{"as_of":"2026-08-08T08:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2e0524417631e5f667b381ee1c4672697b5e3f32e0c872bde19845009e91471c","coverage":[{"denominator":142,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T13:21:59.302552Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2507.20853/citation-record","integrity":"/paper/2507.20853/integrity","json":"/paper/2507.20853/citation-record.json","paper":"/paper/2507.20853"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:21:58.901442Z","title":"The neural tangent kernel in high dimensions: Triple descent and a multi-scale theory of generalization","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.901442Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:691ee749abff298cfafc8fbcc54336cc387bccf0c1ce5326a412ace66cfd5add","observation_id":"6360896a-ced4-46d9-82ca-ceccadf9f493","resolution":{"observed_at":"2026-08-06T13:21:58.901442Z","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":"2026-08-06T13:21:58.906111Z","title":"Agrachev and Yu","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.906111Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:d00f31ecccfd50595ac04fee7ebded17105e475c2abd2e208e26090749bae8b5","observation_id":"b7326e92-6aee-45a7-bffd-79d774cbeff1","resolution":{"observed_at":"2026-08-06T13:21:58.906111Z","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":"2026-08-06T13:21:58.911930Z","title":"Akametalu, Shahab Kaynama, Jaime Fern \\'a ndez Fisac, Melanie Nicole Zeilinger, Jeremy H","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.911930Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a9ce383151c7c5c4bbf9246cd549c5c03e883004041bb03b774ddf74d02c4c42","observation_id":"8d9c4524-2163-47d3-89fb-0e0a6bafa578","resolution":{"observed_at":"2026-08-06T13:21:58.911930Z","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":"2026-08-06T13:21:58.916182Z","title":"Learning and generalization in overparameterized neural networks, going beyond two layers","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.916182Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c0d146a1323a852b98792b3db93a98a7e93620bd1551a0f28ce7dfdfecc4fe4f","observation_id":"53b8c495-73fc-40c1-9ce3-62affd571ff9","resolution":{"observed_at":"2026-08-06T13:21:58.916182Z","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":"2026-08-06T13:21:58.920055Z","title":"A convergence theory for deep learning via over-parameterization","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.920055Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:652ec100dbca9e899df64fb76540c686017a3c43c08b40c8d28c985627072b67","observation_id":"6372e168-6d58-429d-9c90-e68ac2d1cdb4","resolution":{"observed_at":"2026-08-06T13:21:58.920055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.08718","last_updated":"2020-10-06T19:43:50Z","snapshot_observed_at":"2026-08-06T16:02:58.877029Z","submitted_at":"2020-06-15T19:33:47Z","title":"Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control","version":2},"cited_work":{"arxiv_id":"2006.08718","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.08718","snapshot_observed_at":"2026-08-06T13:22:00.524610Z","title":"Analytic Manifold Learning: Unifying and Evaluating Representations for Continuous Control","venue":"cs.LG","work_id":"3773137b-f6a3-48fe-b788-61cceb4a0c5a","year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.923694Z"},"links":{"cited_paper":"/paper/2006.08718","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:1aeb8b68e68da068766883d73390f07623e431df3608f3e0e922c125e37496b2","observation_id":"d94f80ca-67a0-4f92-b510-a829032d2c3a","resolution":{"observed_at":"2026-08-06T13:22:00.632782Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:58.928408Z","title":"Robust locally-linear controllable embedding","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.928408Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:cc3ae044f7204156ebf8891833e9a9e2fb0af0548a6db09a4384242e188052c8","observation_id":"afc55583-8b1c-466f-94bd-9f6ecc2b92a6","resolution":{"observed_at":"2026-08-06T13:21:58.928408Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.04723","last_updated":"2016-02-15T16:16:56Z","snapshot_observed_at":"2026-08-06T16:02:57.643671Z","submitted_at":"2016-02-15T16:16:56Z","title":"Efficient Representation of Low-Dimensional Manifolds using Deep Networks","version":1},"cited_work":{"arxiv_id":"1602.04723","doi":null,"metadata_source":"pith","pith_arxiv_id":"1602.04723","snapshot_observed_at":"2026-08-06T13:22:00.345590Z","title":"Efficient Representation of Low-Dimensional Manifolds using Deep Networks","venue":"cs.NE","work_id":"14a8dbea-c2f4-4f94-89ac-81a84977f3de","year":2016},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.932509Z"},"links":{"cited_paper":"/paper/1602.04723","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:0ceec8ca61696213478aaa9ffefcd047b6e22ef002403deb9f6159fc8ca6e49d","observation_id":"3d0ddd87-e67e-4eff-b578-8cc59f93c5fe","resolution":{"observed_at":"2026-08-06T13:22:00.437498Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:58.936672Z","title":"High-dimensional limit theorems for sgd: Effective dynamics and critical scaling","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.936672Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:14efcccfe9084e7e08f317183481ac0811cb0eadbbdcd6287feb8bfe3cccc2d4","observation_id":"060b156b-c286-45ca-b0d2-4f02aa55ab66","resolution":{"observed_at":"2026-08-06T13:21:58.936672Z","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":"2026-08-06T13:21:58.940225Z","title":"Dynamic programming and optimal control: Volume I, volume 4","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.940225Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ed971c5aaa6a1ac233e96f5d0157920b6cbb4bb1806b9422a24c6f4e0e610863","observation_id":"941500ae-5396-4415-9e3c-584fef61f928","resolution":{"observed_at":"2026-08-06T13:21:58.940225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.00592","last_updated":"2024-06-30T19:17:33Z","snapshot_observed_at":"2026-07-06T18:23:52.659446Z","submitted_at":"2024-06-02T02:01:03Z","title":"Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming","version":3},"cited_work":{"arxiv_id":"2406.00592","doi":null,"metadata_source":"pith","pith_arxiv_id":"2406.00592","snapshot_observed_at":"2026-08-06T13:22:00.272416Z","title":"Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming","venue":"eess.SY","work_id":"a1987fad-238a-4295-bd10-3b68eed4f6c1","year":2024},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.943735Z"},"links":{"cited_paper":"/paper/2406.00592","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:02d0f8b543c1dfa05d7ba1fbb7f8a099eb4b5c16ae92b09010bb37c69f5e5078","observation_id":"7719d306-9df8-44f8-af1a-10845bdfc5c4","resolution":{"observed_at":"2026-08-06T13:22:00.286463Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:58.947691Z","title":"An