{"as_of":"2026-08-14T11:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:02688d237c057b900c9788e476230b5aa50b285ef7bd6dfb603772cb08036540","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:47:19.458404Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.20008/citation-record","integrity":"/paper/2412.20008/integrity","json":"/paper/2412.20008/citation-record.json","paper":"/paper/2412.20008"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:47:20.771502Z","title":"Steepest descent algorithms for optimization under unitary matrix constraint","venue":null,"work_id":"b7757a60-3d24-47b2-9478-c61aa06d89aa","year":2008},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.113220Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:e4e30519250c20852e2ca38a39986e21a320f01af4cb9f4adc39b90668769f2f","observation_id":"8eda736d-25b6-4222-ae4e-ffa96e30fb8b","resolution":{"observed_at":"2026-08-10T23:47:20.777754Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.749852Z","title":"Trust-region methods on riemannian manifolds","venue":null,"work_id":"77f26b2b-8490-4101-bedd-d4e1ae5d2ea1","year":2007},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.121739Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:5ec80b83e2b50d0396b87d404cc1142ddcc7b680d7a9fb62a1d89378475b2ad0","observation_id":"aa85100a-ea21-406c-a5db-c203613d588e","resolution":{"observed_at":"2026-08-10T23:47:20.755931Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.729107Z","title":"Absil, R","venue":null,"work_id":"03af2fb0-96c1-4c7a-bc03-6d720bfdeb75","year":2008},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.139470Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:b5644c9eccd51c90d11c26fa86f4b74f2487b07c6027810452d9f1c049d3b691","observation_id":"f8df705f-790d-4a66-9d98-ea2e5acfc42b","resolution":{"observed_at":"2026-08-10T23:47:20.735532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.706750Z","title":"Newton’s method on riemannian manifolds and a geometric model for the human spine","venue":null,"work_id":"9554e5df-f8eb-4152-a435-a99bd5543cf7","year":2002},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.146412Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:9280ba88e6d8e0fe4ea9d7ebbe4d6fdfac3055f0617341d1623cb436473aecc1","observation_id":"d25fb050-ad25-4d5d-ab3c-6fb444d300c0","resolution":{"observed_at":"2026-08-10T23:47:20.712784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.686922Z","title":"Stochastic approx- imation for canonical correlation analysis","venue":null,"work_id":"4b8f81f2-a9d7-4f2d-a198-ffaa0c55a17b","year":2017},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.153334Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:b69bf61d2ff42fcedd28ef627c523a7690f86fb754f4c1d39727f233d1d6ae40","observation_id":"32a62b12-30d8-444f-94d5-6affbec578d3","resolution":{"observed_at":"2026-08-10T23:47:20.692789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.666226Z","title":"Riemannian manifold trust-region methods with applications to eigenprob- lems","venue":null,"work_id":"d2505f5b-84c0-4da3-8c78-ee871040c0d9","year":2008},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.162464Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:a32d68a828c8f2af8781918c7f02070a5a1b7c8079ab9f71cbd52609970f7428","observation_id":"7264dcdb-5633-4077-a7b0-671ef0e1eccc","resolution":{"observed_at":"2026-08-10T23:47:20.672934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.646684Z","title":"Learning sparse feature representa- tions using probabilistic quadtrees and deep belief nets","venue":null,"work_id":"679ee973-0d02-465b-93f4-e7e34454144b","year":2017},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.170149Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:9f57b1d83e0767247a8810e8d7249b2e7bbbde6211230843e57ee834b3548865","observation_id":"fdaf1881-a1e3-4035-8512-8c56a26db458","resolution":{"observed_at":"2026-08-10T23:47:20.652580Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.628415Z","title":"Stochastic approximations and differential inclusions","venue":null,"work_id":"c2b0bd4f-e92a-471a-b28c-047082c71c32","year":2005},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.177202Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:d45fbad53b2591d71c70960fe2dcf997fc8d5b72b031578ca294dbd684011608","observation_id":"5eff538e-a96c-4364-b37e-06ea06a33f4c","resolution":{"observed_at":"2026-08-10T23:47:20.634670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.607539Z","title":"Non-convex phase retrieval from stft measurements","venue":null,"work_id":"42190b15-3c6d-48b6-87e9-3e0028d15b64","year":2016},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.183037Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:596a50c762d3ddb47e0ab0cacb72981f1b267c6fada24c672a87896fa21cd0c3","observation_id":"517f3966-86c4-4c5f-b1f4-a76bde86aaf9","resolution":{"observed_at":"2026-08-10T23:47:20.613463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.588548Z","title":"Subgradient