Convex optimization algorithms","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.388986Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:b3dfc00468ed77def07263ec94c50e2e1a3db23eb68fde8610c5eb771740a3ba","observation_id":"7b4c0c11-94c1-4ecc-81ce-a063a51747ef","resolution":{"observed_at":"2026-08-12T05:16:51.388986Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.392841Z","title":"A method for solving the convex programming problem with convergence rate𝑂(1/𝑘2),","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.392841Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:5aa8981182a1d64c69d24bff21849425bed17c53704907411e5c2828a0f8163b","observation_id":"5b2e4baf-8c10-4f37-8bc6-94a6f8dcf9be","resolution":{"observed_at":"2026-08-12T05:16:51.392841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.396773Z","title":"Heavy-ball method in nonconvex optimization problems,","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.396773Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:b242b137f19c71b6cb753edcff876ef5c1b52ec6ece2fa248850c60dbab8a337","observation_id":"2dcba610-29f9-470f-8b44-eed03b43b32a","resolution":{"observed_at":"2026-08-12T05:16:51.396773Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.400475Z","title":"iPiano: Inertial proximal algorithm for nonconvex optimization,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.400475Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:ea62e5da6d8e4387c1109066b147d22bf60d1be4c83c3bb2d7d615e570b74324","observation_id":"6ffc5ce9-5187-4ede-8c6a-c021182acdd5","resolution":{"observed_at":"2026-08-12T05:16:51.400475Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.404343Z","title":"Adaptive switching circuits,","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.404343Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d7ea87482cf7c6f565d9bb4d5d97dae76a13e9c361ad9488c9fe1239b9f94790","observation_id":"548c0008-4c01-4100-86a8-99198f92d062","resolution":{"observed_at":"2026-08-12T05:16:51.404343Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.408391Z","title":"An adaptive associative memory principle,","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.408391Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:4778e118b85f20237f33915f91a90401053afadcc73a7a2d9d7bda0e8f6b8ec5","observation_id":"3e2d3ecd-907e-4407-8245-5f2feb281c0f","resolution":{"observed_at":"2026-08-12T05:16:51.408391Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.412414Z","title":"On the convergence of the lms algorithm with adaptive learning rate for linear feedforward networks,","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.412414Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:b60a455c0c37021a8cfb35742c8a544f00d10fdc355db73c04f7c524f6c99036","observation_id":"9cc9c2c8-e1b7-4233-a943-26050beb3053","resolution":{"observed_at":"2026-08-12T05:16:51.412414Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.778526Z","title":"Incremental subgradient methods for nondifferentiable op- timization,","venue":null,"work_id":"fa5aaedd-7cc8-43fb-8f06-3f59c9683736","year":2001},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.416492Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:4e5bbbdd856034325819f98412c127f41b902b7eebd647144eb904c76e32cab3","observation_id":"ab4c409b-bde4-42fe-a8e3-57ad00ccc6b5","resolution":{"observed_at":"2026-08-12T05:16:52.783361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.765798Z","title":"Incremental gradient, subgradient, and proximal methods for convex optimization: A survey,","venue":null,"work_id":"38b51630-6c97-451c-8ec9-086a42d8f0c3","year":2010},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.420722Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:3e228116d79ec3ae4f44aaf87a2ec4836b7d012da06a3863dfa6a67353ae516d","observation_id":"34bccf6f-d277-4bb3-a5d8-08365965e127","resolution":{"observed_at":"2026-08-12T05:16:52.770022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.751978Z","title":"Why random reshuffling beats stochas- tic gradient descent,","venue":null,"work_id":"0e530d2e-c0b0-4de7-9a19-6c109d17a45d","year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.424868Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1220d19618482a0a6330c47bc7ac7e682900efbebca26fe64f650d3845d9b219","observation_id":"03213abb-66cf-462a-9daa-e647449597de","resolution":{"observed_at":"2026-08-12T05:16:52.756710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.739427Z","title":"Random reshuffling: Simple analysis with vast