introduction to aspects of geometric control theory","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.947691Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:2291caf9c079d514119872191144cffe80dd0e7dec7bdc412e34cffe976c2d28","observation_id":"197d0aaf-4199-42c9-86d9-7665b84b3d66","resolution":{"observed_at":"2026-08-06T13:21:58.947691Z","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":"2026-08-06T13:21:58.951528Z","title":"An introduction to differentiable manifolds and Riemannian geometry","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.951528Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:5565437a4977c1f5a5f9f9dcd1189797f8c33407873ecd868afec31282276cb1","observation_id":"9e41dc33-0b2e-4662-aaf3-2ed7faff1e45","resolution":{"observed_at":"2026-08-06T13:21:58.951528Z","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":"2026-08-06T13:21:58.955043Z","title":"Wilkinson","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.955043Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:34c12174c9923201eb962bb5586796c8f5bffeca05a5ec88b0709801d7ca6272","observation_id":"12159db9-1213-4afc-872e-98e065e65a65","resolution":{"observed_at":"2026-08-06T13:21:58.955043Z","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":"2026-08-06T13:21:58.959078Z","title":"Brockett","venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.959078Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:d25081d4ef5f64bee322683286bdc1e984a0be7aa8ade5b76953191a05b8bd94","observation_id":"2ca363fb-8b04-4b3c-941b-411d49f809e3","resolution":{"observed_at":"2026-08-06T13:21:58.959078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1606.01540","last_updated":"2016-06-05T17:54:48Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2016-06-05T17:54:48Z","title":"OpenAI Gym","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1606.01540","snapshot_observed_at":"2026-08-06T13:21:58.964057Z","title":"Openai gym","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.964057Z"},"links":{"cited_paper":"/paper/1606.01540","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:5400c7377adfd22080d7f23abfca3567e25655dd4664f2452ba86bc5ab7f6720","observation_id":"9346b919-dcfe-4fdb-8f9b-1e1bb984ea4a","resolution":{"observed_at":"2026-08-06T13:21:58.964057Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13478","last_updated":"2021-05-02T16:16:03Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-04-27T21:09:51Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13478","snapshot_observed_at":"2026-08-06T13:21:58.969867Z","title":"Bronstein, Joan Bruna, Taco Cohen, and Petar Velivckovi'c","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.969867Z"},"links":{"cited_paper":"/paper/2104.13478","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:747229ed0c430980d799ccb5ce77ec11dbdc895c44a658f423eaaaf10308875a","observation_id":"f225f0ef-9da6-407f-b853-e5f7e2a69bb7","resolution":{"observed_at":"2026-08-06T13:21:58.969867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.11245","last_updated":"2021-05-06T06:55:39Z","snapshot_observed_at":"2026-08-06T04:31:24.861121Z","submitted_at":"2020-08-25T19:20:00Z","title":"Deep Networks and the Multiple Manifold Problem","version":2},"cited_work":{"arxiv_id":"2008.11245","doi":null,"metadata_source":"pith","pith_arxiv_id":"2008.11245","snapshot_observed_at":"2026-08-06T13:22:00.192267Z","title":"Deep Networks and the Multiple Manifold Problem","venue":"stat.ML","work_id":"ef608f36-1a58-460b-9b70-2235ba795c82","year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.975569Z"},"links":{"cited_paper":"/paper/2008.11245","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:29a77f0376be9b8db7ec2d9776a9443033c4c09db7911c86e4393a43fc60ae43","observation_id":"66717ae5-13d6-4568-8d1e-639af621bade","resolution":{"observed_at":"2026-08-06T13:22:00.212322Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:58.979731Z","title":"Geometric control of mechanical systems: modeling, analysis, and design for simple mechanical control systems, volume 49","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.979731Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:7f266b07b7e8923643977aa9e39d937304f1488c0f0409e2e2de51572d9f790e","observation_id":"e53d80b3-692f-42ee-964e-904c704069c0","resolution":{"observed_at":"2026-08-06T13:21:58.979731Z","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":"2026-08-06T13:21:58.983403Z","title":"Manifold embeddings for model-based reinforcement learning under partial observability","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.983403Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:94143d09cc1a47b8a3a76f1cb6ad21f23dcd7ad7b7746ed4d47350f9bd048dea","observation_id":"cc204231-e9a2-456a-86cf-88303501e97f","resolution":{"observed_at":"2026-08-06T13:21:58.983403Z","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":"2026-08-06T13:21:58.988076Z","title":"Cai, Zhuoran Yang, Jason Lee, and Zhaoran Wang","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.988076Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a3dfefc48d61c9e18d8c6fde26ff6d13453165249699cd6933be61185822f260","observation_id":"029a6957-8b97-42c1-a28e-cf54c570c6cc","resolution":{"observed_at":"2026-08-06T13:21:58.988076Z","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":"2026-08-06T13:21:58.991986Z","title":"Lee, and Zhaoran Wang","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.991986Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:09022c59e6879e838283bf0783283e57eae554e1e27a31e7c5ff1b48268d350a","observation_id":"1e16a066-0931-41f1-8118-5fbd11e107f5","resolution":{"observed_at":"2026-08-06T13:21:58.991986Z","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":"2026-08-06T13:21:58.996065Z","title":"Carlsson, T","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:58.996065Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:2e022babf1763a7d94560ad89d1f3600922cd52464bf66cec9b93bb1e7a7a870","observation_id":"641a92cf-bd86-439f-9236-598b35bef11c","resolution":{"observed_at":"2026-08-06T13:21:58.996065Z","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":"2026-08-06T13:21:59.000183Z","title":"Using bisimulation for policy transfer in mdps","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.000183Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:d9f03cb32194c30d2b553fd0f49849c0f8c132d7c2364b7a53b57b62b1b569f7","observation_id":"95050ea5-1ba0-49f3-8956-d13b2d6babdf","resolution":{"observed_at":"2026-08-06T13:21:59.000183Z","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":"2026-08-06T13:21:59.003703Z","title":"Redunet: A white-box deep network from the principle of maximizing rate