{"as_of":"2026-08-09T16:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5cde0b4a78f16805ef21700f9f82df3894a31d33811ea8e5d0a975022b210400","coverage":[{"denominator":81,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":81,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T11:35:29.806274Z","state":"measured"},{"denominator":91,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":91,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":10,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:58:33.061678Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T18:35:00.445011Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-08-07T10:58:33.061678Z","title":"Sign operator for coping with heavy-tailed noise: High probability convergence bounds with extensions to distributed optimization and comparison oracle","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.04192","last_updated":"2026-07-24T19:09:15Z","snapshot_observed_at":"2026-08-07T10:43:49.592801Z","submitted_at":"2025-06-04T17:39:03Z","title":"Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise","version":3},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-07T10:58:33.061678Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2506.04192"},"observation_digest":"sha256:deecf3c87dcd50d8c511e89159ec0f0519c54324c34b669b3598fd2ffc66e823","observation_id":"41278835-c0fe-4962-a92b-2995e3d0bccf","resolution":{"observed_at":"2026-08-07T10:58:33.061678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-08-04T13:25:35.179592Z","title":"Sign operator for coping with heavy-tailed noise: High probability convergence bounds with extensions to distributed optimization and comparison oracle,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.01377","last_updated":"2026-06-02T08:11:16Z","snapshot_observed_at":"2026-08-06T12:50:41.925411Z","submitted_at":"2025-10-01T19:06:11Z","title":"DeMuon: A Decentralized Muon for Matrix Optimization over Graphs","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T13:25:35.179592Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2510.01377"},"observation_digest":"sha256:8fb4c47110f74b1e3d1d386ba6dd9e01b7239ec7b286b48c928170d25d33bef5","observation_id":"83ee6a9a-555b-4756-86a6-a4dc4ed8ff14","resolution":{"observed_at":"2026-08-04T13:25:35.179592Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2510.06141","last_updated":"2026-05-21T09:57:40Z","snapshot_observed_at":"2026-07-06T22:31:58.848080Z","submitted_at":"2025-10-07T17:15:08Z","title":"High-Probability Convergence Guarantees of Decentralized SGD","version":5},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-18T08:45:22.688243Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2510.06141"},"observation_digest":"sha256:b6a66f7f9862dd8789f672874d32f0738f6a6609a89f24126ad3554928c5bc4d","observation_id":"00cb11f9-5f97-4833-bcff-81ab23f36baa","resolution":{"observed_at":"2026-05-18T08:46:07.850453Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2510.06141","last_updated":"2026-05-21T09:57:40Z","snapshot_observed_at":"2026-07-06T22:31:58.848080Z","submitted_at":"2025-10-07T17:15:08Z","title":"High-Probability Convergence Guarantees of Decentralized SGD","version":6},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-22T13:14:57.263058Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2510.06141"},"observation_digest":"sha256:d621612df2c6eb17fa5042046458ca741af4ad302d4a0f65911d399c7c7bcfe8","observation_id":"3f9ef3d5-de1e-4104-b448-5afd608f8b19","resolution":{"observed_at":"2026-05-22T13:16:34.998210Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-08-03T04:20:57.128342Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.05657","last_updated":"2026-06-03T15:56:31Z","snapshot_observed_at":"2026-08-08T23:26:40.576564Z","submitted_at":"2026-02-05T13:41:13Z","title":"Tight Long-Term Tail Decay of (Clipped) SGD in Non-Convex Optimization","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T04:20:57.128342Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2602.05657"},"observation_digest":"sha256:bad14aecde4cb90e52c81f207deed61b8648ecf95d85822434304735af0ee5af","observation_id":"366e9823-8238-435f-9bdf-87946c3be793","resolution":{"observed_at":"2026-08-03T04:20:57.128342Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2605.06615","last_updated":"2026-05-07T17:32:09Z","snapshot_observed_at":"2026-07-06T23:19:05.764765Z","submitted_at":"2026-05-07T17:32:09Z","title":"When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\\ell_1$-norm Lower Bounds","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-08T12:14:28.866499Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2605.06615"},"observation_digest":"sha256:5ab1878ac068971da3131cd84aa7e7172dbbcc44b9e022341bed2b2dd3bc41b3","observation_id":"a9057654-2d38-4ed0-9665-bec19aa20f2d","resolution":{"observed_at":"2026-05-11T19:21:07.726962Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2605.11850","last_updated":"2026-05-12T09:36:13Z","snapshot_observed_at":"2026-08-02T13:15:16.257288Z","submitted_at":"2026-05-12T09:36:13Z","title":"Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-13T05:34:48.195468Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2605.11850"},"observation_digest":"sha256:43d13f842f6859eb7aa6429997c7e2d82c7bce47e6d09c99811984fa9d1777f2","observation_id":"a8c23f07-80d2-4090-8c92-0253f030f253","resolution":{"observed_at":"2026-05-13T05:37:19.221765Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2605.19811","last_updated":"2026-06-21T10:26:37Z","snapshot_observed_at":"2026-07-06T23:30:30.141040Z","submitted_at":"2026-05-19T13:07:59Z","title":"LionMuon: Alternating Spectral and Sign Descent for Efficient Training","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-20T07:24:55.516803Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2605.19811"},"observation_digest":"sha256:0cd476344b286dc1e5f470a160703647e18ef82a8656f819c2ec3391ab8f1a15","observation_id":"11a0073c-9ee4-4515-b0a2-51e645e29b91","resolution":{"observed_at":"2026-05-20T07:28:06.839931Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2605.19811","last_updated":"2026-06-21T10:26:37Z","snapshot_observed_at":"2026-07-06T23:30:30.141040Z","submitted_at":"2026-05-19T13:07:59Z","title":"LionMuon: Alternating Spectral and Sign Descent for Efficient Training","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-30T18:30:51.719396Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2605.19811"},"observation_digest":"sha256:fe77d071b444fdc4d305bd7e88eab80e7517caa1691d86455a6318d0c2aafdbf","observation_id":"dc04b226-d658-48f2-94b7-b5215330ee41","resolution":{"observed_at":"2026-06-30T18:35:00.446615Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"cited_work":{"arxiv_id":"2502.07923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2502.07923","snapshot_observed_at":"2026-06-30T18:35:00.445011Z","title":"Sign