improvements,","venue":null,"work_id":"f8cc2761-a028-4793-b32c-42fb236494f7","year":2020},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.429666Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:489f6020cacf5bb806928f19038ea3fa2308cab878fbda01e1e59cdea887d4fd","observation_id":"e0752615-e712-4016-b399-e8a7670b8e44","resolution":{"observed_at":"2026-08-12T05:16:52.744034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.725551Z","title":"A unified convergence analysis for shuffling-type gradient methods,","venue":null,"work_id":"61dc3c06-08f9-42a9-b233-84f576e4dcdd","year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.434017Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:5eb29d56ed9d769f86296cf3c9e5b71761aa13eed5f508bd976f28bf97712d82","observation_id":"d7394bbf-1201-4da1-b651-f9a58ef4b1a2","resolution":{"observed_at":"2026-08-12T05:16:52.730757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.711592Z","title":"Incremental without replacement sampling in nonconvex optimization,","venue":null,"work_id":"5e272180-9cbd-489b-920e-f21195c91bdf","year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.438257Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:0287d7717e415a4b1ace1ada38a4c5d8a0dd774b99ded3b2da72a5bea1aa9ee5","observation_id":"3bbb68e2-8ada-49ba-a1bf-7c3cb38a5024","resolution":{"observed_at":"2026-08-12T05:16:52.717673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.698449Z","title":"Convergence of random reshuffling under the kurdyka– łojasiewicz inequality,","venue":null,"work_id":"a5546ca6-2561-4866-ad8c-8ada7bea9269","year":2023},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.442080Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:4bad4283114a1204e858c98ae822c09b475f0d082713122859fdb21a48094137","observation_id":"26378519-a92e-4eb8-9183-fc29caefc2c5","resolution":{"observed_at":"2026-08-12T05:16:52.703477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.683483Z","title":"On the importance of initialization and momentum in deep learning,","venue":null,"work_id":"9d308c13-91a6-4095-b2cc-013aae9672fc","year":2013},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.446635Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f264e564c567019548887848e1e09d71a8c8f5d01ce6b7287c6384b9251f1a1e","observation_id":"d9df9354-bfd2-4adb-bfa1-4bab71707da7","resolution":{"observed_at":"2026-08-12T05:16:52.688758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.670156Z","title":"Smg: A shuffling gradient-based method with momentum,","venue":null,"work_id":"2cb43682-cf6b-4670-a1b5-7b48fe504761","year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.451803Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:a076697d7f6dd4d61f3177db7f746f6919f5dafd55520d1277641734bee7d306","observation_id":"75cb68f0-a135-462a-9a98-caf37fe6db32","resolution":{"observed_at":"2026-08-12T05:16:52.675207Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.656039Z","title":"Nesterov accelerated shuffling gradi- ent method for convex optimization,","venue":null,"work_id":"4322393c-5b91-4d49-901d-a59d44d3c1ae","year":2022},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.455588Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:ed1f3715234414d7f400aeb15ca04cc6dd07ef48c646042546d2ed6ac7ffb762","observation_id":"cc11de64-e0c3-4517-ae2c-03607392b732","resolution":{"observed_at":"2026-08-12T05:16:52.660715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.643902Z","title":"Coordinate descent algorithms,","venue":null,"work_id":"b387de38-bf6d-4d7f-bfb8-b230e451655e","year":2015},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.459541Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:ddf8b20ab37cf3d7705161682d4bbca8d9f657b00d32fa7cc08341eaa41b08a2","observation_id":"26b2e51a-86ea-4ff9-9480-969112904ec7","resolution":{"observed_at":"2026-08-12T05:16:52.648016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.631256Z","title":null,"venue":null,"work_id":"80ee9aff-a66f-4f81-9529-43ed8c117e9e","year":1970},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.464335Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d183d4aa70bb41bfe34ba59c16e251bdff51f55cf73c0113c70f4a91e01db09c","observation_id":"b22dffe7-49a9-46bc-a16d-e5e1b052b7a2","resolution":{"observed_at":"2026-08-12T05:16:52.635925Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.619136Z","title":"On the convergence of the coordinate descent method for convex differentiable minimization,","venue":null,"work_id":"1704fb80-f32e-40ad-921c-ec26eddca27d","year":1992},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.468188Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:bca8433462827f77d02909d43cce69493aaf8f30a684beaa60c90b53d4df2723","observation_id":"a033e2d7-f5e8-492b-9279-a947915cd8ec","resolution":{"observed_at":"2026-08-12T05:16:52.623479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.607077Z","title":"Efficiency