reduction","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.003703Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:aabbb6bdab5f84a0951881d50262b817130c16a9da9b0e9a144d497f378a7a65","observation_id":"19b2bff3-83d9-45a0-85bc-de9983d75f0b","resolution":{"observed_at":"2026-08-06T13:21:59.003703Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.01842","last_updated":"2022-02-22T23:41:01Z","snapshot_observed_at":"2026-08-07T14:12:55.104775Z","submitted_at":"2019-08-05T20:22:29Z","title":"Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery","version":5},"cited_work":{"arxiv_id":"1908.01842","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.01842","snapshot_observed_at":"2026-08-06T13:22:00.135312Z","title":"Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery","venue":"cs.LG","work_id":"b3fab93d-dbec-4ea9-914a-29dadf4fc2a2","year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.007104Z"},"links":{"cited_paper":"/paper/1908.01842","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:7d5be3b52e44a4f8c3a7eedbaa5ec6cc1dd8f7f09a9bb076ad6b8929e3791728","observation_id":"7d4b3e5d-a75f-4fbb-b68d-bd63b9c8491e","resolution":{"observed_at":"2026-08-06T13:22:00.154112Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:59.010842Z","title":"Analysis and design of nonlinear control systems","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.010842Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:107ad919eeb3307ccd359108edbe4fac0918a4df501a307036e99a7ed4aedd2d","observation_id":"e524b71e-d5db-4c82-ba40-2ec1ffdcb85d","resolution":{"observed_at":"2026-08-06T13:21:59.010842Z","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":"2026-08-06T13:21:59.014778Z","title":"Stochastic gradient and langevin processes","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.014778Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c13e71afb6e670a08e73137007d46dadb50aa59635d287dce3d4835adf632366","observation_id":"1521213f-2248-48af-ab8d-a2906de4ab9c","resolution":{"observed_at":"2026-08-06T13:21:59.014778Z","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":"2026-08-06T13:21:59.018368Z","title":"On the global convergence of gradient descent for over-parameterized models using optimal transport","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.018368Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a197647f75064b8e9fe148a7650a8f6f5cf21eb45de16e505e314687a2da4ae1","observation_id":"df626636-e071-4a88-bbe6-ad4297acefc9","resolution":{"observed_at":"2026-08-06T13:21:59.018368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.02545","last_updated":"2021-04-26T09:05:48Z","snapshot_observed_at":"2026-07-06T09:45:01.182512Z","submitted_at":"2020-08-06T09:50:29Z","title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain","version":3},"cited_work":{"arxiv_id":"2008.02545","doi":null,"metadata_source":"pith","pith_arxiv_id":"2008.02545","snapshot_observed_at":"2026-08-06T13:22:00.080600Z","title":"A deep network construction that adapts to intrinsic dimensionality beyond the domain","venue":"stat.ML","work_id":"9d56b87e-4300-4cd5-a5ba-64f888473102","year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.021811Z"},"links":{"cited_paper":"/paper/2008.02545","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:d7bc00f319e75f277b73496a2e204231d65e5baa0ce313dd8c53a8777147ac25","observation_id":"18e78182-2133-43cd-b0f4-c06d67d9d51b","resolution":{"observed_at":"2026-08-06T13:22:00.099013Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:59.025680Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.025680Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:14e78bfba8c611bc9f9274da3c50b9369878bedbefd40010712a2ca127fc73db","observation_id":"24a810fc-0832-41a3-8e1e-058cd77fff6c","resolution":{"observed_at":"2026-08-06T13:21:59.025680Z","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":"2026-08-06T13:21:59.029605Z","title":"Pilco: A model-based and data-efficient approach to policy search","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.029605Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:71922ecf8e28e17b6e94a7812b5549696e1d4990a971657fd1f98280e2ef13df","observation_id":"18018751-5ace-4428-afc1-f52aefebab50","resolution":{"observed_at":"2026-08-06T13:21:59.029605Z","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":"2026-08-06T13:21:59.032977Z","title":"Reinforcement learning in continuous time and space","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.032977Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:4db174fa700377fe2d86e4ad3c8a8fec6976f03746964fc1aee5f1faad858f76","observation_id":"2258ef83-7c81-4d64-9fd8-85e7892c9c34","resolution":{"observed_at":"2026-08-06T13:21:59.032977Z","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":"2026-08-06T13:21:59.036433Z","title":"Reinforcement learning in continuous time and space","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.036433Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8c92dd2197fcb2282117475ec1d1b631f023f9a5532be43e575ad77b1da361e8","observation_id":"a939c79d-1a12-4b5b-849b-5b4378f13028","resolution":{"observed_at":"2026-08-06T13:21:59.036433Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.03804","last_updated":"2019-05-28T19:01:22Z","snapshot_observed_at":"2026-07-06T07:13:41.232277Z","submitted_at":"2018-11-09T07:39:59Z","title":"Gradient Descent Finds Global Minima of Deep Neural Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03804","snapshot_observed_at":"2026-08-06T13:21:59.039966Z","title":"Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.039966Z"},"links":{"cited_paper":"/paper/1811.03804","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:1bb2f64d9d738860ceaf4eab20ae80fcf02300ae7f5e427dd6feecd917e92dd6","observation_id":"3be9a2a0-869b-46c7-b299-a2acb9e67198","resolution":{"observed_at":"2026-08-06T13:21:59.039966Z","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":"2026-08-06T13:21:59.043509Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.043509Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:232f9a85328b429b96ae1318336c1b37aad56359489958c84c53e5ee75417a75","observation_id":"28c74da0-3aa3-4683-ac2e-29fe1971e7c8","resolution":{"observed_at":"2026-08-06T13:21:59.043509Z","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":"2026-08-06T13:21:59.046999Z","title":"Estimating the intrinsic dimension of datasets by a minimal neighborhood information","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.046999Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:565e6084d74bedd4e9a785402076b7d061e456e5f74e8789e8ed089fed109b8e","observation_id":"6531f338-7c11-411e-bc05-c4afa39ed9d4","resolution":{"observed_at":"2026-08-06T13:21:59.046999Z","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":"2026-08-06T13:21:59.050319Z","title":"Fefferman, S","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.050319Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:cc5c023bd76d1f3a510c64f811cea95ae0a473ca098280e0c4b3d26a951b1b0a","observation_id":"4c1313d1-a32f-48e2-8bb1-1b1b2f235250","resolution":{"observed_at":"2026-08-06T13:21:59.050319Z","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":"2026-08-06T13:21:59.053712Z","title":"Panangaden, and