Operator for Coping with Heavy-Tailed Noise: High Probability Convergence Bounds with Exten- sions to Distributed Optimization and Comparison Oracle","venue":null,"work_id":"d76b17d4-35ea-4b8b-856b-fe7f8be5ba81","year":2025},"citing_paper":{"arxiv_id":"2605.31371","last_updated":"2026-05-29T14:41:36Z","snapshot_observed_at":"2026-08-07T08:56:05.149276Z","submitted_at":"2026-05-29T14:41:36Z","title":"Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-28T22:51:38.488754Z"},"links":{"cited_paper":"/paper/2502.07923","citing_paper":"/paper/2605.31371"},"observation_digest":"sha256:126898c707147682bd828f0b1211d879347e91ed84e7429600a978772c567ea6","observation_id":"aac7424a-6135-467e-995e-1fcd0a569ad4","resolution":{"observed_at":"2026-06-28T22:52:44.819197Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2502.07923/citation-record","integrity":"/paper/2502.07923/integrity","json":"/paper/2502.07923/citation-record.json","paper":"/paper/2502.07923"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T11:35:29.559732Z","title":"Differentially private learning with adaptive clipping","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.559732Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1e99087a870ebe237bf40d721edc35ec83c67d65df0183ed80c5915f4d931957","observation_id":"e8933ab5-e7d3-4e6b-b6e0-6039b12e426f","resolution":{"observed_at":"2026-08-08T11:35:29.559732Z","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":"2026-08-08T11:35:29.564005Z","title":"Lower bounds for non-convex stochastic optimization","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.564005Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:4263aa239e2089875ea9a609a4c7ee80e4ef74225f9d58eb2f34c703bdc6b70e","observation_id":"58a0fa68-50e3-4201-a9cb-06ae3765bd3e","resolution":{"observed_at":"2026-08-08T11:35:29.564005Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.18784","last_updated":"2024-05-01T02:30:23Z","snapshot_observed_at":"2026-08-09T14:45:19.700634Z","submitted_at":"2023-10-28T18:53:41Z","title":"High-probability Convergence Bounds for Nonlinear Stochastic Gradient Descent Under Heavy-tailed Noise","version":7},"cited_work":{"arxiv_id":"2310.18784","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.18784","snapshot_observed_at":"2026-08-08T11:35:29.993878Z","title":"High-probability Convergence Bounds for Nonlinear Stochastic Gradient Descent Under Heavy-tailed Noise","venue":"cs.LG","work_id":"fa2ee8aa-87dc-4f11-b625-a70cb0b64c0d","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.568099Z"},"links":{"cited_paper":"/paper/2310.18784","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:291c3f809e2133b3c3f3d2800f104afdbddb1fd47ace056c0d677e950a0c8615","observation_id":"ee542676-78ba-4ff9-8502-06b959be78f0","resolution":{"observed_at":"2026-08-08T11:35:29.998575Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.15637","last_updated":"2025-03-22T03:59:25Z","snapshot_observed_at":"2026-07-06T19:36:49.949466Z","submitted_at":"2024-10-21T04:50:57Z","title":"Large Deviation Upper Bounds and Improved MSE Rates of Nonlinear SGD: Heavy-tailed Noise and Power of Symmetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.15637","snapshot_observed_at":"2026-08-08T11:35:29.572008Z","title":"Large deviations and improved mean-squared error rates of nonlinear sgd: Heavy-tailed noise and power of symmetry","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.572008Z"},"links":{"cited_paper":"/paper/2410.15637","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:f4518f0b182b129b1374c64c736e49b1bdfe353cd59080c36f54c1700ff5e9f5","observation_id":"572cd5c0-e405-444e-b68b-2cfb0a13ded0","resolution":{"observed_at":"2026-08-08T11:35:29.572008Z","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":"2026-08-08T11:35:29.575843Z","title":"signsgd: Compressed optimisation for non-convex problems","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.575843Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:21d19c3ee7735345806ab8d3d7e9e79c8f8e0ba1ab5a475f88dee568f4a4cb3f","observation_id":"2fc48a6c-7a0b-4c1a-967f-c21f04b600af","resolution":{"observed_at":"2026-08-08T11:35:29.575843Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.05291","last_updated":"2019-02-22T19:55:48Z","snapshot_observed_at":"2026-07-06T07:07:34.689643Z","submitted_at":"2018-10-11T23:50:32Z","title":"signSGD with Majority Vote is Communication Efficient And Fault Tolerant","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.05291","snapshot_observed_at":"2026-08-08T11:35:29.579143Z","title":"signsgd with majority vote is communication efficient and fault tolerant","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.579143Z"},"links":{"cited_paper":"/paper/1810.05291","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:6fef8607bed3579a9f93cca202fec748cd00b18d16cc2bed5355621b2c2f306f","observation_id":"6b1e8e1e-9898-4952-ac4d-d6d078ec5b26","resolution":{"observed_at":"2026-08-08T11:35:29.579143Z","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":"2026-08-08T11:35:30.508720Z","title":"Stochastic gradient descent tricks","venue":null,"work_id":"0e9e3d39-cb46-40a4-bde2-e99326f8d810","year":2012},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.582860Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:7aa4f929d9d46cdda4d1c77ca8763efb055f66d7b81924b8481a41ff16170d0e","observation_id":"f97dab42-6112-42f8-8920-2f320cadcbe2","resolution":{"observed_at":"2026-08-08T11:35:30.511987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.498774Z","title":"Convex optimization","venue":null,"work_id":"68a6af1c-827a-4bad-af9c-1648f6ca60d4","year":2004},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.585980Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1460964905a80952da0b7f4880d93b8af4aae06ac2c5823e5694d92f7a0ab07d","observation_id":"be3fe7cc-b260-44da-9477-3ad46e72e5e7","resolution":{"observed_at":"2026-08-08T11:35:30.502917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.488849Z","title":"Libsvm: a library for support vector machines","venue":null,"work_id":"93281dfa-64eb-4b9c-a26d-aec5db6d4fba","year":2011},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.589252Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:bf9b4c82a5b51d37470374debc91ce1d0df6709d5c8b078cdfcd5b1fd897a06c","observation_id":"fab60b58-38e9-4657-903f-b26aa3b013ef","resolution":{"observed_at":"2026-08-08T11:35:30.492612Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.479534Z","title":"Understanding gradient clipping in private sgd: A geometric perspective","venue":null,"work_id":"5f3fb10e-9a70-40d5-abf4-15d2d087d49e","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.592303Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:27a2a23af36f73cad88150d3950f5eba9c93cc04e4334b5da67d797c22b3d6ec","observation_id":"ddcf3035-a74e-4c46-adf6-c2d3d578843d","resolution":{"observed_at":"2026-08-08T11:35:30.482865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.469953Z","title":"Generalized-smooth