of coordinate descent methods on huge-scale optimization prob- lems,","venue":null,"work_id":"852865a1-421b-4235-9b73-9a07e1e836e4","year":2012},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.472352Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:0e1b74b7ff8ecd358c5ed9763407cb3f29276f8cb9bf8b20544bdf16427a407c","observation_id":"f4e401ee-4b6a-4cd5-bd6c-9bca75b94be9","resolution":{"observed_at":"2026-08-12T05:16:52.611539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.594209Z","title":"Randomness and per- mutations in coordinate descent methods,","venue":null,"work_id":"26fcbf6e-fae0-4897-8096-e525e44bbb75","year":2020},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.476349Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:9837bef650d969cb332c16328e708c1a6f44bb518480be58b33a6338e82d363c","observation_id":"99a53ffb-f590-42ef-810b-a5139fc34e8f","resolution":{"observed_at":"2026-08-12T05:16:52.598895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.580860Z","title":"On the convergence of block coordinate descent type meth- ods,","venue":null,"work_id":"b4a49f79-a6b7-42b6-b845-89ed206b61be","year":2013},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.480626Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:ee71a02df665d8d159a31cafecac8f1439db676d2e0fd569e0592619e5002480","observation_id":"64bb4810-13b5-4867-8301-63d4df30f919","resolution":{"observed_at":"2026-08-12T05:16:52.585422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.566605Z","title":"Random permutations fix a worst case for cyclic coordinate descent,","venue":null,"work_id":"0323bdc9-f824-4e04-8e5f-4c72e932ec77","year":2019},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.484519Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:8739948ff2049daa3421009ab9229c7d21c2a1eb5ff019e2a7793cd4005f8786","observation_id":"d0c95008-0ae3-4afb-8d4e-bdaab0c619f4","resolution":{"observed_at":"2026-08-12T05:16:52.571651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.551508Z","title":"Euler, Institutiones calculi integralis","venue":null,"work_id":"8542bded-b078-4598-9d4d-b32f6501b44d","year":null},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.488124Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1e3ced7ed909c861ff1d48b2caf2ba99f43fb256e4b7862480f7415e3933d64b","observation_id":"ecfd80f7-e3d6-4aa7-9567-4b88545d7ac3","resolution":{"observed_at":"2026-08-12T05:16:52.557217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.538352Z","title":"Blanton, Foundations of Differential Calculus","venue":null,"work_id":"058042ad-f949-4b77-a1f0-1596cb75b865","year":2006},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.492744Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:29244b90cce004a06e3a1ee038c30c7e1d749454d65806cfacdbfc22bbf3c54d","observation_id":"15bf9183-b95b-4d1d-bb99-52d2312744b7","resolution":{"observed_at":"2026-08-12T05:16:52.543294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.526043Z","title":null,"venue":null,"work_id":"ad650aee-13c4-4153-b299-15acbc50da4a","year":1955},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.496494Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:8be7a198915ef4c0291e2b36f2569ac3698b63b980c6e3c598a166343b8891d2","observation_id":"03ccd5b5-0f87-4fb9-915d-b611fc0007b1","resolution":{"observed_at":"2026-08-12T05:16:52.530348Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.511152Z","title":"Analysis of recursive stochastic algorithms,","venue":null,"work_id":"f28d150e-1f62-4398-91ad-65aeab3c2ee2","year":1977},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.500912Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:cf5fe5312cf29fce73059966610874491d6865baafdeb672d68cb441c09fe45b","observation_id":"108a98fe-153f-4884-80d6-8e042783788c","resolution":{"observed_at":"2026-08-12T05:16:52.515805Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.496348Z","title":"General convergence results for stochastic approximations via weak con- vergence theory,","venue":null,"work_id":"1ac031fc-3f25-4bab-9f8a-accc62e9a7d5","year":1977},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.505584Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:6c1f61bc3e3169fbf237de07a0443682f76724dd30b5d906efc9a04927d0c5ed","observation_id":"8bf377a1-275a-4260-b088-25119eb26aa1","resolution":{"observed_at":"2026-08-12T05:16:52.500949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.482848Z","title":"Convergence of recursive adaptive and identification procedures via weak convergence