sampling for nonsmooth nonconvex minimization","venue":null,"work_id":"d751ff40-2368-458e-8f9c-e6802198023d","year":2023},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.192392Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:32904023b7687c610c75899230c6456fc471b142cd537f7883b7ccb26dc3e5a8","observation_id":"111dfc7c-e84f-474c-b35f-f305b6c027da","resolution":{"observed_at":"2026-08-10T23:47:20.594369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.570271Z","title":"Stochastic first-order methods for convex and nonconvex functional constrained optimization","venue":null,"work_id":"30f8c06a-d473-4d6a-8700-2a1ee619ae61","year":2022},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.200285Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:68db667c3ca41a66b75c5aefb929cbe36ee2a99ea009d1b1119c32abc31b9c79","observation_id":"4ad95a0d-9366-4f5e-8a06-3c5ea3ec8965","resolution":{"observed_at":"2026-08-10T23:47:20.576105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.207334Z","title":"An introduction to optimization on smooth manifolds","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.207334Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:b20d91899d0dbe33134d5af8da66e13db25f6e73dec5e97a46ff1f89e7b7adc7","observation_id":"01368d39-ac58-4fe0-b584-c963f95920b9","resolution":{"observed_at":"2026-08-10T23:47:19.207334Z","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":"2026-08-10T23:47:20.539206Z","title":"Manopt, a matlab toolbox for optimization on manifolds","venue":null,"work_id":"e6876d73-010a-4aa7-9cde-fc21197fa9c1","year":2014},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.213558Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:5ee5765fd06ff947d1367ce7e54fb4e92713db8066532412489e28139b2f2296","observation_id":"450eedad-6d47-4287-9bdd-374806d319c9","resolution":{"observed_at":"2026-08-10T23:47:20.544618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1311.6186","last_updated":"2013-11-24T23:50:20Z","snapshot_observed_at":"2026-07-06T03:29:06.186072Z","submitted_at":"2013-11-24T23:50:20Z","title":"Sparse CCA via Precision Adjusted Iterative Thresholding","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1311.6186","snapshot_observed_at":"2026-08-10T23:47:19.222553Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.222553Z"},"links":{"cited_paper":"/paper/1311.6186","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:9a72ae53126538dc7bcf4fe42dd489043cda5d308f10ee567d242a59cb97ce39","observation_id":"6f802841-8ddb-4c21-bf43-a2e22e7b23c3","resolution":{"observed_at":"2026-08-10T23:47:19.222553Z","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":"2026-08-10T23:47:20.520656Z","title":"Solving stochastic compositional optimization is nearly as easy as solving stochastic optimization","venue":null,"work_id":"42b0dbcb-c90e-490e-82d4-a0d7a68f3f8e","year":2021},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.231108Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:dad52fd5f41d399c24fab0756fa36b582062d9dcb4527daca7671856d7a0fdad","observation_id":"bf3f9dc7-5628-411a-9525-ef72ab886277","resolution":{"observed_at":"2026-08-10T23:47:20.526928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1808.02941","last_updated":"2019-03-10T00:48:35Z","snapshot_observed_at":"2026-08-07T09:56:34.669633Z","submitted_at":"2018-08-08T21:14:07Z","title":"On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.02941","snapshot_observed_at":"2026-08-10T23:47:19.238322Z","title":"On the convergence of a class of adam-type algorithms for non-convex optimization","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.238322Z"},"links":{"cited_paper":"/paper/1808.02941","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:327b8c8c8d4a1d27597b19a868d66e3b321bf984427861a81342138595e54491","observation_id":"cb1cd21b-0e0c-41c2-8ab9-e1c8419f1a28","resolution":{"observed_at":"2026-08-10T23:47:19.238322Z","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":"2026-08-10T23:47:20.500382Z","title":"An Orthogonalization-Free Parallelizable Framework for All-Electron Calculations in Density Functional Theory","venue":null,"work_id":"c3e8764a-67f8-4040-8d76-56b7d589f507","year":2022},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.249318Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:bec1df902de43cb2510945b00f2d64fd81264fa52aa5b4f1cb6a2a73393436e7","observation_id":"857eec86-947e-499b-aa78-f97ab49c6236","resolution":{"observed_at":"2026-08-10T23:47:20.507134Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2107.00371","last_updated":"2023-02-06T05:42:52Z","snapshot_observed_at":"2026-08-02T08:16:46.824920Z","submitted_at":"2021-07-01T11:15:20Z","title":"Sparse