nonconvex op- timization is as efficient as smooth nonconvex optimization","venue":null,"work_id":"b94c0de8-36f6-4bd1-a153-5b26dd110049","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.595640Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:9c28c0a6f752dcb0585d6c16fc412a8905da2410fe793cc442a804696e935759","observation_id":"82ac2c21-be7c-477b-8c57-b59ad104d75d","resolution":{"observed_at":"2026-08-08T11:35:30.473653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.460145Z","title":"Optimal mean estimation without a variance","venue":null,"work_id":"dd71a79f-7136-4fc5-b782-c6dfebf63873","year":2022},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.599496Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:e6249c952411e87ba418b0b28bd25c2952e32c1bd6c9b3430093dc7228db92be","observation_id":"3d68cc4a-0b74-4fb3-aa08-7b4448e3adee","resolution":{"observed_at":"2026-08-08T11:35:30.463374Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.17009","last_updated":"2025-02-28T00:12:11Z","snapshot_observed_at":"2026-08-07T17:53:46.721072Z","submitted_at":"2025-02-24T09:39:17Z","title":"Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs","version":2},"cited_work":{"arxiv_id":"2502.17009","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.17009","snapshot_observed_at":"2026-08-08T11:35:29.965694Z","title":"Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs","venue":"cs.LG","work_id":"81fc1987-d30d-43b5-974c-65a461b1db53","year":2025},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.602604Z"},"links":{"cited_paper":"/paper/2502.17009","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:72ebf14371ef54c2cf4933955827c02633621da81ff6c95d869dec3d6cacea0e","observation_id":"99cd7cb5-4417-45a4-a0d7-9eb503ac8961","resolution":{"observed_at":"2026-08-08T11:35:29.969935Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.15958","last_updated":"2025-03-10T23:28:01Z","snapshot_observed_at":"2026-07-06T19:56:12.654263Z","submitted_at":"2024-11-24T19:07:31Z","title":"Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15958","snapshot_observed_at":"2026-08-08T11:35:29.606079Z","title":"Adaptive methods through the lens of sdes: Theoretical insights on the role of noise","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.606079Z"},"links":{"cited_paper":"/paper/2411.15958","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1e1bdf75655dfee68d09a9628264668985b9a68c778b6aab1ff74ab2992c4ee3","observation_id":"160b0a5a-5451-4262-976f-343d284dff67","resolution":{"observed_at":"2026-08-08T11:35:29.606079Z","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":"2026-08-08T11:35:30.448933Z","title":"Complexity lower bounds of adaptive gradient algorithms for non-convex stochastic optimization under relaxed smoothness, 2025","venue":null,"work_id":"e6a124d0-1016-4ec9-ba3d-eef324ae2a5a","year":2025},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.609675Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:b1092284e8fa4855f89fa2f31d48aee8d73e298965dd97c1c0f639c5ba59d602","observation_id":"4e72220c-993f-4772-9b93-649cc8a786a5","resolution":{"observed_at":"2026-08-08T11:35:30.452870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.438199Z","title":"Robustness to unbounded smoothness of generalized signsgd","venue":null,"work_id":"2a27da12-4522-4815-a317-e16aa22e0002","year":2022},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.612704Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1b6c3a99a49143c87052a0f34fe521b9fe56c891b89fcec1716abd936015778b","observation_id":"45ce3836-4636-4cdc-8e6c-490727c64d40","resolution":{"observed_at":"2026-08-08T11:35:30.442320Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.429109Z","title":"Momentum improves normalized sgd","venue":null,"work_id":"479e00f1-7d3c-4c3d-9865-bcffb9841e7a","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.615983Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:9bf926b4c6f8eb4fddf698d7d3f41aad17cdbbee54920b971a733a76e89e7bd3","observation_id":"a29ec436-39cc-4bfb-b6ad-ed121065a7bf","resolution":{"observed_at":"2026-08-08T11:35:30.432366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.419728Z","title":"High-probability bounds for non-convex stochastic opti- mization with heavy tails","venue":null,"work_id":"74a4c487-c05a-4464-a636-368e4b4fcc6c","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.619002Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:dbc03e5dda42b4347a80fcd2a64c3f57a6923da008fc7c3b42c291284e3581ce","observation_id":"18f7d251-39df-48e0-87b4-284284319bc1","resolution":{"observed_at":"2026-08-08T11:35:30.423130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.410333Z","title":"From low probability to high confidence in stochastic convex optimization","venue":null,"work_id":"4e8e8fe0-7afe-4032-81f7-695df56e37c8","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.622211Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:bbf67ec89a6fb590cc5cae3b3e67baa8127cead8b646d7d4bb734e30cb9b3a5a","observation_id":"eefcf3c0-d753-4807-8b95-7ae83150bc5a","resolution":{"observed_at":"2026-08-08T11:35:30.413699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.401225Z","title":"The gauss–tchebyshev inequality for uni- modal distributions","venue":null,"work_id":"6e26a023-7772-44e6-aaca-5d96345b5bad","year":1986},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.625108Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:657b16b1b4fa2b507b30d633dcb24a809440473b76594b52c374ed38a3d269f8","observation_id":"b4e99507-b3f1-4b93-881d-b17c158d1b5e","resolution":{"observed_at":"2026-08-08T11:35:30.404532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.628012Z","title":"Switch transformers: Scaling to trillion parameter models with simple and efficient sparsity","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.628012Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:26c3bd50a6fdc377f6bbc99d6995fb46df7bdd836d4d7a3eaf8f4b7afd2cf513","observation_id":"05ecdf65-b00f-45d2-bcb8-7303182d3ece","resolution":{"observed_at":"2026-08-08T11:35:29.628012Z","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":"2026-08-08T11:35:30.386650Z","title":"Stochastic first-and zeroth-order methods for nonconvex stochastic programming","venue":null,"work_id":"7cc21e03-5de9-425b-ae58-3aa78aa2749a","year":2013},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.630943Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a4c70fa393195948e118cd9f80d427f96ee6764f2837532cb949735c7935965f","observation_id":"17f8e85c-702f-49c6-a56a-7f11a7a45f2c","resolution":{"observed_at":"2026-08-08T11:35:30.390023Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.376911Z","title":"A