{"as_of":"2026-08-11T18:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5d74ec2198e8c003486fb14620433934fc6b07beb99e2624bfcca8117f200943","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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":"2026-08-07T06:04:35.135917Z","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":"2026-07-04T10:09:44.617472Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2502.07529","last_updated":"2025-06-06T13:42:19Z","snapshot_observed_at":"2026-08-03T03:50:14.086851Z","submitted_at":"2025-02-11T13:10:34Z","title":"Training Deep Learning Models with Norm-Constrained LMOs","version":2},"reference_index":156,"source":"arxiv_source","source_observed_at":"2026-05-21T21:22:36.870292Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2502.07529"},"observation_digest":"sha256:dfa98c12b8e636870e04fb152c1fdc3a046572919ca37814142fafd6a856cef2","observation_id":"f31b3914-cdee-4130-8209-3bdcfbd97135","resolution":{"observed_at":"2026-05-21T21:22:37.000960Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-08-07T06:04:35.135917Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2506.06606","last_updated":"2025-06-07T00:47:07Z","snapshot_observed_at":"2026-08-09T18:41:53.384740Z","submitted_at":"2025-06-07T00:47:07Z","title":"Stacey: Promoting Stochastic Steepest Descent via Accelerated $\\ell_p$-Smooth Nonconvex Optimization","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T06:04:35.135917Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2506.06606"},"observation_digest":"sha256:ff718cd06f88b37b609def7a6e1225a203ea0a7e772ac30a08f167ed5d7488d8","observation_id":"8a7a798b-7578-496f-9e38-1b29fce794a4","resolution":{"observed_at":"2026-08-07T06:04:35.135917Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-08-06T17:13:42.950570Z","title":"Balles, F","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.12091","last_updated":"2025-07-16T09:54:08Z","snapshot_observed_at":"2026-08-09T00:59:12.919541Z","submitted_at":"2025-07-16T09:54:08Z","title":"Improved Analysis for Sign-based Methods with Momentum Updates","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T17:13:42.950570Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2507.12091"},"observation_digest":"sha256:d52436cffd34c6295e84382e5ae93164f4dd5e1ab2591f788bef0dfcf23d9446","observation_id":"fb2eb7c3-ae2f-4b2c-b0ef-56e7d8547bef","resolution":{"observed_at":"2026-08-06T17:13:42.950570Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2604.17423","last_updated":"2026-05-01T14:46:49Z","snapshot_observed_at":"2026-08-02T20:20:49.115675Z","submitted_at":"2026-04-19T13:07:51Z","title":"A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-10T07:19:59.335184Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2604.17423"},"observation_digest":"sha256:e3f3f7e711e648e71966f50fc0d3c9e1640a0903e010ffef65007df22c72d222","observation_id":"dba5c5b5-20ea-4d03-88a6-9fb3b1d7c2be","resolution":{"observed_at":"2026-05-10T07:26:59.831701Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2605.06615","last_updated":"2026-05-07T17:32:09Z","snapshot_observed_at":"2026-08-11T12:51:56.931920Z","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":2,"source":"pdf_text","source_observed_at":"2026-05-08T12:14:28.866499Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2605.06615"},"observation_digest":"sha256:37650219f765694bfb0d0167a6fae49b88e5ea15dc6c1cc09bc20cad80802bc8","observation_id":"6e66c2d5-ab08-4275-844a-826008ed54e0","resolution":{"observed_at":"2026-05-11T19:21:07.752228Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2605.06654","last_updated":"2026-05-07T17:57:02Z","snapshot_observed_at":"2026-08-10T23:39:15.387009Z","submitted_at":"2026-05-07T17:57:02Z","title":"Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T12:00:49.127471Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2605.06654"},"observation_digest":"sha256:326be1f6916fdf3686d83ea05f2ad26cc883c5b074b56653762b94f17605f80a","observation_id":"1a26534a-2a18-4038-9238-482c3f75d6d6","resolution":{"observed_at":"2026-05-11T19:26:08.613799Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2606.02078","last_updated":"2026-06-01T11:07:35Z","snapshot_observed_at":"2026-08-06T21:39:19.199731Z","submitted_at":"2026-06-01T11:07:35Z","title":"Beyond $\\ell_2$-norm and $\\ell_\\infty$-norm: A Curvature-Inspired $\\ell_p$-Norm Scheme for Deep Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T15:34:55.812512Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2606.02078"},"observation_digest":"sha256:77f6953c81749a8dfec3c5023fb6880f1322c5cef3fa993e56fee2890418e6ce","observation_id":"957ae3ab-4180-4345-94ff-d30afab10f9d","resolution":{"observed_at":"2026-07-01T22:16:16.321542Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2606.14970","last_updated":"2026-06-22T08:40:27Z","snapshot_observed_at":"2026-07-06T23:52:28.557859Z","submitted_at":"2026-06-12T21:46:54Z","title":"Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning","version":2},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-06-27T04:33:10.554853Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2606.14970"},"observation_digest":"sha256:f26f65e6bad2f14ff0078e6abcad7339ea1b4873c1c07b9824a73b8bf2d3d7fd","observation_id":"99521690-d7bd-4000-af7c-09199bda5652","resolution":{"observed_at":"2026-07-03T17:08:43.681857Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":"2002.08056","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-07-04T10:09:44.617472Z","title":"The geometry of sign gradient descent.arXiv preprint arXiv:2002.08056","venue":null,"work_id":"f21e3dd4-b8a2-4d68-a027-50f7a8adb90a","year":2002},"citing_paper":{"arxiv_id":"2606.23676","last_updated":"2026-06-22T17:58:52Z","snapshot_observed_at":"2026-08-06T14:32:57.924655Z","submitted_at":"2026-06-22T17:58:52Z","title":"Open Problem: Is AdamW Effective Under Heavy-Tailed Noise?","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-26T09:08:41.993925Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2606.23676"},"observation_digest":"sha256:1a20944c23ba05b5cfe2d291433ec93fcae0a5480574b0040ddc402ab410b183","observation_id":"3fdd39a4-53e3-43a9-9da4-a0c674edcf74","resolution":{"observed_at":"2026-07-04T10:09:44.619336Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.08056","snapshot_observed_at":"2026-08-06T21:42:14.072979Z","title":"arXiv preprint arXiv:2002.08056 (2020)","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.04584","last_updated":"2026-08-05T08:49:16Z","snapshot_observed_at":"2026-08-10T07:04:11.835242Z","submitted_at":"2026-08-05T08:49:16Z","title":"Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T21:42:14.072979Z"},"links":{"cited_paper":"/paper/2002.08056","citing_paper":"/paper/2608.04584"},"observation_digest":"sha256:f6dcd8b7589e8f6f22053557814f739e019c504e7b820f803e2cc73ad495b0bc","observation_id":"72915bd1-5b5d-4b25-88e5-24a2556d677b","resolution":{"observed_at":"2026-08-06T21:42:14.072979Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2002.08056/citation-record","integrity":"/paper/2002.08056/integrity","json":"/paper/2002.08056/citation-record.json","paper":"/paper/2002.08056"},"outbound":[],"paper":{"arxiv_id":"2002.08056","last_updated":"2020-02-19T08:45:54Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T23:45:52.241190Z","submitted_at":"2020-02-19T08:45:54Z","title":"The Geometry of Sign Gradient Descent"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 10 inbound Pith citation observations for arXiv:2002.08056."}