{"as_of":"2026-08-13T04:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b33690314f9f23fe1d73798ab160c8536d0705198e89f7725935d78e942e8b04","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:00:01.413267Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2608.06843/citation-record","integrity":"/paper/2608.06843/integrity","json":"/paper/2608.06843/citation-record.json","paper":"/paper/2608.06843"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.04108","last_updated":"2024-11-06T18:36:21Z","snapshot_observed_at":"2026-08-12T22:06:16.693607Z","submitted_at":"2024-11-06T18:36:21Z","title":"Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04108","snapshot_observed_at":"2026-08-10T20:00:01.160630Z","title":"Weighted Sobolev approximation rates for neural networks on unbounded domains.arXiv preprint arXiv:2411.04108, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.160630Z"},"links":{"cited_paper":"/paper/2411.04108","citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:818c661af96f1b9b66477dd1ad8a0955d449212ddeeaf1143da7f0475ba60f4f","observation_id":"9f0d443f-ff5a-409f-8fa0-bcbce96b1ea0","resolution":{"observed_at":"2026-08-10T20:00:01.160630Z","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":"2026-08-10T20:00:02.209769Z","title":"Approximations with deep neural networks in Sobolev time-space.Anal","venue":null,"work_id":"d09c993a-f049-4411-a520-2a1181d4b257","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.170039Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:576ca139bd7e5a5ae89297d9f511bb339e34b6283b074d9119481d371fe2a22a","observation_id":"8e5751f0-af9e-481f-b08f-2385bcfc677c","resolution":{"observed_at":"2026-08-10T20:00:02.216216Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.190723Z","title":"Breaking the curse of dimensionality with convex neutral networks.J","venue":null,"work_id":"1eb2a950-e23f-4e50-a7a3-f3f97d4e7861","year":2017},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.178448Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:94fcd1d86c706ab539de8e3ce341e8c55b610ef3467dc867e029324b31c0ae9d","observation_id":"34ae0e28-8c32-4bcd-979f-f2ff30b1472d","resolution":{"observed_at":"2026-08-10T20:00:02.197100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.171789Z","title":null,"venue":null,"work_id":"a03a6a72-e96b-40b8-af53-43e48d45e210","year":1993},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.187305Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:aff0c6e74437530dc2d8ff3b6224f15d28c45bb25f4cb2d0a2401ef7ccf0ceca","observation_id":"e8d27bb1-82d4-4491-80fa-e2a0de5f07c3","resolution":{"observed_at":"2026-08-10T20:00:02.178065Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.152726Z","title":"Analysis of Tikhonov regularization for function approximation by neural networks.Neural Networks, 16(1):79–90, 2003","venue":null,"work_id":"4a22f00e-2c40-47b2-9ab0-f4eb9ba04ac0","year":2003},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.193713Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:63a588827f131d47a17b31c55048fbea4588f0ad8d992512f2325e1f4a715835","observation_id":"20d30bd2-1550-4f64-b36b-b1f9d29a3184","resolution":{"observed_at":"2026-08-10T20:00:02.158298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.133401Z","title":"A regularity theory for static Schrödinger equations onRd in spectral Barron spaces.SIAM J","venue":null,"work_id":"dc23818e-e670-43f1-85c2-fd7c832bf535","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.201088Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:90adee2e9e7361ad481dd29bd77b6fda164fee580693017d7824ce36bc238240","observation_id":"e5cc8ce1-c38f-4d20-a03a-06012f39b931","resolution":{"observed_at":"2026-08-10T20:00:02.139870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.06778","last_updated":"2026-05-16T00:05:58Z","snapshot_observed_at":"2026-08-07T07:05:26.657640Z","submitted_at":"2025-07-09T12:10:58Z","title":"Functional analysis and partial differential equations in spectral Barron spaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.06778","snapshot_observed_at":"2026-08-10T20:00:01.209020Z","title":"Functional analysis and partial differential equations in spectral Barron spaces.arXiv:2507.06778; to appear at SIAM J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.209020Z"},"links":{"cited_paper":"/paper/2507.06778","citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:32f1bcc57ab679d3e2a84391b26a5523b31e7d9b65ef812e170e23987619c4ed","observation_id":"514acb82-c015-4608-911f-502619594868","resolution":{"observed_at":"2026-08-10T20:00:01.209020Z","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":"2026-08-10T20:00:02.112472Z","title":"Cohn.Measure