Doina Precup","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.053712Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:60c936d8ce1f4fb570bd04cf4a83c7db7c590e7ed2d2ff961028ee2b7cd2be9c","observation_id":"4682e0eb-dac7-4aea-baf4-1e65d393568a","resolution":{"observed_at":"2026-08-06T13:21:59.053712Z","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":"2026-08-06T13:21:59.057639Z","title":"Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the neural tangent kernel","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.057639Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:01d2d095c40e4b686f46cafbf3409f17e49112cb783784247ec5e0e8c4002729","observation_id":"5d56282c-6df1-44f7-b79b-d48aaf4697a6","resolution":{"observed_at":"2026-08-06T13:21:59.057639Z","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":"2026-08-06T13:21:59.062158Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.062158Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ac22098b3a3117e34518073fa04c34b917c00887dd0bb29bec883271f95a170e","observation_id":"daba7c58-f9ab-426a-98e2-11462cf15873","resolution":{"observed_at":"2026-08-06T13:21:59.062158Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.02736","last_updated":"2019-06-06T17:55:17Z","snapshot_observed_at":"2026-07-06T07:58:33.660998Z","submitted_at":"2019-06-06T17:55:17Z","title":"DeepMDP: Learning Continuous Latent Space Models for Representation Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.02736","snapshot_observed_at":"2026-08-06T13:21:59.066940Z","title":"Bellemare","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.066940Z"},"links":{"cited_paper":"/paper/1906.02736","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c912472564f0298c76c8873108efce80bd2e7af40c78cd6c5d993b726b8717aa","observation_id":"d144d254-f2f0-47fa-967b-34acd13e5d9c","resolution":{"observed_at":"2026-08-06T13:21:59.066940Z","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":"2026-08-06T13:21:59.071283Z","title":"Dean, and Matthew Greig","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.071283Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a2edeba35971e91d721950d46a00a926f1e782248dbbb3783921882f2a9e9793","observation_id":"76e8b799-ceac-4fdc-bf58-5be77980d902","resolution":{"observed_at":"2026-08-06T13:21:59.071283Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.11500","last_updated":"2020-12-03T16:48:43Z","snapshot_observed_at":"2026-07-06T08:24:29.472112Z","submitted_at":"2019-09-25T13:56:56Z","title":"Modelling the influence of data structure on learning in neural networks: the hidden manifold model","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.11500","snapshot_observed_at":"2026-08-06T13:21:59.076281Z","title":"Modelling the influence of data structure on learning in neural networks","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.076281Z"},"links":{"cited_paper":"/paper/1909.11500","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:6621e35b1f310fe1a41a1ca9fec79a0eb4f052af0dda926a3c916e9f2491ad24","observation_id":"42b5ccb4-cf05-45b5-ba70-a06f8da45991","resolution":{"observed_at":"2026-08-06T13:21:59.076281Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1901.10902","last_updated":"2023-12-05T19:00:24Z","snapshot_observed_at":"2026-07-06T07:30:02.711178Z","submitted_at":"2019-01-30T15:33:58Z","title":"InfoBot: Transfer and Exploration via the Information Bottleneck","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.10902","snapshot_observed_at":"2026-08-06T13:21:59.080576Z","title":"Botvinick, H","venue":null,"work_id":null,"year":1901},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.080576Z"},"links":{"cited_paper":"/paper/1901.10902","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:e9f9afb6fae1a8c2cb30bdc01fbd2e78b059d394b698490c10dc41be2a210fd3","observation_id":"16d329ad-e52d-43d1-aa24-275f6b226a1f","resolution":{"observed_at":"2026-08-06T13:21:59.080576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.10667","last_updated":"2019-06-25T17:04:48Z","snapshot_observed_at":"2026-08-03T23:56:12.795379Z","submitted_at":"2019-06-25T17:04:48Z","title":"Reinforcement Learning with Competitive Ensembles of Information-Constrained Primitives","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.10667","snapshot_observed_at":"2026-08-06T13:21:59.084880Z","title":"Reinforcement learning with competitive ensembles of information-constrained primitives","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.084880Z"},"links":{"cited_paper":"/paper/1906.10667","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:f7a87860a26c814385555a7f284d6586cda14527e0ad323129e985641b5c7af8","observation_id":"c3c1d950-00bf-406f-882d-60665d99b055","resolution":{"observed_at":"2026-08-06T13:21:59.084880Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2004.11935","last_updated":"2020-04-24T18:29:31Z","snapshot_observed_at":"2026-07-06T09:15:04.500758Z","submitted_at":"2020-04-24T18:29:31Z","title":"The Variational Bandwidth Bottleneck: Stochastic Evaluation on an Information Budget","version":1},"cited_work":{"arxiv_id":"2004.11935","doi":null,"metadata_source":"pith","pith_arxiv_id":"2004.11935","snapshot_observed_at":"2026-08-06T13:21:59.937447Z","title":"The Variational Bandwidth Bottleneck: Stochastic Evaluation on an Information Budget","venue":"stat.ML","work_id":"e0abe2f7-acba-4c6f-839a-265aef2218b9","year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.089129Z"},"links":{"cited_paper":"/paper/2004.11935","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:18b58f9d84ded50b90da7e7b2c8463993e7e3e9d834490644850c0596a6ec382","observation_id":"ff286f95-761f-45eb-86d6-7b40c8ec82a2","resolution":{"observed_at":"2026-08-06T13:21:59.963661Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:59.093643Z","title":"Differential Topology","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.093643Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:79bf42a2e53a0df489efd5bbda2201fa67950c4b2a6fe179b0eec93aacdbd04b","observation_id":"44f87cf0-d50b-4288-a3da-9e052f1e9223","resolution":{"observed_at":"2026-08-06T13:21:59.093643Z","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":"2026-08-06T13:21:59.097914Z","title":"Abbeel, and Sergey Levine","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.097914Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:232ad2787a1ce1e5e077045a292361f729d66a3dd60fc3ffa59f9d6c364acc49","observation_id":"9845de0f-5c01-40e2-a103-c1178fe1917d","resolution":{"observed_at":"2026-08-06T13:21:59.097914Z","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":"2026-08-06T13:21:59.101775Z","title":"Abbeel, and