nearly optimal single loop algorithm for stochastic bilevel optimization under unbounded smoothness","venue":null,"work_id":"4ee60b70-48d3-4afa-a6fe-dd0e9c990530","year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.633647Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a6dcbfbc4fcf80f3a4297519848ec73610d38a46b7c35eb91ecd1b77160a094b","observation_id":"e1c95593-97aa-4359-afdc-aff198f90dcf","resolution":{"observed_at":"2026-08-08T11:35:30.380409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.636582Z","title":"Deep learning","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.636582Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:2858f596f61bf4a746d59d1c766dcebfb4e6d868c89e8891f07b2f3868fdcb0a","observation_id":"663ebf67-f20f-4739-bb75-75d632ed4c0f","resolution":{"observed_at":"2026-08-08T11:35:29.636582Z","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":"2026-08-08T11:35:29.639519Z","title":"Stochastic optimization with heavy-tailed noise via accelerated gradient clipping.Advances in Neural Information Processing Systems, 33:15042–15053, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.639519Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:8e5c35cda64689d66ac4ee63c88155bc050c85968070c3201ea4f0c785c57b2f","observation_id":"a67727d9-e98d-4039-a728-7dbdbdca553d","resolution":{"observed_at":"2026-08-08T11:35:29.639519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.14989","last_updated":"2024-12-25T15:02:32Z","snapshot_observed_at":"2026-08-01T19:23:09.616554Z","submitted_at":"2024-09-23T13:11:37Z","title":"Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.14989","snapshot_observed_at":"2026-08-08T11:35:29.642173Z","title":"Methods for convex (l_0, l_1)-smooth optimization: Clipping, acceleration, and adaptivity","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.642173Z"},"links":{"cited_paper":"/paper/2409.14989","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:e5128bc288cba6708adcb82b4ed6a07289d0c1bc2b3f554b6ada3ba3bf20d909","observation_id":"a1f71baf-9fff-4f0d-9ee9-5b1bda34b963","resolution":{"observed_at":"2026-08-08T11:35:29.642173Z","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":"2026-08-08T11:35:30.355208Z","title":"The heavy-tail phenomenon in sgd","venue":null,"work_id":"c2dabab6-9e62-471f-ac90-fc0ec712becf","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.645478Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:90be59f0e81d6020cdfff9e6afde00d5bceeb3a18ed785df3ff2afeded366337","observation_id":"b9f54ba7-e408-45ab-a39f-e19c77899167","resolution":{"observed_at":"2026-08-08T11:35:30.358657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.345799Z","title":"Bilevel optimization under unbounded smoothness: A new algorithm and convergence analysis","venue":null,"work_id":"7158144b-6703-4563-884d-49360e919f48","year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.648224Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:bf7def5e7dc138718e05404756dd2d9f9f2fde6166a4afed05706f817003b829","observation_id":"bf6f42d5-9dc5-4876-9f6e-ab8124119487","resolution":{"observed_at":"2026-08-08T11:35:30.349201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.336358Z","title":"Beyond convexity: Stochastic quasi-convex optimization","venue":null,"work_id":"c9021866-ee88-4b64-a4c5-fb1fddcbb221","year":2015},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.651340Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:2cd46d98b592f399303aeb2f1ccb56959856a5af1bf8f7f6c38c340b200de7ba","observation_id":"62852387-2513-46d2-a83a-22189f814b4c","resolution":{"observed_at":"2026-08-08T11:35:30.339711Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.13849","last_updated":"2025-07-09T12:01:30Z","snapshot_observed_at":"2026-07-06T19:35:30.732080Z","submitted_at":"2024-10-17T17:59:01Z","title":"From Gradient Clipping to Normalization for Heavy Tailed SGD","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.13849","snapshot_observed_at":"2026-08-08T11:35:29.654217Z","title":"From gradient clipping to normalization for heavy tailed sgd","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.654217Z"},"links":{"cited_paper":"/paper/2410.13849","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:9795398ada18e58424fdf1f63381769b0436158c7b942759c8b733850bb03fa0","observation_id":"753df5e4-3ce7-4448-a215-f3f8b3a16286","resolution":{"observed_at":"2026-08-08T11:35:29.654217Z","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":"2026-08-08T11:35:30.326825Z","title":"Parameter-agnostic optimization under relaxed smoothness","venue":null,"work_id":"2a636e06-94f7-45eb-90c2-ee8af4324af0","year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.657215Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:04fb55f0e6f445e94161d33358dce10a49e0eb43786ade65ba2e3b7b3a783a80","observation_id":"f36c873f-a420-4696-ad68-ba357b994689","resolution":{"observed_at":"2026-08-08T11:35:30.330256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.317275Z","title":"Nonlinear gradient mappings and stochastic optimization: A general framework with applications to heavy-tail noise","venue":null,"work_id":"96cc9ec6-e937-4a19-9d90-5cdab379a79a","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.660050Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:c0f5b729c73261d37b3433b7408cfc90f8e959dd0a9d76817547faf8a1dd158b","observation_id":"7688429f-b71a-4e89-b4ab-0165f55e77d0","resolution":{"observed_at":"2026-08-08T11:35:30.320724Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.308372Z","title":"Non-convex distributionally robust optimization: Non-asymptotic analysis","venue":null,"work_id":"21528dd6-90a5-4709-8ca2-91a53efe5823","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.662983Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:d616bb3fb67f47973e07c0e5f06b531c9d42525af5303356ee15d3e554d6f050","observation_id":"4eb06c58-441d-4890-9870-f52cc63ba4aa","resolution":{"observed_at":"2026-08-08T11:35:30.311641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.10940","last_updated":"2021-09-27T21:16:21Z","snapshot_observed_at":"2026-08-09T16:30:02.185904Z","submitted_at":"2020-02-25T15:12:15Z","title":"Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.10940","snapshot_observed_at":"2026-08-08T11:35:29.665720Z","title":"Stochastic-sign sgd for federated learning with theoretical guarantees","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.665720Z"},"links":{"cited_paper":"/paper/2002.10940","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:68ce6980edf8f1ff876ffdeea0cfda1deb6cdd7d5e3ad6566ef11a2693523c0c","observation_id":"18de87ef-29fd-40ad-a805-85677420daf0","resolution":{"observed_at":"2026-08-08T11:35:29.665720Z","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":"2026-08-08T11:35:30.299122Z","title":"Learning