theory","venue":null,"work_id":"f56c5fc2-7624-4aee-8ddb-4a5d58ee99d6","year":2013},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.214932Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:e516b4df189ed73514ad29cf5f9c663f4e91c4e251c9e134fa3b92f9176c7b37","observation_id":"67351a61-3bc9-4e8e-8e91-6be3a5588a48","resolution":{"observed_at":"2026-08-10T20:00:02.118598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.092735Z","title":"Approximation by superpositions of a sigmoidal function.Math","venue":null,"work_id":"84cec764-b2de-4544-bf8a-1e72cbbdc0ff","year":1989},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.220313Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:ac617d4624c9466423da53725c289c03e4f2f1a5148441f93bbe81042c778d21","observation_id":"67a1f26c-f8f4-435a-bf3e-024d428f0234","resolution":{"observed_at":"2026-08-10T20:00:02.098936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.071731Z","title":"Neural network approximation.Acta Numer., 30:327–444, 2021","venue":null,"work_id":"7054ab51-2f98-4191-92d6-5455aba60f0f","year":2021},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.227582Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:01600534327bc643b7ed7864b2d8548cfcbca75224d0053541aace23f15a511f","observation_id":"a3436e75-a999-427f-900d-71c96540a037","resolution":{"observed_at":"2026-08-10T20:00:02.078114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.053169Z","title":"The Barron space and the flow-induced function spaces for neural network models.Constr","venue":null,"work_id":"eaef3147-158b-4789-a5cb-ebdf3b1525fd","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.237781Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:b6d276c56fcf7dc3d2b078b1237ba649fc857bd37be87b699c1b396c0c215b7c","observation_id":"d5664784-e7a1-40b7-8bc6-086be01493fb","resolution":{"observed_at":"2026-08-10T20:00:02.058699Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.035781Z","title":"Engl, Martin Hanke, and Andreas Neubauer.Regularization of inverse problems","venue":null,"work_id":"64cb987d-4255-4f8f-b878-ebd61474c126","year":1996},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.244556Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:f1da7fe58ea4b8e0c7536d1e5d3f0e010cb704a293f8fe14b81f6177eefc1302","observation_id":"479580c3-d1f6-4710-bdb3-3a7fbbda8073","resolution":{"observed_at":"2026-08-10T20:00:02.040875Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.019233Z","title":"Approximation spaces of deep neural networks.Constr","venue":null,"work_id":"cbdf122c-1c3c-438e-acde-2a90e0c1a491","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.253315Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:eaa055ece319c8bd804af3e3e26385f6881b9b4e197280f771520e2a51b34b77","observation_id":"0a4639bd-f82b-451c-96ea-5521ad0676c9","resolution":{"observed_at":"2026-08-10T20:00:02.024930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:02.002231Z","title":"Schwenninger, and Christoph Brune","venue":null,"work_id":"432050b5-1c07-4214-b5c5-9f7c1fc9ebd6","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.260423Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:a08ccc756f80d9ba2c541564c3f0c1b5d887c6830f5c76310aa6cbfac705fc05","observation_id":"3dc86fbd-1474-4c55-8927-b51c9f917ae3","resolution":{"observed_at":"2026-08-10T20:00:02.007954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.267672Z","title":"Approximation capabilities of multilayer feedforward networks.Neural Networks, 4(2):251–257, 1991","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.267672Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:aab8ea2e142d190a82c4a5c89e02968878965b53fe6c29732f4d379d8eef6e82","observation_id":"4219ae39-0d7d-4ec4-a8ad-381f625a815a","resolution":{"observed_at":"2026-08-10T20:00:01.267672Z","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":"2026-08-10T20:00:01.972131Z","title":"Deep neural networks with ReLU-sine-exponential activations break curse of dimensionality in approximation on Hölder class.SIAM J","venue":null,"work_id":"eeb557aa-c462-46aa-a134-0662b49a1cc7","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.273145Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:89d1623c937389f80343e1f2974c7880b73b4a3ea8cffba5c585cdbd4a343411","observation_id":"58ccef6d-1b43-486d-bcf8-6246de01097a","resolution":{"observed_at":"2026-08-10T20:00:01.977983Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.956132Z","title":"Klusowski and Andrew R","venue":null,"work_id":"9dd46742-f9fe-4a06-81d5-c3b96fe954c8","year":2018},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.282603Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:314bed66ed0166ee8b56263d383bb9f6fe8ae5da3b9815a2ee81f9772a9bffed","observation_id":"cf467cef-c16b-4b7f-87af-218b2d486d72","resolution":{"observed_at":"2026-08-10T20:00:01.961068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.292305Z","title":"Deep learning.Nature, 521(7553):436–444, May 