GCA and Thresholded Gradient Descent","version":2},"cited_work":{"arxiv_id":"2107.00371","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.00371","snapshot_observed_at":"2026-08-10T23:47:19.855531Z","title":"Sparse GCA and Thresholded Gradient Descent","venue":"stat.ML","work_id":"db9881e7-773a-46cc-a232-0e3906905936","year":2021},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.256179Z"},"links":{"cited_paper":"/paper/2107.00371","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:bb9cac385d00bba0538474e09555123770077ef3c4fa5a8aeb54c03b811a9ea6","observation_id":"2c86febf-dfa9-49ec-823e-7ab0e173f8b2","resolution":{"observed_at":"2026-08-10T23:47:19.862045Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.481050Z","title":"Efficient algorithms for large- scale generalized eigenvector computation and canonical correlation analysis","venue":null,"work_id":"1b7ead3c-b096-4d2f-8a65-3c16cf5a9af5","year":2016},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.267135Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:f4788580b8d314e2377b3e527eebc36956ccfb511a2276abea03f1d693bffd8c","observation_id":"3af1b293-c5d8-4d81-b50a-0ab0f58753f4","resolution":{"observed_at":"2026-08-10T23:47:20.487066Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.456999Z","title":"A single timescale stochastic approxi- mation method for nested stochastic optimization","venue":null,"work_id":"a79880b8-397b-4f88-bc87-6173fa8affbb","year":2020},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.274406Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:cf2f40fa2b50d4edce7572fc64e1b8d17c537d36f35f6a2c6b46f7059f592b99","observation_id":"c9cb4984-2f22-42f2-a96e-63b79d45a724","resolution":{"observed_at":"2026-08-10T23:47:20.464855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.437405Z","title":"Hardoon, Sandor Szedmak, and John Shawe-Taylor","venue":null,"work_id":"3e7d6602-5036-4328-83d1-da77c25ccb0e","year":2004},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.280603Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:8532279a3572a835b01b9c401856a4e12581439e8f9acf62166448fb6efe14fa","observation_id":"5adbec97-bb51-4c36-91fa-cae003b89868","resolution":{"observed_at":"2026-08-10T23:47:20.443349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.415728Z","title":"Relations between two sets of variables","venue":null,"work_id":"750b0b62-4ac6-4765-9c03-394e684b7c21","year":1936},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.286504Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:4df2d01c942f5a3e31ff61b6591fb086630e6ec6abb13f0f43aacf119fc76465","observation_id":"8d9d1866-ff2f-42aa-8057-03747c6e3e8d","resolution":{"observed_at":"2026-08-10T23:47:20.423149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.391417Z","title":"Generalized canonical correlations and their application to experimental data","venue":null,"work_id":"f06c809c-7cf3-4c31-919c-c5ae9a11f46a","year":1961},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.292290Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:6571ce9888cf26698db7d9cbc9293ecd5cdfc2cb507d651b318d99aa0d59e49a","observation_id":"aa8e283f-49e6-46c9-9351-80c7043f64af","resolution":{"observed_at":"2026-08-10T23:47:20.397516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.372804Z","title":"A brief introduction to manifold opti- mization","venue":null,"work_id":"9190ef61-0e69-4386-b9ef-e50d16b935f4","year":2020},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.298777Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:615be2e4105bcf572323997e9cab375f8bb6ba9c80dd538dc4a3ee5b90a00857","observation_id":"95ca01b8-d45e-4326-aa6e-cd6e2a581312","resolution":{"observed_at":"2026-08-10T23:47:20.378694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.353057Z","title":"A broyden class of quasi-newton methods for riemannian optimization","venue":null,"work_id":"4d02dcbe-ae43-493c-918b-13c0c6308e76","year":2015},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.304156Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:ddd002308952f27aa033aaab9c9eedd10431965eb28abd0baae28506d2c69a80","observation_id":"ab19b73c-2d99-4be6-be81-c9d8281c8ba7","resolution":{"observed_at":"2026-08-10T23:47:20.359593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.324465Z","title":"Robust estimation of a location parameter","venue":null,"work_id":"7710f33a-6a07-479c-a5f8-aa2d8e0e0fbb","year":1992},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.310476Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:16a6bd9a1b9dcc16ed9b0c94c406e3ef866e71301bffdf8a7209bae2921650e4","observation_id":"714755b0-8ed4-48dc-8075-c36d79a43557","resolution":{"observed_at":"2026-08-10T23:47:20.330938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.294278Z","title":"The