Sergey Levine","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.101775Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:2ff71738af578c391aeb39e4e4d6a9921b49e9208a55a3d591cfe129d2bb0a11","observation_id":"6f284e50-0545-498e-bbd5-488a4694f3d9","resolution":{"observed_at":"2026-08-06T13:21:59.101775Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.05989","last_updated":"2019-09-13T00:21:53Z","snapshot_observed_at":"2026-07-06T08:21:22.995250Z","submitted_at":"2019-09-13T00:21:53Z","title":"Finite Depth and Width Corrections to the Neural Tangent Kernel","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.05989","snapshot_observed_at":"2026-08-06T13:21:59.105846Z","title":"Finite depth and width corrections to the neural tangent kernel","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.105846Z"},"links":{"cited_paper":"/paper/1909.05989","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:20efcd2c75b7bd9eaa7032cac90bd2682f41de4e7820ffd4ad332bde8ecd5126","observation_id":"fa5e187f-70e8-4010-9a74-2e23a7bae86e","resolution":{"observed_at":"2026-08-06T13:21:59.105846Z","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":"2026-08-06T13:21:59.109960Z","title":"Gaussian error linear units (gelus)","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.109960Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c1f93bbbb1637452e037a0061c6c2735a586c50f4781bdf3a12cdce5bf85f747","observation_id":"313ed717-dd00-49a3-bee8-dfa259495b13","resolution":{"observed_at":"2026-08-06T13:21:59.109960Z","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":"2026-08-06T13:21:59.113523Z","title":"Cleanrl: High-quality single-file implementations of deep reinforcement learning algorithms","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.113523Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:1a67d16df03bd78e89be83716f97c830a86bc7029bc4ccf7ce97d5e368dceb86","observation_id":"cc1d54d6-9129-430f-87c1-83b38a46a01c","resolution":{"observed_at":"2026-08-06T13:21:59.113523Z","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":"2026-08-06T13:21:59.117412Z","title":"Safe reinforcement learning on autonomous vehicles","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.117412Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c2a72c1bf4b9662fedf41baf9ced3b4aadccecd6fa6b79ec882de3a8b2ea5b95","observation_id":"4fd384e7-e9c5-4e1b-8009-67a969e68f0d","resolution":{"observed_at":"2026-08-06T13:21:59.117412Z","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":"2026-08-06T13:21:59.121292Z","title":"Nonlinear control systems: an introduction","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.121292Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:09b72c407332753aaf2f0f29e25a6a95c1845df07cffca3f3038f48ba844b501","observation_id":"5cf97488-ecb2-46e2-a387-bc4c0a1cd99a","resolution":{"observed_at":"2026-08-06T13:21:59.121292Z","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":"2026-08-06T13:21:59.125020Z","title":"Mofijul Islam, Samin Yeasar Arnob, Tariq Iqbal, Xin Li, Anirudh Goyal, Nicolas Manfred Otto Heess, and Alex Lamb","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.125020Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:e1a3ede65a86e0f5d4021b944508c0f87d1a1627af669cd60c08d2191215b9cf","observation_id":"001f273a-613e-4830-9a33-68e1e72c7228","resolution":{"observed_at":"2026-08-06T13:21:59.125020Z","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":"2026-08-06T13:21:59.128694Z","title":"Gabriel, and C","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.128694Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:16e7312854505d1f696ff113514999c9a45aa79d902505817ce61903a466216d","observation_id":"03c49da4-1cd6-47c1-9849-00adffffb0e8","resolution":{"observed_at":"2026-08-06T13:21:59.128694Z","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":"2026-08-06T13:21:59.132170Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.132170Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:0138fb824f09a0188b3878c0ea02fda0b20a56d55e428d74691755cffe97ca57","observation_id":"3b89959c-3098-4c57-aa47-f42782c57686","resolution":{"observed_at":"2026-08-06T13:21:59.132170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.02887","last_updated":"2022-10-04T01:39:32Z","snapshot_observed_at":"2026-07-06T13:18:02.186241Z","submitted_at":"2022-06-06T20:25:20Z","title":"Sample Complexity of Nonparametric Off-Policy Evaluation on Low-Dimensional Manifolds using Deep Networks","version":2},"cited_work":{"arxiv_id":"2206.02887","doi":null,"metadata_source":"pith","pith_arxiv_id":"2206.02887","snapshot_observed_at":"2026-08-06T13:21:59.872881Z","title":"Sample Complexity of Nonparametric Off-Policy Evaluation on Low-Dimensional Manifolds using Deep Networks","venue":"cs.LG","work_id":"320982d7-3843-45a5-aad5-6b0095916a72","year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.135940Z"},"links":{"cited_paper":"/paper/2206.02887","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:554642e92088b6f3438d53b58502a15fc512caaa596d7739dbe8bbb4a2293ef8","observation_id":"53e649d8-2575-40cc-b872-374ba143f0d0","resolution":{"observed_at":"2026-08-06T13:21:59.891311Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:21:59.139829Z","title":"Policy gradient and actor-critic learning in continuous time and space: Theory and algorithms","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.139829Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:c1cfe96b721d196412f5d2d9e3cffff02d90b4797bf220a4baeaa75e974d07db","observation_id":"754a29fb-4b0d-463e-a9a1-2b3d5a0b96c7","resolution":{"observed_at":"2026-08-06T13:21:59.139829Z","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":"2026-08-06T13:21:59.143360Z","title":"Policy gradient and actor-critic learning in continuous time and space: Theory and algorithms","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.143360Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:57248f63d666305442d579bba03ba55683d0e22d6941c62058469d04a8ce060b","observation_id":"4e7479a2-9b62-49da-93c3-e222a55429e2","resolution":{"observed_at":"2026-08-06T13:21:59.143360Z","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":"2026-08-06T13:21:59.146759Z","title":"q-learning in continuous time","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.146759Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:91cf448ab81bc4e36cf793338638f4c1921ba48f7bbbbb930e1693bcd476ed8c","observation_id":"018fa734-7ba4-478b-84dd-704b159a2a9f","resolution":{"observed_at":"2026-08-06T13:21:59.146759Z","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":"2026-08-06T13:21:59.150931Z","title":"Machado, and George Dimitri Konidaris","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.150931Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8bf43b6a08cae6e15ffb2c35dc4522167a00edb2242a84a397d373d326fd77ea","observation_id":"948edcbd-5ed7-4ca4-9fe1-2faa77a81189","resolution":{"observed_at":"2026-08-06T13:21:59.150931Z","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":"2026-08-06T13:21:59.154990Z","title":"Geometric