from history for byzantine robust optimization","venue":null,"work_id":"aff0a135-3861-4d04-98f9-d28de4f2dbf8","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.669050Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:bc33cea694d0017df1b255a83abd8fbd3363447f30b7b88278e387ed8346d6f4","observation_id":"e01e336b-d4ef-4d02-813b-d2749555b291","resolution":{"observed_at":"2026-08-08T11:35:30.302706Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.671879Z","title":"Error feedback fixes signsgd and other gradient compression schemes","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.671879Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:784eeab9def8bceda88a51a92afc55a6e2c45b4f8d68125a55ac0e44ab1d9024","observation_id":"9afd8804-6d37-4290-8983-232d7b761f78","resolution":{"observed_at":"2026-08-08T11:35:29.671879Z","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":"2026-08-08T11:35:29.674918Z","title":"Adam: A method for stochastic optimization","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.674918Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:89326a67f3283bb344c8ff2cb8a020391309e12ca4d03d01ca5cf495cf27b2df","observation_id":"d71ba791-19e9-4ef4-b2a9-e3780723477c","resolution":{"observed_at":"2026-08-08T11:35:29.674918Z","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":"2026-08-08T11:35:30.282824Z","title":"Revisiting gradient clipping: Stochastic bias and tight convergence guarantees","venue":null,"work_id":"05f35c83-de33-4528-a9be-bb585b223fb4","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.678111Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:8c7ef08af4d42a7c110dd8c013b0d2cd38dccee0a3d387bdf2d783fa2bfd350f","observation_id":"d5517e50-1f3e-4f62-b653-ac073fa704a0","resolution":{"observed_at":"2026-08-08T11:35:30.286468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.272719Z","title":"Accelerated zeroth-order method for non-smooth stochastic convex optimization problem with infinite variance","venue":null,"work_id":"785f9954-a43d-43f5-9ac1-da3b65792a3e","year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.680972Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:5828db0907fd6517ee630ff244bc07741301d10598cafc2731fb6bb1fae8da30","observation_id":"0822eae1-6ac7-4492-bf48-004778eaa555","resolution":{"observed_at":"2026-08-08T11:35:30.276016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.263411Z","title":"Large-scale methods for distributionally robust optimization","venue":null,"work_id":"dfdf8845-8ce4-4fcf-b19a-ba2fb6eddbdb","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.683896Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:950c2555cd544ebdb78a21b1c853da7168af221907713cbd01156abed33dca07","observation_id":"f944eec7-1764-4229-a081-5d371f89945e","resolution":{"observed_at":"2026-08-08T11:35:30.266881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.253680Z","title":"Convex and non- convex optimization under generalized smoothness","venue":null,"work_id":"3df92efa-2663-42d2-8ab6-952f7b7eebfb","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.686595Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:26e19b8f7238828f5a798409ce7bbd6c9dd47ae92e49ce3edbdd33aaf0cd9bc8","observation_id":"7b79c360-516a-4881-9dec-bcd6537aafd9","resolution":{"observed_at":"2026-08-08T11:35:30.257029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.244011Z","title":"Convergence of adam under relaxed assumptions","venue":null,"work_id":"f5bc49ef-483d-47c4-9d1a-eb95f0ac6d64","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.689480Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:d57f7c141ed3bd24d218514ccec8d5be9430a1ea66c39858db7ab19c98eaed68","observation_id":"3256861c-0377-4058-8350-5ef35cc2fe8d","resolution":{"observed_at":"2026-08-08T11:35:30.247436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.14294","last_updated":"2020-07-28T15:06:22Z","snapshot_observed_at":"2026-08-09T12:38:45.647502Z","submitted_at":"2020-07-28T15:06:22Z","title":"A High Probability Analysis of Adaptive SGD with Momentum","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.14294","snapshot_observed_at":"2026-08-08T11:35:29.692489Z","title":"A high probability analysis of adaptive sgd with momentum","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.692489Z"},"links":{"cited_paper":"/paper/2007.14294","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:5e2254f18b7ca4995799d2110e2722ca3b7033bdff4e8df94452152da6453649","observation_id":"3bb1aab8-b3a4-46f1-98c3-aab8b62c63c6","resolution":{"observed_at":"2026-08-08T11:35:29.692489Z","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":"2026-08-08T11:35:30.233537Z","title":"Relora: High- rank training through low-rank updates","venue":null,"work_id":"5764db22-d1f0-4a21-ba48-a8abad3c12af","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.695566Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:4b917893deb985e8b405e66e5510f57efef09324718d7234e6c584bd8c201a89","observation_id":"a3506364-330b-4160-9517-6fda0f1d31f4","resolution":{"observed_at":"2026-08-08T11:35:30.237219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.223090Z","title":"Loss landscapes and optimization in over- parameterized non-linear systems and neural networks","venue":null,"work_id":"3d8e90d7-74ae-4b5a-ab4e-e040172dd744","year":2022},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.698479Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:64190cc9809126d1979f5663b18c39a81f885cdec9f7617680a8427ef978ec4f","observation_id":"5d939d75-a244-4364-afed-cac1e1ca9c83","resolution":{"observed_at":"2026-08-08T11:35:30.226988Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.213624Z","title":"A communication-efficient distributed gradient clipping algorithm for training deep neural networks","venue":null,"work_id":"89e716ca-7805-41ea-b518-4398cc06363d","year":2022},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.701274Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:28c308ad5fa6a0776c23852e82bd2555aea4b9ede5638915b5b7c445d80fdb73","observation_id":"72e43639-1328-4465-b050-4ad1898c8f66","resolution":{"observed_at":"2026-08-08T11:35:30.217153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.704203Z","title":"Pre-train, prompt, and predict: A systematic survey of prompting methods in natural language processing","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.704203Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:77a42070031add1c72a76a059b0dd42291205192e47e56ba28ab71bf8e9dd20e","observation_id":"e5befed6-959b-4ab2-995f-f62e2cafa272","resolution":{"observed_at":"2026-08-08T11:35:29.704203Z","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":"2026-08-08T11:35:30.198497Z","title":"Breaking the lower bound with (little) structure: Acceleration in