riemannian barzilai–borwein method with non- monotone line search and the matrix geometric mean computation","venue":null,"work_id":"ae4218c7-7408-47db-a97c-2da2b305869d","year":2018},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.316791Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:8d07c5cc72c56ad3fb3069a67022e4a7092a283bf476c62640b48627f93bee80","observation_id":"4a3d968f-3adb-4060-ab94-cb71c4b7ef8f","resolution":{"observed_at":"2026-08-10T23:47:20.308793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.272468Z","title":"Riemannian stochastic recursive gradient algorithm","venue":null,"work_id":"c3e24207-c1e4-4635-8fe0-346c5dd24f08","year":2018},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.322731Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:9f153a7fa4cfd408012d3d40c68aeae84332692ef84bc9e0898e637a763a5c1d","observation_id":"e4a18c19-9588-45d2-a39e-c98b9b56b0bc","resolution":{"observed_at":"2026-08-10T23:47:20.280215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.246085Z","title":null,"venue":null,"work_id":"7dba966f-cd71-4220-ad81-16f34e7a0fcd","year":1971},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.328730Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:48792aac0ead5aad385d8413f086f58df4bbafccd75e6f3bf3da984fcbfe23a8","observation_id":"16b4432c-2449-49b0-9de3-94d67f03d8fe","resolution":{"observed_at":"2026-08-10T23:47:20.251841Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2026-08-10T23:47:19.334918Z","title":"Adam: A method for stochastic optimization","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.334918Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:420d2dc1d78fdd0b4ce40ce903fb529911b28aab067e479f65a727dc282fc8b5","observation_id":"fec66ed7-eb0c-4464-bcf9-2508112de02a","resolution":{"observed_at":"2026-08-10T23:47:19.334918Z","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":"2026-08-10T23:47:20.226125Z","title":"Nonsmooth nonconvex stochastic heavy ball","venue":null,"work_id":"5fdc05e2-9188-415d-8557-baa64fc53be6","year":2024},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.341856Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:aa3446bfba5d93f82ccda19f2b785a19f7a571062ee3f4b6b0e369fff1e9becf","observation_id":"a66505fb-526b-47b4-9348-8448ee8452a9","resolution":{"observed_at":"2026-08-10T23:47:20.233276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.348103Z","title":"The mnist database of handwritten digits","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.348103Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:4bda49356e29625cf49db951817300bc06fda7bc72ac104dff0bbf8ceec0dda4","observation_id":"3d045f2f-0bbb-411a-b212-268cf4cb008d","resolution":{"observed_at":"2026-08-10T23:47:19.348103Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2212.09513","last_updated":"2022-12-19T14:48:54Z","snapshot_observed_at":"2026-08-13T13:19:01.055393Z","submitted_at":"2022-12-19T14:48:54Z","title":"Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization","version":1},"cited_work":{"arxiv_id":"2212.09513","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.09513","snapshot_observed_at":"2026-08-10T23:47:19.796501Z","title":"Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization","venue":"math.OC","work_id":"13846df6-4b61-4dbe-9f62-5903e01433dd","year":2022},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.353887Z"},"links":{"cited_paper":"/paper/2212.09513","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:10474793e0bd0e3fe39d611a8d7172c249ac5ef7b0546901e5449afe20690dec","observation_id":"12f153bc-c83a-4d66-ba06-92255014624c","resolution":{"observed_at":"2026-08-10T23:47:19.804539Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.184727Z","title":"Linear discriminant analysis: New formulations and overfit analysis","venue":null,"work_id":"81617a64-5f46-4772-9ce8-fa6fc4e7f632","year":2011},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.359909Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:b73852827b73d86fc91a08e8a9decf3f102cefa88f6ae2cb7027f849f1a93102","observation_id":"4aaad49c-5a17-4802-a13a-5054714492f4","resolution":{"observed_at":"2026-08-10T23:47:20.190431Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.01871","last_updated":"2023-03-23T04:05:54Z","snapshot_observed_at":"2026-08-13T07:51:00.110304Z","submitted_at":"2019-08-05T21:39:24Z","title":"Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints","version":3},"cited_work":{"arxiv_id":"1908.01871","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.01871","snapshot_observed_at":"2026-08-10T23:47:19.769178Z","title":"Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints","venue":"math.OC","work_id":"32d01b98-a7eb-40e1-891d-81ac9422d41b","year":2019},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.365667Z"},"links":{"cited_paper":"/paper/1908.01871","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:8d09811f64e9d9f095381b73d57c93fa8e726d29d2fea9ad0e7d1206d95cecb5","observation_id":"b138697c-7c3d-476f-b6f9-d9b8d71d9cb9","resolution":{"observed_at":"2026-08-10T23:47:19.775657Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.161000Z","title":"Finding