theory,","venue":null,"work_id":"07be5ff5-925c-42c6-97a8-c870dd56f823","year":1977},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.509569Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f55d7cd3be4a0b9e3743e4a5dee18d8b4a1fc05ff675d470a1aba708ed165811","observation_id":"3b50eef9-e457-45b1-b373-e82dc28ab35e","resolution":{"observed_at":"2026-08-12T05:16:52.488368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.470215Z","title":"Stochastic approximations and differential inclu- sions,","venue":null,"work_id":"8c0289b3-2a6e-44ec-af72-358d7b048f91","year":2005},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.513574Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:0172eae3c86db4ee47ec07b697717311431ed4a6300825b557f974f1f51fe465","observation_id":"7e38ce05-1188-44ef-9974-53dbe10c003c","resolution":{"observed_at":"2026-08-12T05:16:52.474584Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.456357Z","title":"Stochastic approximations and differential inclu- sions, part ii: Applications,","venue":null,"work_id":"01468b79-f78d-4451-9b70-b651d9bea647","year":2006},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.517914Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:c2d9e3f67091099cfae075087b147c4ecba457724bde5fefb4e763b95c5ed5b8","observation_id":"59138bed-64d9-4829-b95e-47c1609c4efd","resolution":{"observed_at":"2026-08-12T05:16:52.461670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.443357Z","title":"Dynamics of stochastic approximation algorithms,","venue":null,"work_id":"1257c1b5-f4ef-431a-97cc-0e16f85f3777","year":2006},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.521920Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:808982160cc7452251bb249ff117c1bbf35bf0dcd2faf97d871d36d7dea9a2d9","observation_id":"1a7cbc52-e390-4965-8cbd-8c5b814fa7eb","resolution":{"observed_at":"2026-08-12T05:16:52.447968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.525669Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.525669Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:98cfccaebffea75264b57b55e803e002802caef7629d19142778a86df724f437","observation_id":"557c7be8-ec6c-4e78-b819-4c0e0ee09115","resolution":{"observed_at":"2026-08-12T05:16:51.525669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.421577Z","title":"Stochastic methods for composite and weakly convex optimiza- tion problems,","venue":null,"work_id":"2cc64d2e-ccd7-4b29-b151-30d1c1727035","year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.529511Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:255c98d96ad61ef60edac3edd0ff13cca0d8f053405a9ec2e5ed201eead72608","observation_id":"203578d7-d059-4124-8971-5bc6158153f7","resolution":{"observed_at":"2026-08-12T05:16:52.426792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.407191Z","title":"Conservative set valued fields, automatic differentiation, stochas- tic gradient methods and deep learning,","venue":null,"work_id":"85d9bc8c-8d0b-42ac-b359-c3f157ceb7c7","year":2020},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.533377Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:a0637af1b37092d0b0ef9279ac05949fe9c91c53e71188d39a61f3658cadb3c2","observation_id":"f1509e88-a81a-4538-804c-259868866651","resolution":{"observed_at":"2026-08-12T05:16:52.411712Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.393366Z","title":"Random monotone operators and application to stochastic optimization,","venue":null,"work_id":"2991d582-4bcc-41b8-8f73-5cf37d01a07e","year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.537241Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d9d74f5ad209a97caf2ecbc30839dc9a6c3b126e72f3cc06ff6e025914813ad2","observation_id":"5ae65100-fd7c-44e5-b7c6-c6a0abcb0099","resolution":{"observed_at":"2026-08-12T05:16:52.398569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.379982Z","title":"Adam-family methods for nonsmooth optimiza- tion with convergence guarantees,","venue":null,"work_id":"2e5287f7-d266-415a-b6bd-d6c37e19dcc8","year":2024},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.541127Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f5d2c4560add5e392ea5cbe114ed22401042cc36241c1ad5491b2d8dfbb0e24c","observation_id":"d61b1c1d-086d-4b00-b916-22df139f6527","resolution":{"observed_at":"2026-08-12T05:16:52.385015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.365480Z","title":"Global stability of first-order methods for coercive tame functions,","venue":null,"work_id":"56cef1a4-d809-4c95-b27e-dd35b8959c50","year":2023},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.544823Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:92115f0bdaf00ab6c5792b68e63d24e81a47ae699dc8e2e90bd2fc89c89127cf","observation_id":"fc8e26db-f23d-4a13-8222-3a08e52bc7c6","resolution":{"observed_at":"2026-08-12T05:16:52.370272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.352792Z","title":"Converging