control theory","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.154990Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:2c9655566b0c2d0ec3376d77b2b73a23152cc1d7f60700b0093906994953bc71","observation_id":"2b86181b-5ce2-4bb3-a52a-e989f1d78995","resolution":{"observed_at":"2026-08-06T13:21:59.154990Z","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":"2026-08-06T13:21:59.159120Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.159120Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8d2e97ac3218078cbafaa6789434db5a24eea99cb2620174a973bea08745bfc0","observation_id":"721b182a-a593-4aa5-a06c-e82dc64cdaa8","resolution":{"observed_at":"2026-08-06T13:21:59.159120Z","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":"2026-08-06T13:21:59.162606Z","title":"On the general theory of control systems","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.162606Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:1344404db5fc4596de72ad38e462964f9ddb8d9adb3542f109d0433ebad270fa","observation_id":"85cefb57-eb36-4e86-9214-590ae3f2c417","resolution":{"observed_at":"2026-08-06T13:21:59.162606Z","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":"2026-08-06T13:21:59.166339Z","title":"Brownian motion and stochastic calculus, volume 113","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.166339Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:7986264c3f68a14e0c7235a5c6a7de3d6fdb4b2d2ae54a057b7472a628beca28","observation_id":"63ebd142-7283-431b-85be-318f0072a0bc","resolution":{"observed_at":"2026-08-06T13:21:59.166339Z","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":"2026-08-06T13:21:59.170377Z","title":"Champion-level drone racing using deep reinforcement learning","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.170377Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:fcc0aed40bae36b12ffa5f57db43e6d5a39e5820a3c629e1a51d3041886842c0","observation_id":"1bba5805-7e3d-4091-a553-a7f6f1105538","resolution":{"observed_at":"2026-08-06T13:21:59.170377Z","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":"2026-08-06T13:21:59.174054Z","title":"Actor-critic algorithms","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.174054Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:e1f966e6335ab49bfa18d01f3419f6808f86a33d2969191ce5f6442acb1d2982","observation_id":"2753443b-2e3a-4201-8966-377c87870e2f","resolution":{"observed_at":"2026-08-06T13:21:59.174054Z","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":"2026-08-06T13:21:59.178439Z","title":"Bellemare, and Pablo Samuel Castro","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.178439Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8ea33b72ea227538c82c4564f8cddcf559b2ea2bc67f599279f3dba0dcaee925","observation_id":"9fca9d99-69f2-4503-a96c-db6e6512667d","resolution":{"observed_at":"2026-08-06T13:21:59.178439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.00165","last_updated":"2018-03-03T00:45:00Z","snapshot_observed_at":"2026-08-04T10:06:19.819372Z","submitted_at":"2017-11-01T02:13:25Z","title":"Deep Neural Networks as Gaussian Processes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.00165","snapshot_observed_at":"2026-08-06T13:21:59.182108Z","title":"Deep neural networks as gaussian processes","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.182108Z"},"links":{"cited_paper":"/paper/1711.00165","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:2944907ee7c6ffb7475147fbad5238f8be26ba9daa31c0d9c6d8c2b8466b4af1","observation_id":"89a122e8-b1cc-451d-ab03-194395c7c7ea","resolution":{"observed_at":"2026-08-06T13:21:59.182108Z","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":"2026-08-06T13:21:59.186382Z","title":"Wide neural networks of any depth evolve as linear models under gradient descent","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.186382Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a00fe20ed15a68eb17f22522683586c9d98211f3a469efd8edc51bcb6ee293cf","observation_id":"d4448537-51a4-4e6f-bdac-0a848020d41f","resolution":{"observed_at":"2026-08-06T13:21:59.186382Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1504.00702","last_updated":"2016-04-19T01:33:13Z","snapshot_observed_at":"2026-08-07T08:47:12.679573Z","submitted_at":"2015-04-02T22:23:51Z","title":"End-to-End Training of Deep Visuomotor Policies","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1504.00702","snapshot_observed_at":"2026-08-06T13:21:59.190442Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.190442Z"},"links":{"cited_paper":"/paper/1504.00702","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8f5d710ca3e1679fa524e4d927f2bd777b97c0cc7b449b64982e968135bfa4b5","observation_id":"5fc29351-5b4b-4792-8835-3e7aa74a33e2","resolution":{"observed_at":"2026-08-06T13:21:59.190442Z","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":"2026-08-06T13:21:59.194445Z","title":"Convergence analysis of two-layer neural networks with relu activation","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.194445Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:b5979d49f41e99f0e89be05448640da062447ba765c549516eef3fbb55cdbbfb","observation_id":"249eee52-e398-48db-83d9-1230ed2cc91c","resolution":{"observed_at":"2026-08-06T13:21:59.194445Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1509.02971","last_updated":"2019-07-05T10:47:27Z","snapshot_observed_at":"2026-07-06T04:29:24.362640Z","submitted_at":"2015-09-09T23:01:36Z","title":"Continuous control with deep reinforcement learning","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1509.02971","snapshot_observed_at":"2026-08-06T13:21:59.202353Z","title":"Continuous control with deep reinforcement learning","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.202353Z"},"links":{"cited_paper":"/paper/1509.02971","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ea0d893f63b6535e6bfde35958ed3606dd5febdb2db7fa6531116289a09040ac","observation_id":"481ffa8c-ac0a-40d6-96f3-a683d85ebb39","resolution":{"observed_at":"2026-08-06T13:21:59.202353Z","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":"2026-08-06T13:21:59.206240Z","title":"Robot reinforcement learning on the constraint manifold","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.206240Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:eab0a8d868ff3d8fb7199efdec6c4e1be3b1cb77606756b1b2319b848364adcd","observation_id":"3d902293-65b4-4ce7-ac8c-0f3e35923b53","resolution":{"observed_at":"2026-08-06T13:21:59.206240Z","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":"2026-08-06T13:21:59.210040Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.210040Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:84abeecf742d88e2026d346f4dce25d9c0f85f78e6bbe21e5b077714f1a53fd4","observation_id":"551c0001-0c3c-496c-bb21-2b6f5c3c748c","resolution":{"observed_at":"2026-08-06T13:21:59.210040Z","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":"2026-08-06T13:21:59.213977Z","title":"Segmentation