linear structure in large datasets with scalable canonical correlation analysis","venue":null,"work_id":"602a43cb-d819-4cb6-a874-7f0b58792b3c","year":2015},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.371694Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:faff43053c146374b39dc477dc31fa3c18a745fb812b5d4345ba62e42f9d9c7e","observation_id":"754e4acd-81ee-4f38-9e2f-e20b20e84627","resolution":{"observed_at":"2026-08-10T23:47:20.168430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.140364Z","title":"An online riemannian pca for stochastic canonical correlation analysis","venue":null,"work_id":"1fe29fc8-24f2-4992-9cac-c14544dfb32f","year":2021},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.377931Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:cee6e5282d06d3cc9613fc645ad0a5f4160644c9f4669e9747a574c4912d5561","observation_id":"94f4bfbc-d2b4-4417-85be-7b56585df594","resolution":{"observed_at":"2026-08-10T23:47:20.146479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.384301Z","title":"Numerical optimization","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.384301Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:083c13b57d50be649722a0d179339b9dabbe654809f499f660ed3e59762ce12a","observation_id":"afc17ca9-791b-4527-a485-9c437a416af1","resolution":{"observed_at":"2026-08-10T23:47:19.384301Z","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":"2026-08-10T23:47:20.101362Z","title":"Riemannian conjugate gradient methods: General framework and specific algo- rithms with convergence analyses","venue":null,"work_id":"6ab78c1b-b885-4f5e-80f6-558fc8b889c0","year":2022},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.390289Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:9a40015dfd613478e94331436c4537a28a1213d2f4dd08641b3be0d086fc3c9c","observation_id":"2642a459-a2a4-48aa-83da-530b3ddec712","resolution":{"observed_at":"2026-08-10T23:47:20.108393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.076973Z","title":"Cholesky QR-based retraction on the generalized Stiefel manifold","venue":null,"work_id":"4905bdca-6276-4a25-be5c-65efe4c5f046","year":2019},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.396277Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:28bbfdc62e777db780aec7c3637e71dfe07319fcbe3d418df17046890fe39e72","observation_id":"4941a08e-a4b3-4cb2-a010-689f1ce133f8","resolution":{"observed_at":"2026-08-10T23:47:20.084037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.044435Z","title":"A new, globally convergent riemannian conjugate gradient method","venue":null,"work_id":"93ce9552-3ade-4483-90eb-c953d5fb0d4f","year":2015},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.402145Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:6afbdce12cf9f4b00ac2468b7ce0ed997e694fd0383260989714929583e87283","observation_id":"857b9d8d-9100-4ff4-80b6-6ab9a3b0d536","resolution":{"observed_at":"2026-08-10T23:47:20.056855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.01635","last_updated":"2022-11-15T17:02:24Z","snapshot_observed_at":"2026-08-04T07:28:09.724402Z","submitted_at":"2019-02-05T10:42:00Z","title":"Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold","version":4},"cited_work":{"arxiv_id":"1902.01635","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.01635","snapshot_observed_at":"2026-08-10T23:47:19.738331Z","title":"Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold","venue":"math.NA","work_id":"c0636435-a103-4a54-a03a-885e1a8ada7a","year":2019},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.409715Z"},"links":{"cited_paper":"/paper/1902.01635","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:85473056a03f30057be3e2aab80e2cccd480ab73dce6b79189b2e33c59a3788f","observation_id":"2198431e-d197-4a93-b668-bb8e771dc916","resolution":{"observed_at":"2026-08-10T23:47:19.745769Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:20.015897Z","title":"The challenge problem for automated detection of 101 semantic concepts in multi- media","venue":null,"work_id":"8dd50467-700f-4916-b1cb-0075344d007a","year":2006},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.416181Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:c094238d8747d0c25e340f53a0b8c6c2d18ad0a470f0c5ac04d829babc236a27","observation_id":"027b71c7-f755-4570-8ae2-3b330a658d26","resolution":{"observed_at":"2026-08-10T23:47:20.025083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.993160Z","title":"Minimum