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.292305Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:68e2d41a3200a70ab0b133d3a0d21686a0ad64b7104cef06718e29da1de7635f","observation_id":"9d150868-6019-4213-83e0-e059ffadd54f","resolution":{"observed_at":"2026-08-10T20:00:01.292305Z","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":"2026-08-10T20:00:01.928062Z","title":"Pereverzev","venue":null,"work_id":"c79854d5-e4e1-4378-b5df-9129b3d408b7","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.298607Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:609378290965342bf99008d2dc9310c8a2fa1449442123dc3622fbbb89d5b90d","observation_id":"92e943c8-618b-4ae3-bd80-6aaea644507a","resolution":{"observed_at":"2026-08-10T20:00:01.933246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.911614Z","title":"Spectral Barron space for deep neural network approximation","venue":null,"work_id":"678d81e4-5dc4-4424-a2bf-2236857494c0","year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.304300Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:b917c6fc753b9660047ce811f47c56fcc1df52674414cfc59bf8694b382667fd","observation_id":"1c8680ec-4914-431a-b56e-30dcab36a47e","resolution":{"observed_at":"2026-08-10T20:00:01.916868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.312423Z","title":"Interpolation and inverse problems in spectral Barron spaces","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.312423Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:15866f9e6807a7dbaff1f3036f5d6be399b81add2279c06b46ba7cc8c4891758","observation_id":"8170ec7e-c1ee-4aaa-a374-b8ef561bd1cc","resolution":{"observed_at":"2026-08-10T20:00:01.312423Z","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":"2026-08-10T20:00:01.895007Z","title":"Pereverzev.Regularization theory for ill-posed problems, volume 58","venue":null,"work_id":"87a91b72-850f-4ad6-8671-50ea03b88f18","year":2013},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.317983Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:06f79c7f857453e4746abcf0da2dcc80f6954f7521f61d782daf2ae9842f0631","observation_id":"2beae09d-f5ea-4534-8e71-a43862fe5675","resolution":{"observed_at":"2026-08-10T20:00:01.900574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.875831Z","title":"A logical calculus of the ideas immanent in nervous activity (1943)","venue":null,"work_id":"81583e9d-4434-483d-8644-6a757a88f794","year":1943},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.324669Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:3238a50516f9cdaf5dc53fad501908dc82cbdb054cd56ee1dd5e096a0d2326a1","observation_id":"3faaf871-ca4a-4e94-a34e-4990a9d1fd9e","resolution":{"observed_at":"2026-08-10T20:00:01.880920Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.860456Z","title":"A new function space from Barron class and application to neural network approximation.Commun","venue":null,"work_id":"9d791e52-86a7-4199-a1e4-e9399b8da334","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.331103Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:6189bc1c4dac1e1b24d36773cac582cb562d857c9526d62a6100d486effd6c74","observation_id":"7c7aa1f8-f9b8-42d3-85a6-031966d44a03","resolution":{"observed_at":"2026-08-10T20:00:01.865661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.843843Z","title":null,"venue":null,"work_id":"a8a97cf2-17e5-4bcf-907e-1e0b2da685b6","year":1996},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.337673Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:7e62b628045eaae44cd3acd03f45526ec424a7e55168f888926073201d5b3902","observation_id":"7f22574c-2a5b-4f17-a381-96575048ca62","resolution":{"observed_at":"2026-08-10T20:00:01.848768Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.826923Z","title":null,"venue":null,"work_id":"e4ef9ca0-2e8c-474b-b485-ad481792500b","year":2021},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.342847Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:8861865af9f7714179e684d36f449ee121782f26d96267ed62d962e64e560b62","observation_id":"05c1584e-7f2f-4f64-906f-d70d467bf543","resolution":{"observed_at":"2026-08-10T20:00:01.831873Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.804386Z","title":"Longman Scientific & Technical, Harlow, 1993","venue":null,"work_id":"2046982e-ef38-45f1-a820-614148f177c5","year":1993},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.348198Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:6c97362dbcabb94e26c51a7217bca0d8657fd9582b6b3468a21ef909b3c0782f","observation_id":"4ad39eb6-084e-4146-ab47-0eb7278d28cc","resolution":{"observed_at":"2026-08-10T20:00:01.811896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.785662Z","title":"The perceptron: a probabilistic model for information storage and orga- nization (1958)","venue":null,"work_id":"3096b70f-beae-4aa8-b4f1-4e00cc2df4c7","year":1958},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.353821Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:834249420369c07688646bef1cbbc5acb50cc28fe35e1680c7e3452b9dd774d2","observation_id":"53219cb2-5348-4446-bb8c-4b09c2ef666d","resolution":{"observed_at":"2026-08-10T20:00:01.791975Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.767004Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"d1c5f6db-8f2c-4a5e-a7f6-e2a2e1b1bea2","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.359410Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:7e27ad14adc2cc5481ead61f5e21f61d1f8d6d7b76e1c6f8547226bf29988c9f","observation_id":"8f1f9d6e-c406-4a82-a9a2-44ff152598a7","resolution":{"observed_at":"2026-08-10T20:00:01.772217Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.748708Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"c8706e9a-28d7-4709-b37f-668ad9d6567f","year":2022},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.364298Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:6f2ff0979e463f87eec4384642cbe3fea93e3313063316b2da9b540abc323f44","observation_id":"1569c073-242a-460c-8357-cd0efc995d9c","resolution":{"observed_at":"2026-08-10T20:00:01.754661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.730170Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"df56cba2-3069-44aa-893a-3bdb88506571","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.370285Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:c92151e06cf1f3ce8e6d6001af65a61a00c056b4955feb847bab4aecfea51369","observation_id":"71744ada-ef9e-498d-afbc-0c490f6c9b8a","resolution":{"observed_at":"2026-08-10T20:00:01.735833Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.711866Z","title":"Siegel and Jinchao Xu","venue":null,"work_id":"256ad381-1849-4a21-a6d7-a0653fc87c3f","year":2024},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.376245Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:6665edbadf69be03ba6a1fda8bc32f4651b538810f5a8a2381654239d81c9a63","observation_id":"51b12a8c-bae7-45e6-8355-458fa47b9a11","resolution":{"observed_at":"2026-08-10T20:00:01.717471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.682769Z","title":"Implicit neural representations with periodic activation functions","venue":null,"work_id":"fc0b2c25-e3a1-4e81-aff3-fe1b6bc0681c","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.383019Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:536f6b3fb115e25368e301cc3472e1d12af0228d2e3e31b576fdd13dd425912d","observation_id":"cd5ecba6-e2e6-404d-a08d-e1bab533308a","resolution":{"observed_at":"2026-08-10T20:00:01.691050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.661710Z","title":"Embedding inequalities for Barron-type spaces.J","venue":null,"work_id":"7ae88621-b046-4c60-999d-838daf1f3ffa","year":2023},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.389325Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:aae86ffafe92f0ba5133a9c25feb79665e0bbd179999dfc9bb171e9af19dfd8a","observation_id":"7ae1ae9f-13b9-4c93-96ed-41fbb2258786","resolution":{"observed_at":"2026-08-10T20:00:01.667198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.640287Z","title":"Finite neuron method and convergence analysis.Commun","venue":null,"work_id":"b3b13309-2453-401f-a912-d7260cb6330f","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.397956Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:c8844bacdd8b91fc64513101eb7d4404d9be21e7ee5d3793d2378624e02be984","observation_id":"396f2e50-09fe-4658-88bb-2226429af796","resolution":{"observed_at":"2026-08-10T20:00:01.647085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-10T20:00:01.404048Z","title":"Error bounds for approximations with deep ReLU networks.Neural Networks, 94:103–114, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.404048Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:9ba28d000706348720f9b76a2b7ae0e2c0b6939d5267d34d88708a123ce881b8","observation_id":"edfd1d0d-71dc-4e53-a0eb-ee8bb91a3278","resolution":{"observed_at":"2026-08-10T20:00:01.404048Z","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":"2026-08-10T20:00:01.608271Z","title":"Universality of deep convolutional neural networks.Appl","venue":null,"work_id":"a51a06c4-cb9a-4815-b743-b3472b45df74","year":2020},"citing_paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T20:00:01.413267Z"},"links":{"citing_paper":"/paper/2608.06843"},"observation_digest":"sha256:8e067af68431c713c8ac194d091aa5d5c90eb1f9aa19d4b06ef8a29d660f58de","observation_id":"98703297-2cdf-499a-9fa1-6bbe89347188","resolution":{"observed_at":"2026-08-10T20:00:01.615855Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06843","last_updated":"2026-08-07T06:04:08Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-12T23:11:23.922352Z","submitted_at":"2026-08-07T06:04:08Z","title":"On Generalized Barron Spaces for Shallow Neural Networks"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":28},"total_outbound_references":37},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.06843."}