multistep methods for initial value problems involving multival- ued maps,","venue":null,"work_id":"1e1c4fc0-62b3-48a2-8926-34e06fd76241","year":1981},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.548833Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:d12774406293b4899d86f627dec584a7381b38ed883c6868c5dd9811bd6827c2","observation_id":"9afd5c15-5abc-44fb-aa51-55b585b8ef21","resolution":{"observed_at":"2026-08-12T05:16:52.357041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:51.552713Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.552713Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:93f1bd6df59c2d9091b3d5f4e2cdb4f15c42ebb4f5d75024af18f997912d66e0","observation_id":"152df49c-cc30-4820-87a7-d6e75d19754f","resolution":{"observed_at":"2026-08-12T05:16:51.552713Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.330502Z","title":"Difference methods for differential inclusions: A survey,","venue":null,"work_id":"eafee3ac-9c79-4726-b067-34d3878a29db","year":1992},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.557092Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:7eb1385560102b5bb93820d80070aa508cded27b94ec6dbade80b8d9a9a6f931","observation_id":"1c1d6405-3fc7-4e64-bc4d-240aa15a5c81","resolution":{"observed_at":"2026-08-12T05:16:52.335758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.317508Z","title":"Subgradient methods for sharp weakly convex functions,","venue":null,"work_id":"9242f76c-0f86-40f3-aae6-d0269a691efd","year":2018},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.561198Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:753cb1ca6e8cd6585bda713b32bc97767d791ed8d72792bf2cf000012561d15a","observation_id":"97fffbd4-23d8-46db-880b-e1ee78d5d189","resolution":{"observed_at":"2026-08-12T05:16:52.321997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1907.09547","last_updated":"2019-07-22T19:52:11Z","snapshot_observed_at":"2026-07-06T08:09:25.854208Z","submitted_at":"2019-07-22T19:52:11Z","title":"Stochastic algorithms with geometric step decay converge linearly on sharp functions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.09547","snapshot_observed_at":"2026-08-12T05:16:51.565603Z","title":"Stochastic algorithms with geometric step decay converge linearly on sharp functions,","venue":null,"work_id":null,"year":1907},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.565603Z"},"links":{"cited_paper":"/paper/1907.09547","citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:1120af4fc656bde54b65bfcf036f0475cefba89ba8c638ce89fd7e17ec9d1d6d","observation_id":"9419fa9c-b992-4c3a-b35d-359ed505e719","resolution":{"observed_at":"2026-08-12T05:16:51.565603Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.303347Z","title":"Low-rank matrix recovery with composite optimization: Good conditioning and rapid convergence,","venue":null,"work_id":"c881143c-3deb-4fb0-b9f9-a3c444bbe022","year":2021},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.570033Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:a59c014b3879ca5c0027ca1f5395f538dc424f9052d4de5c36a5f20764cadc2e","observation_id":"26d2bdc3-07dc-4a23-a5f7-43c65b0f89b1","resolution":{"observed_at":"2026-08-12T05:16:52.307778Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.290586Z","title":"On the stable equilibrium points of gradient systems,","venue":null,"work_id":"959d9673-9333-45d2-8371-c2478fa4f07d","year":2006},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.573677Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:7895d508e558803cd14d2abe6e51058b013df99dcd67f1d32962aa6254ff6fe5","observation_id":"b986769d-3694-48bb-b65c-f1bca667af78","resolution":{"observed_at":"2026-08-12T05:16:52.294794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.278302Z","title":"Favorable classes of lipschitz continuous functions in subgradient opti- mization,","venue":null,"work_id":"a53b8368-ed03-41ba-bf56-1fe9e9e40018","year":1981},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.578345Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:169ae65935c0d5db1bf177846f874fe327dc6aca8c5bd6e13aa153b6947ce0cb","observation_id":"34ad5a8e-4c8f-462e-a909-864e4eabdb75","resolution":{"observed_at":"2026-08-12T05:16:52.282704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.266003Z","title":"Generic differentiability of lipschitzian