non-convex stochastic optimization with heavy-tailed noise","venue":null,"work_id":"5c12cd97-be55-4e35-b72c-03fc284f78d3","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.706965Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:ad91def515bb55fab53671c4b7fa0ba722ab674db127d05df1ad822802d495d6","observation_id":"347903b2-c5a1-42f9-a247-07473692df39","resolution":{"observed_at":"2026-08-08T11:35:30.202021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1711.05101","last_updated":"2019-01-04T21:01:49Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2017-11-14T14:24:06Z","title":"Decoupled Weight Decay Regularization","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.05101","snapshot_observed_at":"2026-08-08T11:35:29.709724Z","title":"Decoupled weight decay regularization","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.709724Z"},"links":{"cited_paper":"/paper/1711.05101","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:c1e2d9d266ed63174853698a74a8a183ff9ed2a5779547ca2d6fe5ce52cf8a2d","observation_id":"d1b6af07-b2da-44e6-b3b1-5dc5c3eed863","resolution":{"observed_at":"2026-08-08T11:35:29.709724Z","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":"2026-08-08T11:35:30.188886Z","title":"Algorithms of robust stochastic optimization based on mirror descent method","venue":null,"work_id":"a06be50d-4f7b-4720-bff5-2d932349acb0","year":2019},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.712708Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:d25a11646c5caff1682b3c820c3ac1f487881379978ee0ea73ba7f2ff304d07c","observation_id":"67ccee8a-a559-4109-8bc7-32341e2eab7b","resolution":{"observed_at":"2026-08-08T11:35:30.192377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.715722Z","title":"Robust stochastic approximation approach to stochastic programming","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.715722Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:19b5cc61df327c2965d44fd1b18d439f76b69c3aded82fa9ba46ee49aeb9d523","observation_id":"e4a0229b-4e4f-4759-844d-14f1087c7a94","resolution":{"observed_at":"2026-08-08T11:35:29.715722Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.01119","last_updated":"2023-04-04T17:27:53Z","snapshot_observed_at":"2026-08-03T14:28:17.886291Z","submitted_at":"2023-04-03T16:34:11Z","title":"Improved Convergence in High Probability of Clipped Gradient Methods with Heavy Tails","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.01119","snapshot_observed_at":"2026-08-08T11:35:29.718613Z","title":"Improved convergence in high probability of clipped gradient methods with heavy tails","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.718613Z"},"links":{"cited_paper":"/paper/2304.01119","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a20ac2413dab7e7fa545c9473dac5d96d3b7af7fc01a4d6d761a2021c939ffe3","observation_id":"6eecd9a1-45f0-4d88-a812-2f4f22e93e26","resolution":{"observed_at":"2026-08-08T11:35:29.718613Z","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":"2026-08-08T11:35:30.173846Z","title":"On the difficulty of training recurrent neural networks","venue":null,"work_id":"691cbcc9-30d5-4d39-ade2-1a627be16132","year":2013},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.721699Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:65398c0b1a9c0723120645871035d1d5c9ce1f00273dffc3cc62017b2fae56fc","observation_id":"3479780a-6819-4597-bc19-63a9270eef81","resolution":{"observed_at":"2026-08-08T11:35:30.177253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.17557","last_updated":"2024-10-31T11:37:49Z","snapshot_observed_at":"2026-08-02T15:25:02.551919Z","submitted_at":"2024-06-25T13:50:56Z","title":"The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.17557","snapshot_observed_at":"2026-08-08T11:35:29.724539Z","title":"The fineweb datasets: Decanting the web for the finest text data at scale","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.724539Z"},"links":{"cited_paper":"/paper/2406.17557","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:7ee79924692590e4138c77ce3a563fd8ce8a3ec0bb9691baaa17666f234eb97d","observation_id":"02c4e61f-4206-422a-b764-0ea3d8a9373a","resolution":{"observed_at":"2026-08-08T11:35:29.724539Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-08T11:35:30.163754Z","title":"Breaking the heavy-tailed noise barrier in stochastic optimization problems","venue":null,"work_id":"3accbe59-7931-48f3-9860-1a22d9c00700","year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.727670Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1336f7d85b778c9f1583e4794d1133020c1b17a4dd779fadc84ca04d21c80392","observation_id":"966c5df5-6ca0-410f-b24d-a3476850d349","resolution":{"observed_at":"2026-08-08T11:35:30.167921Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.153955Z","title":"High probability convergence of clipped distributed dual averaging with heavy-tailed noises","venue":null,"work_id":"cd14b93c-d181-4228-9518-343af9460c18","year":2025},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.730417Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:241da28abe9ea9438d0818860deb7fcd4dce1680233a606f24e9b4cc9dad5ee6","observation_id":"c1a08760-a7ee-4e7a-b119-7652394c449f","resolution":{"observed_at":"2026-08-08T11:35:30.157530Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.733045Z","title":"Exploring the limits of transfer learning with a unified text-to-text transformer","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.733045Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:33457b0be90763ce7f6271d8f781a18f407b359a12c3fbbb29382dad12b7c8b8","observation_id":"a48f63fc-3f19-4bed-97ef-cb578f79e9f5","resolution":{"observed_at":"2026-08-08T11:35:29.733045Z","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":"2026-08-08T11:35:30.140105Z","title":"Variance-reduced clipping for non-convex optimization","venue":null,"work_id":"1f1a0c5d-6be8-4459-8e40-6f66f7575b1f","year":2025},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.735737Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:e2b21199a5c2e2fe2c92b30a715413d40706a8b91e866e9be98974ca7fc73ed0","observation_id":"2cafe87d-3759-4195-8127-657e2c5f32d2","resolution":{"observed_at":"2026-08-08T11:35:30.143278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.738584Z","title":"A stochastic approximation