of multivariate mixed data via lossy data coding and compression","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.213977Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:dd7d2029a915c635275c82356bbc32a8d513d2948fb1fd42d442793d7c583438","observation_id":"c3bd6b6a-7bdd-45a3-a061-13c9c0647c5a","resolution":{"observed_at":"2026-08-06T13:21:59.213977Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1703.00956","last_updated":"2017-06-16T02:52:21Z","snapshot_observed_at":"2026-07-06T05:32:10.485822Z","submitted_at":"2017-03-02T21:31:29Z","title":"A Laplacian Framework for Option Discovery in Reinforcement Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1703.00956","snapshot_observed_at":"2026-08-06T13:21:59.218530Z","title":"Machado, Marc G","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.218530Z"},"links":{"cited_paper":"/paper/1703.00956","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ddd0a8e0160d92c4f4189ec080c2e1208caaca12fb94bfd5ba0598e20c38e619","observation_id":"1d8863d3-150e-436e-9137-53a73fb1006a","resolution":{"observed_at":"2026-08-06T13:21:59.218530Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.11089","last_updated":"2018-02-23T21:55:05Z","snapshot_observed_at":"2026-07-06T06:06:48.906444Z","submitted_at":"2017-10-30T17:36:19Z","title":"Eigenoption Discovery through the Deep Successor Representation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.11089","snapshot_observed_at":"2026-08-06T13:21:59.222723Z","title":"Machado, Clemens Rosenbaum, Xiaoxiao Guo, Miao Liu, Gerald Tesauro, and Murray Campbell","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.222723Z"},"links":{"cited_paper":"/paper/1710.11089","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:970e9ab6e9f57965d9a7c16d1fbc4c5968baea6fac66e32c23c3603ed0a87ae0","observation_id":"d8400d7f-3e3b-4d0b-8397-b22e6845d0e0","resolution":{"observed_at":"2026-08-06T13:21:59.222723Z","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":"2026-08-06T13:21:59.226702Z","title":"Proto-value functions: developmental reinforcement learning","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.226702Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:b8c59663eeae555db700c622ff056b2b7407763d57885bfffc15e71939784d23","observation_id":"68381462-0967-4edf-9eb5-04461aa72ab5","resolution":{"observed_at":"2026-08-06T13:21:59.226702Z","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":"2026-08-06T13:21:59.230316Z","title":"Proto-value functions: A laplacian framework for learning representation and control in markov decision processes","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.230316Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:36e84bfd83fbe3515b84fdac0e670b5f60c4e3a10bad7c2599b76f2dde47692b","observation_id":"db08da4b-e919-4e4d-9b5d-c4dc93897eb1","resolution":{"observed_at":"2026-08-06T13:21:59.230316Z","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":"2026-08-06T13:21:59.233902Z","title":"Approximate gradient methods in policy-space optimization of markov reward processes","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.233902Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:bd94d71fdf2c5bf031e1d87b90140644f17519228f6699b47d873f6da89939ec","observation_id":"00498fb3-d68d-46d7-ae4e-eda7e526abdd","resolution":{"observed_at":"2026-08-06T13:21:59.233902Z","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":"2026-08-06T13:22:06.472764Z","title":"A mean field view of the landscape of two-layer neural networks","venue":null,"work_id":"41d6d394-b52c-4738-91f2-8641c46dfdcd","year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.237872Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:052a8d7d29559756f8ee2211931173193acaf8ff036593eac98a7384d95e31e4","observation_id":"7889a8d7-e95c-48c9-b11d-6b55c10d6425","resolution":{"observed_at":"2026-08-06T13:22:06.534016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:06.344810Z","title":"A mean field view of the landscape of two-layer neural networks","venue":null,"work_id":"b7d99ce7-2f36-4d7e-9d1e-641038c5317b","year":2018},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.241408Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:73c021eb7b95e74b2c04c75d3b7aefa227b1d73ddf41a77a15aeafcb6f6c84f9","observation_id":"0a70f1fa-3a35-4fbb-b718-ee1c48e424a2","resolution":{"observed_at":"2026-08-06T13:22:06.445200Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:06.175423Z","title":"Rusu, Joel Veness, Marc G","venue":null,"work_id":"daacc7db-4852-4dfd-8953-3c89cab53ab8","year":2015},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.244994Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:0852ebf3c70d92b35d87630a94444ac49e5e2e6841f7d508f59ee35272354a66","observation_id":"5bb4512c-e3c0-44c0-80eb-b7fe66e2d5c2","resolution":{"observed_at":"2026-08-06T13:22:06.266209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.954674Z","title":"A case study in approximate linearization: The acrobat example","venue":null,"work_id":"652c83fc-9e04-43f8-ba02-5775899914bf","year":1991},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":88,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.248880Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:fdd44e474805de663f1e389fe235276d9fe774fb69982eef442442550952297b","observation_id":"617e6dbb-4e78-4a87-9904-4effbcd11578","resolution":{"observed_at":"2026-08-06T13:22:06.063336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.801141Z","title":"Nair and Geoffrey E","venue":null,"work_id":"ac3fccaa-364c-4d45-8c9c-04bdedbaa273","year":2010},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":89,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.252539Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:0aeac9520a4d0352b9ff6df0f56586ef720a002f916f9baa780172de40010631","observation_id":"72414ee1-42a6-49cb-bb42-00519f9dcd5e","resolution":{"observed_at":"2026-08-06T13:22:05.887242Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.634966Z","title":"Non-linear dynamical control systems","venue":null,"work_id":"66b2ffa7-994a-4ed5-8e26-115a4594e855","year":1990},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.256103Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:8b3ff7e6878c80a28a2594f8f3f7c1d592a17b31952e63a4e0a749fdc7a2c50c","observation_id":"a6933872-83c9-44b5-86d9-2c647672107b","resolution":{"observed_at":"2026-08-06T13:22:05.709793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.418854Z","title":"Geometric compression of invariant manifolds in neural