generalized variance for a set of linear functions","venue":null,"work_id":"e0f33c9c-232c-413b-84bc-da5e691c1df5","year":1951},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.421753Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:38d4c73981a7153f1cd400c64d39fcd4f4e2e9d83c56e3bd1665ce87ef44d777","observation_id":"51c06b11-f319-4f4b-a7d5-e9a8fc82408f","resolution":{"observed_at":"2026-08-10T23:47:19.999959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.11205","last_updated":"2020-03-25T04:04:25Z","snapshot_observed_at":"2026-08-08T10:09:31.798332Z","submitted_at":"2020-03-25T04:04:25Z","title":"Generalized Canonical Correlation Analysis: A Subspace Intersection Approach","version":1},"cited_work":{"arxiv_id":"2003.11205","doi":null,"metadata_source":"pith","pith_arxiv_id":"2003.11205","snapshot_observed_at":"2026-08-10T23:47:19.710266Z","title":"Generalized Canonical Correlation Analysis: A Subspace Intersection Approach","venue":"cs.LG","work_id":"1018abd3-3f2e-45db-b19d-90ad69bcbb12","year":2020},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.427534Z"},"links":{"cited_paper":"/paper/2003.11205","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:a3d4fff8fbea52ac3cd704f5d2d21975f417bc4f448c5cf08266945b57f860df","observation_id":"2847e2ce-42ac-4d4e-8e02-1de0415c7676","resolution":{"observed_at":"2026-08-10T23:47:19.716864Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.433099Z","title":"Optimization without retraction on the random generalized stiefel manifold","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.433099Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:07290c213b9c95696b7735670779bf5c8d3dfd8303a75907db1a9496a0a5b496","observation_id":"fbaa098c-77a3-4359-9e2d-cf858cf9778e","resolution":{"observed_at":"2026-08-10T23:47:19.433099Z","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":"2026-08-10T23:47:19.973455Z","title":"Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions","venue":null,"work_id":"db4ae3c0-b0c8-416a-a451-0c03c4b90433","year":2017},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.438931Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:a8b0e872b144f5ad6d4e4b5daed48e96984240ffac1b8d105fd904a3012c410e","observation_id":"daf513eb-93ce-4350-a22d-7e829873e25e","resolution":{"observed_at":"2026-08-10T23:47:19.980141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.945125Z","title":"Accelerating stochastic composition optimization","venue":null,"work_id":"109fe1d5-3e1b-4cff-9501-76b78861fd55","year":2017},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.446393Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:96e91721e990126bf274f52aba6da1bccea098e6357da4f66243696787ff1c87","observation_id":"425f49d0-32e0-4bf0-b519-9f700f69ff91","resolution":{"observed_at":"2026-08-10T23:47:19.952118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.10319","last_updated":"2022-10-15T00:58:59Z","snapshot_observed_at":"2026-08-13T16:19:34.682846Z","submitted_at":"2022-03-19T13:01:08Z","title":"Dissolving Constraints for Riemannian Optimization","version":3},"cited_work":{"arxiv_id":"2203.10319","doi":null,"metadata_source":"pith","pith_arxiv_id":"2203.10319","snapshot_observed_at":"2026-08-10T23:47:19.508163Z","title":"Dissolving Constraints for Riemannian Optimization","venue":"math.OC","work_id":"e4c6b331-f1cb-4f22-8094-d646c177a727","year":2022},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.451667Z"},"links":{"cited_paper":"/paper/2203.10319","citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:ce8a6619485db2efd9be3d22c4f36f095897c9ae96359dfc6a8352614289a130","observation_id":"69515468-3184-4c5e-a4dd-55bc3a9581d1","resolution":{"observed_at":"2026-08-10T23:47:19.517576Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T23:47:19.923068Z","title":"A stochastic composite gradient method with incremental variance reduction","venue":null,"work_id":"76a3ac94-dec6-4342-b5fa-3621d482864b","year":2019},"citing_paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-10T23:47:19.458404Z"},"links":{"citing_paper":"/paper/2412.20008"},"observation_digest":"sha256:f6410b6206d8b856d1229f570c3cb7808f660e44e1c285745db15358b594536c","observation_id":"e1f02ee6-d075-4fb4-b9fa-e2bcf7f26dd2","resolution":{"observed_at":"2026-08-10T23:47:19.928974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.20008","last_updated":"2024-12-28T04:07:50Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-14T06:43:58.971017Z","submitted_at":"2024-12-28T04:07:50Z","title":"Stochastic optimization over expectation-formulated generalized Stiefel manifold"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":8,"verified_exact":5,"verified_fuzzy":36},"total_outbound_references":50},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2412.20008."}