method","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.738584Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:f4a9c8fd88eff6fbd64d6d46a3444e3b2ea8b6c82196b73d7f9948f1e76cafa5","observation_id":"10fcf077-862e-47e0-b071-907eedfdae61","resolution":{"observed_at":"2026-08-08T11:35:29.738584Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.00999","last_updated":"2023-07-18T14:19:07Z","snapshot_observed_at":"2026-08-03T05:02:26.782826Z","submitted_at":"2023-02-02T10:37:23Z","title":"High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance","version":2},"cited_work":{"arxiv_id":"2302.00999","doi":null,"metadata_source":"pith","pith_arxiv_id":"2302.00999","snapshot_observed_at":"2026-08-08T11:35:29.882604Z","title":"High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance","venue":"math.OC","work_id":"db0b94a5-64a3-40ea-960f-eac4b1e6a509","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.741382Z"},"links":{"cited_paper":"/paper/2302.00999","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:789e6907ca906d9ed126dc635c0fba42f0e4dbf7959fbbdabc8df43053b01108","observation_id":"567073aa-8fd9-4f21-b7fa-90e1a2a21d72","resolution":{"observed_at":"2026-08-08T11:35:29.887783Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.124209Z","title":"Stochastic sign descent methods: New algorithms and better theory","venue":null,"work_id":"41e8cc2d-ed36-46d3-a11f-87c36c4f3a4c","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.744182Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:4cf5716f0332ec847270d3095ba987cf9497a47cb659a9acaec0cc3d9daf3439","observation_id":"e229d3e6-ffd4-4183-9b4f-a4672e7726a8","resolution":{"observed_at":"2026-08-08T11:35:30.127872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.114082Z","title":"1-bit stochastic gradient descent and its application to data-parallel distributed training of speech dnns","venue":null,"work_id":"65442fbc-7ee2-4982-946d-92d2dac4ce2e","year":2014},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.746788Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:03e0da6cba57466c88041c8e4e8b226b3fe9d886fbd4abd28705f06a4788aa86","observation_id":"154c885f-b530-4ee2-875d-2b2458d6ac00","resolution":{"observed_at":"2026-08-08T11:35:30.117452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.749543Z","title":"Understanding machine learning: From theory to algorithms","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.749543Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:2ab7e46fa56790884e164878169fa5b34e18a01b4f782e41157191a46c8d13c8","observation_id":"840d7485-1560-4e50-bbaf-f4c472988716","resolution":{"observed_at":"2026-08-08T11:35:29.749543Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.05202","last_updated":"2020-02-12T19:57:13Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2020-02-12T19:57:13Z","title":"GLU Variants Improve Transformer","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.05202","snapshot_observed_at":"2026-08-08T11:35:29.752359Z","title":"Glu variants improve transformer","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.752359Z"},"links":{"cited_paper":"/paper/2002.05202","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:4bcf07db0fb5c99b981d2f4d54a7344e030644e1631963ba69df154914291640","observation_id":"0bbe2dd3-f9ec-49bd-94d6-97700db81892","resolution":{"observed_at":"2026-08-08T11:35:29.752359Z","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":"2026-08-08T11:35:30.099701Z","title":"A tail-index analysis of stochastic gradient noise in deep neural networks","venue":null,"work_id":"1ef17bd7-fa36-4321-81f6-6db94f519d88","year":2019},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.755567Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:6017edbf8e9ffd7e062e9aabcd5c8ebf9527994a0b22360e1038139cc8a61837","observation_id":"c9a754d2-5894-4d09-9310-4ebeef5e8337","resolution":{"observed_at":"2026-08-08T11:35:30.103116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.090057Z","title":"Momentum ensures convergence of signsgd under weaker assumptions","venue":null,"work_id":"d2e68e57-077f-460c-bb4e-b23c34f8e49a","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.758446Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:22f1d69766bf973aa39e1c09c2f6d959986063655b66fb12d2f2ec9b3fc2a528","observation_id":"2ee1b205-7f63-4a0e-8bda-fbb9c3f5e064","resolution":{"observed_at":"2026-08-08T11:35:30.094235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.13971","last_updated":"2023-02-27T17:11:15Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-02-27T17:11:15Z","title":"LLaMA: Open and Efficient Foundation Language Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.13971","snapshot_observed_at":"2026-08-08T11:35:29.761565Z","title":"Llama: Open and efficient foundation language models","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.761565Z"},"links":{"cited_paper":"/paper/2302.13971","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:9a759191765695f991ea5009bade7cba6f2d3b78715b685415d30106cd342e41","observation_id":"a686756d-bdb1-4d36-a2b9-3ee09edaaf79","resolution":{"observed_at":"2026-08-08T11:35:29.761565Z","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":"2026-08-08T11:35:30.080190Z","title":"Convergence of adagrad for non-convex objectives: Simple proofs and relaxed assumptions","venue":null,"work_id":"57a38ec0-347c-4f41-aafc-34f8c26f329e","year":2023},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.764829Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:b7ed7ffe1e27e976ca86527d88d8c30668c644a8624baeab47072aa6ba34bb46","observation_id":"778b925b-0764-47d7-9d3e-ceca3d4af2d3","resolution":{"observed_at":"2026-08-08T11:35:30.084355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.15146","last_updated":"2024-03-22T11:57:51Z","snapshot_observed_at":"2026-07-06T17:48:59.440247Z","submitted_at":"2024-03-22T11:57:51Z","title":"On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.15146","snapshot_observed_at":"2026-08-08T11:35:29.767863Z","title":"On the convergence of adam under non-uniform smoothness: Separability from sgdm and beyond","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.767863Z"},"links":{"cited_paper":"/paper/2403.15146","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:44b72931d566ba4dfe8c034f4fc7a53dd3787ad32184d5a4138b1de35d12f764","observation_id":"57e254e7-b633-4305-8ab9-0f88eeffc9ef","resolution":{"observed_at":"2026-08-08T11:35:29.767863Z","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":"2026-08-08T11:35:29.771207Z","title":"Provable adaptivity of adam under non-uniform smoothness","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.771207Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:77e65af1318e88a2871e47cb9182f1a874568f59cac12af2043db904d04e454b","observation_id":"61867539-52f4-4397-aa1b-d882d9ce0da9","resolution":{"observed_at":"2026-08-08T11:35:29.771207Z","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":"2026-08-08T11:35:30.065641Z","title":"Two sides of one coin: the limits of untuned sgd and the power of adaptive methods","venue":null,"work_id":"d05441ba-94b5-4807-bf7e-e79ec2848930","year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.774241Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:6c36880fe30f593c5390fa346894b7993a098aff4e50cfb2a4c29c1ba0ea93af","observation_id":"b7fc47fc-c9ef-4eef-9709-5bb08c920b93","resolution":{"observed_at":"2026-08-08T11:35:30.069347Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:29.777156Z","title":"Root