functions,","venue":null,"work_id":"810a0695-e61a-48f0-abc9-a4556518a4a0","year":1979},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.582464Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:219256b4dba1b8226f7fb13f80304da5649f52bbd6fb423c5479e94767a8fdd6","observation_id":"f6ab1e0e-9687-4416-b42b-4be5e1562c96","resolution":{"observed_at":"2026-08-12T05:16:52.270680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.253577Z","title":"Convergence of the iterates of descent methods for analytic cost functions,","venue":null,"work_id":"b1c94948-118a-419d-acf9-d46d19f84b6b","year":2005},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.586493Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:67ef70aba65fdae3140370f3a6cca2ef8dac8441ebef31de41ae552290eeca6f","observation_id":"ab375fe1-0222-42cd-9081-177a62a43f99","resolution":{"observed_at":"2026-08-12T05:16:52.257876Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.240358Z","title":"Abadi et al","venue":null,"work_id":"50bd4196-cee1-4915-b967-744a7512b0b0","year":2015},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.590443Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:f7815c7c1e96430aecb8a8a5d9186ae52c367eebcbbfd7be5e2f66ebafcc8519","observation_id":"0f0a5b31-ff8f-4cce-9784-158a246934e7","resolution":{"observed_at":"2026-08-12T05:16:52.244737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.226160Z","title":"Pytorch: An imperative style, high-performance deep learning library,","venue":null,"work_id":"dd619d9b-1cbe-4906-abf3-00f211347fca","year":2019},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.594666Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:b2e1885280fcd90d3f2ef2401165508859dcbc2ec4ee4e347c20cb57e3701107","observation_id":"46348cf6-6adc-4282-a49d-515336733d57","resolution":{"observed_at":"2026-08-12T05:16:52.230859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.211879Z","title":"A simple weight decay can improve generalization,","venue":null,"work_id":"0294a005-3d52-4a21-bf15-300c34dba0ae","year":1991},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.598653Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:a9b444fbbf2dd1f10c54d79b8f1bc5275c491ecd2e8fee40b365051f436c57a8","observation_id":"ff5cf138-5746-49b1-adbf-0754d51c379e","resolution":{"observed_at":"2026-08-12T05:16:52.216737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.196042Z","title":"Regression shrinkage and selection via the lasso,","venue":null,"work_id":"3f9b96a7-ca1c-4194-bfaa-b919b8e94a38","year":1996},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.602958Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:c79649278527603f4c5b91f86f6bbeeabf612ab7890224917fe7cd8ce1de144a","observation_id":"cc54ec23-6046-4d70-9b4c-37e1e2885a6b","resolution":{"observed_at":"2026-08-12T05:16:52.201723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.183737Z","title":"Matrix Completion has No Spurious Local Minimum,","venue":null,"work_id":"7baf8e10-172f-4eef-8e43-3250c9c3c640","year":2016},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.607696Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:df9585f58bab1a645f5982546f68bff3d3a2e154fe2c3b5f329b228b81eb8418","observation_id":"bc081d89-66ae-4624-8e1a-2f01495fc42e","resolution":{"observed_at":"2026-08-12T05:16:52.188076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.171236Z","title":"Beck, First-order methods in optimization","venue":null,"work_id":"dae837ee-84f2-47d5-8fef-a84cd4a77f50","year":2017},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.611688Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:58dff00f17230e5f6a5e84dcc9643647d6afbb7a50292bdb75171b68af7c5595","observation_id":"bcc4f8ca-460b-491a-934d-1792aaebaba8","resolution":{"observed_at":"2026-08-12T05:16:52.176160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T05:16:52.159368Z","title":null,"venue":null,"work_id":"f0ec93d2-0604-4b50-9c11-d373692c30c1","year":1961},"citing_paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-12T05:16:51.615837Z"},"links":{"citing_paper":"/paper/2412.00640"},"observation_digest":"sha256:549f3d87f4823037ebfab8f25d5cc209b56756690277de5d94953894bda91596","observation_id":"5f52bec6-236f-4ec4-9cf3-29fd2bcb42a0","resolution":{"observed_at":"2026-08-12T05:16:52.163537Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.00640","last_updated":"2024-12-01T01:39:57Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-13T01:04:21.122503Z","submitted_at":"2024-12-01T01:39:57Z","title":"Stability of first-order methods in tame optimization"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":57,"verified_exact":0,"verified_fuzzy":43},"total_outbound_references":127},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 100 of 127 outbound references and 0 inbound Pith citation observations for arXiv:2412.00640."}