networks","venue":null,"work_id":"fdfdbf01-1af8-4e4e-a655-df0f589a07ad","year":2021},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":91,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.260389Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ad424578e666f0c24c11759a901f0c39cb2ba4533b6b24264480b7dc8c578c8d","observation_id":"ee69a4f9-df4d-4e1a-a7ac-571686b8386c","resolution":{"observed_at":"2026-08-06T13:22:05.542471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.276581Z","title":"Masked completion via structured diffusion with white-box transformers","venue":null,"work_id":"85da2f9f-efc3-4b97-ad83-c2115dbf2b71","year":2024},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":92,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.264809Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:587324012cb8cd41586e6f1a908cade152020395b4f811e4f62e6307cb63cd32","observation_id":"9019261e-98a3-4c24-9c76-ca8987ea43da","resolution":{"observed_at":"2026-08-06T13:22:05.322095Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:05.099201Z","title":"Bronstein, and Ron Kimmel","venue":null,"work_id":"835f3655-b550-4333-a4ea-e5c934488003","year":2019},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":93,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.268582Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:335b47fa41a71973c499d963aa4017fc5ecae520e1b5488966576eb90d3a8336","observation_id":"4a23057f-6955-4503-9557-feefa8953357","resolution":{"observed_at":"2026-08-06T13:22:05.177709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2008.20096","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:21:59.799169Z","title":"A contraction theory approach to stochastic incremental stability","venue":null,"work_id":"bdbb9844-8907-472b-a41f-10e3a99ef2df","year":2009},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":94,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.272275Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:a8885a498b98474a2f0ff51987d2c977b424ae7b14f155afa078f944062484a9","observation_id":"fe315fec-f990-4265-a9ff-ff3e916b4b98","resolution":{"observed_at":"2026-08-06T13:21:59.805638Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:04.994941Z","title":null,"venue":null,"work_id":"8e121b51-2c69-433d-aa6c-ac5418f9484e","year":2001},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":95,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.276027Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:0786ba30ce5dd0ba283b54ba426698ce8d16a61d127af7cfb5170541a5fad49b","observation_id":"6df99f60-73a8-449a-820a-24bb5973f043","resolution":{"observed_at":"2026-08-06T13:22:05.031893Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:04.845310Z","title":null,"venue":null,"work_id":"dce2591e-e469-4ef7-8567-0ee6ab45b92f","year":2002},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":96,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.280043Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:d36cbe72f753f34f146a82c584cfef7694a233d94dd6eb3c6f50062b419eb692","observation_id":"2a571ed7-a38e-42de-b536-0e5d5a68b13f","resolution":{"observed_at":"2026-08-06T13:22:04.907935Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:04.707638Z","title":null,"venue":null,"work_id":"341715b5-7faa-4f4b-9b13-81952d3a7690","year":2003},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":97,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.284750Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:b64a36bdfb70ab2e31247c17e9f08d86bd5926c0ad5e4377ed0a97001ac0183d","observation_id":"1b2b0728-c285-496d-ba1a-44a16968fe52","resolution":{"observed_at":"2026-08-06T13:22:04.796428Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:04.573277Z","title":"Controllability of dynamical systems with constraints","venue":null,"work_id":"6f56a006-ce6b-47de-be7c-4958217be61f","year":2005},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":98,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.289435Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:7687e20346a00b215c218f4e5f0097c6a811b2bdc9d7474ee1d693da376c8c5b","observation_id":"c3516e98-bfa9-44e0-b99f-e3f188c2edb1","resolution":{"observed_at":"2026-08-06T13:22:04.662542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T13:22:04.480750Z","title":"Robbin, Uw Madison, and Dietmar A","venue":null,"work_id":"695b7921-ec2f-4c66-87e7-88ef0eede0e6","year":2011},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":99,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.293841Z"},"links":{"citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:575240c217b84fd1cbc1c530718d63b640c119c7257ee02cad83ae650196d837","observation_id":"2d7c6e26-645a-4788-837b-44e5e543e107","resolution":{"observed_at":"2026-08-06T13:22:04.513009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.00695","last_updated":"2019-08-02T04:01:13Z","snapshot_observed_at":"2026-07-06T08:11:54.225838Z","submitted_at":"2019-08-02T04:01:13Z","title":"Deep ReLU network approximation of functions on a manifold","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.00695","snapshot_observed_at":"2026-08-06T13:21:59.297979Z","title":"Deep relu network approximation of functions on a manifold","venue":null,"work_id":null,"year":1908},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.297979Z"},"links":{"cited_paper":"/paper/1908.00695","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:706abbf3593e0f713d7ded5fc8ec63d6436f6a2d293af8d033bfffd0302e65c7","observation_id":"fca51baf-0015-4f99-9521-56001d4c9882","resolution":{"observed_at":"2026-08-06T13:21:59.297979Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1502.05477","last_updated":"2017-04-20T18:04:12Z","snapshot_observed_at":"2026-07-06T04:09:39.172428Z","submitted_at":"2015-02-19T06:44:25Z","title":"Trust Region Policy Optimization","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1502.05477","snapshot_observed_at":"2026-08-06T13:21:59.302552Z","title":"Levine, P","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces","version":1},"reference_index":101,"source":"arxiv_source","source_observed_at":"2026-08-06T13:21:59.302552Z"},"links":{"cited_paper":"/paper/1502.05477","citing_paper":"/paper/2507.20853"},"observation_digest":"sha256:ef2e792541fe93f979788b099921bc9d743f6766582b3b8854ea61e16cbee9a1","observation_id":"9ea839da-ea4b-45eb-b3c9-9d34e1dd3306","resolution":{"observed_at":"2026-08-06T13:21:59.302552Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.20853","last_updated":"2025-07-28T14:06:44Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T16:02:23.108264Z","submitted_at":"2025-07-28T14:06:44Z","title":"Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":3,"parse_uncertain":0,"unresolved":80,"verified_exact":6,"verified_fuzzy":11},"total_outbound_references":142},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 100 of 142 outbound references and 0 inbound Pith citation observations for arXiv:2507.20853."}