mean square layer normalization","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.777156Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a1237c8a8f5bcfbc001fb2d252ea7219a79b02f151a2b60853045435ade2b69e","observation_id":"6fe1d662-cf00-4ed5-94a0-c0f9010db147","resolution":{"observed_at":"2026-08-08T11:35:29.777156Z","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":"2026-08-08T11:35:30.051804Z","title":"Improved analysis of clipping algorithms for non-convex optimization","venue":null,"work_id":"a235c6e0-2d59-44cf-9b1c-75fa4f88e892","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.780168Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:17dc8dcd9c70aba1cd97b43c24dff4a86ba656f2baa16a9f125e850a9c490b17","observation_id":"df7c9b93-46cb-4bcd-af75-aaebdd25d115","resolution":{"observed_at":"2026-08-08T11:35:30.055015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.042376Z","title":"Why gradient clipping accelerates training: A theoretical justification for adaptivity","venue":null,"work_id":"b8c1261a-926f-4755-8071-c62e41078f76","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.783033Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:3d52808a30e59b307d658778ae34a7cd1da1d16b173d28744cdda8725b560b1e","observation_id":"b6234a6c-6c11-4222-a26a-7ebf1060f727","resolution":{"observed_at":"2026-08-08T11:35:30.045758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.033131Z","title":"Why are adaptive methods good for attention models? Advances in Neural Information Processing Systems, 33:15383–15393, 2020","venue":null,"work_id":"ab4c46b9-dc15-446c-b092-afd1059fa98f","year":2020},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.786171Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a40c4c1d2dcd1340a0a83d18356c46beea6debc5b915d3a55999fd2fe9167d0c","observation_id":"24223a43-2546-4e41-b011-6fc1486bc82c","resolution":{"observed_at":"2026-08-08T11:35:30.036613Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.19440","last_updated":"2025-03-08T20:40:28Z","snapshot_observed_at":"2026-08-08T21:26:27.722837Z","submitted_at":"2024-05-29T18:36:59Z","title":"MGDA Converges under Generalized Smoothness, Provably","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.19440","snapshot_observed_at":"2026-08-08T11:35:29.788923Z","title":"Mgda converges under generalized smoothness, provably","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.788923Z"},"links":{"cited_paper":"/paper/2405.19440","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:f4d76e976080b634706240503cc82859deb1db428e666f6e73853a3b222f7822","observation_id":"a6f30be4-74ca-47b0-92db-72ce23a428a1","resolution":{"observed_at":"2026-08-08T11:35:29.788923Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.01436","last_updated":"2025-03-08T20:11:54Z","snapshot_observed_at":"2026-07-06T17:54:11.726535Z","submitted_at":"2024-04-01T19:17:45Z","title":"Convergence Guarantees for RMSProp and Adam in Generalized-smooth Non-convex Optimization with Affine Noise Variance","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.01436","snapshot_observed_at":"2026-08-08T11:35:29.792126Z","title":"Convergence guarantees for rmsprop and adam in generalized-smooth non-convex optimization with affine noise variance","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.792126Z"},"links":{"cited_paper":"/paper/2404.01436","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:1383959c5f76e604abd29b352f537a7d7e4810d1046477201f2f691da0e4bc7c","observation_id":"64c45bb8-6591-43d5-a03d-7bd07c14bd4e","resolution":{"observed_at":"2026-08-08T11:35:29.792126Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.07972","last_updated":"2025-02-28T01:47:44Z","snapshot_observed_at":"2026-08-08T23:26:09.153970Z","submitted_at":"2024-07-10T18:11:40Z","title":"Deconstructing What Makes a Good Optimizer for Language Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.07972","snapshot_observed_at":"2026-08-08T11:35:29.795327Z","title":"Decon- structing what makes a good optimizer for language models","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.795327Z"},"links":{"cited_paper":"/paper/2407.07972","citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:48b77a282f67ddb5219b6226f39030061df11d40d63fbb2ac49f6b6fb9065146","observation_id":"c06a0683-cccb-4e75-8f15-627151518656","resolution":{"observed_at":"2026-08-08T11:35:29.795327Z","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":"2026-08-08T11:35:30.023709Z","title":"On the convergence and improvement of stochastic normalized gradient descent","venue":null,"work_id":"2c593403-b826-40f1-b9dc-1d6c0c43b25c","year":2021},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.798851Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:3231de49d44a6d303d0196f4a84221770be26c255a0dc78af22533344b9ba466","observation_id":"6d558fc9-375d-4f1a-a207-7fd7551f33f1","resolution":{"observed_at":"2026-08-08T11:35:30.027248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.014578Z","title":"1 + ∥⃗ σ∥1 ε κ κ−1 #! , Optimal tuning for ε ≤ 8L0 L1 √ d : T = O ∆Lδ 0d ε2 , γk ≡ q ∆ 20Lδ 0dT , Bk ≡ 16∥⃗ σ∥1 ε κ κ−1 : N = O ∆Lδ 0d ε2","venue":null,"work_id":"f49a0bd0-f790-4a4f-8543-ec1ff9f3373c","year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.802164Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:e9315630f819325c41b3ae0dae29388fba9cb57ad6be17c3f97c5f5e7b0717c6","observation_id":"4adcaaf6-504c-4d16-a01c-9980d3b4cb13","resolution":{"observed_at":"2026-08-08T11:35:30.017864Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-08T11:35:30.005146Z","title":"We trained the model for 100k steps","venue":null,"work_id":"86b2559a-1c8f-466b-a595-bdc566a1ed3b","year":null},"citing_paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","version":2},"reference_index":256,"source":"pdf_text","source_observed_at":"2026-08-08T11:35:29.806274Z"},"links":{"citing_paper":"/paper/2502.07923"},"observation_digest":"sha256:a4a5883a746ac41c91a1d1b1a03cf8f42efe13205170907405056178a0b49d99","observation_id":"bbc8050e-2cb2-4d9d-822b-0f2d8374a7cd","resolution":{"observed_at":"2026-08-08T11:35:30.008343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.07923","last_updated":"2025-05-27T15:31:20Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-08T23:26:23.316471Z","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness"},"reference_resolution":{"displayed":81,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":3,"verified_fuzzy":47},"total_outbound_references":81},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 81 of 81 outbound references and 10 inbound Pith citation observations for arXiv:2502.07923."}