{"as_of":"2026-08-20T13:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a7615b132db58207c752d713834e1cad089f74e1bcb9126923937ebf490b2bb1","coverage":[{"denominator":87,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":87,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-11T06:01:25.773672Z","state":"measured"},{"denominator":87,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":87,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2607.05546/citation-record","integrity":"/paper/2607.05546/integrity","json":"/paper/2607.05546/citation-record.json","paper":"/paper/2607.05546"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"SIAM Journal on Mathematics of Data Science , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:9ba9465e4b11e825687edc6f5c3a19af8e3ace382a777488af841e1d2726fee1","observation_id":"3b49233f-ad1a-4318-b783-7914e2431cdb","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Annals of Statistics , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:ee464ee64526b1d54065af7dc226f9938670b12f10f214b46055f7a7248c2a58","observation_id":"c7febc6b-e9b7-4893-b563-c8da80094880","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"CSIAM Transactions on Applied Mathematics , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:a58a1c9aa6c2d869588100feb9428cdbc57db7da5d607d2ccdaa168b1be48d8e","observation_id":"179c81bf-0628-42a2-8444-3c2ea13a3dbe","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Calculus of Variations and Partial Differential Equations , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:d9724d257f69da135f26d579e6c660b5e64d9908fec77bd1f0db19942719ff4e","observation_id":"f9486d02-6d28-4f91-80a9-873cae929042","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on Learning Theory , pages=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:427afe66d383af944ad31c4d529e104381a1ea55eb6f2ab78f92ec4372abe207","observation_id":"11b4856d-30a6-4b69-9a0b-8439b10b7ce1","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:259a29e4a355205c1eae2b010ed79eb342b7838bfd024f3cb0675cee075378d6","observation_id":"69db82a0-cbf4-4a68-9be5-dce2674557e3","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of the ACM (JACM) , volume=","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:3f0c3988970bbc0897ac6f544b32e3d830c78f9d5da020076bb8f1546a206a1f","observation_id":"7a2f4af1-4aef-4847-aae0-7a2282041927","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"University of California, Irvine , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:62d7f50b0a740b047b6012ea3d81d963d056510d72c4b05358e4383b755a0d4e","observation_id":"52a34dc3-beb8-48f1-aba9-648de6483217","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"IEEE transactions on Information Theory , volume=","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:e731664e7ffd3a2e5eef70d358aaf2d271f0711220fff395f829a813ca8bd872","observation_id":"9f147a7b-6bee-4313-ba1c-a11fa2632339","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"International Conference on Computational Learning Theory , pages=","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:cb9ebb1067902b9ac5c9ea432b2352bdaac61d9949cfd0b6ffeb44aa223925b8","observation_id":"201d1294-29c9-4c74-87f9-7e2dbf57d4f4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:888e69e4d2bb6af9afc07e2929b302051b68f2dc3c091cf5e2bae738b39d6797","observation_id":"2205a953-cd30-488d-a986-b858188b0681","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"The Thirty Seventh Annual Conference on Learning Theory , pages=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:88d04ffc1709dd416a969660362060e82fb015a793254c4ca72d42390ab958ed","observation_id":"42a4dfc8-542b-4236-bb21-9c0f622fd338","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:dd6f4c0d5929567efa8ea8ac34ab301b7e7b2c2e782e04fe9e63fdc949cb43fd","observation_id":"30c40a14-7deb-43cd-b0ab-cee3e942f2dc","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Constructive Approximation , volume=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:fe2a7838c75e66b5f82f22883c341fcc19352cbd958024bedec7079371f3e0ab","observation_id":"e2a272c4-704a-44af-bd55-980f2c819fa5","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:b3d2ae7788a81c4a2cf99adf991cc4530e5a5ac927fc5d443ea7d6fead625c2e","observation_id":"2b1dac58-48d6-4864-9228-3fe19d118404","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Applied and Computational Harmonic Analysis , volume=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:b1e54c9a243c1b5058506392c9e1d8d09312fd521115663fbd6a52430bad07db","observation_id":"9bbc3628-455a-4dcd-b64b-da73607b6beb","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":", author=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:908b8eed4650d700705462ef245fbc60cd2c5fa884abcf8e757d9c8fd3bac759","observation_id":"fac10248-51dd-4311-bf7b-8f386f5a5290","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Applied and Computational Harmonic Analysis , volume=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:fa09dfd1300e4424d3d665414d8871db78401fbdaee252925f48d058dbfe28b3","observation_id":"cfb5485c-b07d-48ea-b42e-dbdc83564c44","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.03697","last_updated":"2025-01-07T11:01:24Z","snapshot_observed_at":"2026-08-16T12:59:32.178517Z","submitted_at":"2025-01-07T11:01:24Z","title":"Deep Networks are Reproducing Kernel Chains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.03697","snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:2501.03697 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"cited_paper":"/paper/2501.03697","citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:c63f3732e53cee0ba13d0ff60809749673ea762c4e69c64df0d46206cc05d232","observation_id":"00124186-0228-4bef-9825-19a78268fd58","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Proceedings of the American Mathematical Society , volume=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:b96281498cd83fd03fa33c5ced253b880ac9ca2a39bdde1d840803cfec7483e6","observation_id":"eb4174c5-7225-4dd8-a88e-2b3090256a96","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.01528","last_updated":"2018-06-05T07:37:59Z","snapshot_observed_at":"2026-08-19T15:36:23.044892Z","submitted_at":"2018-06-05T07:37:59Z","title":"The universal approximation power of finite-width deep ReLU networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.01528","snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:1806.01528 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"cited_paper":"/paper/1806.01528","citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:f23bc4dd9c2aed88305674bed705da390d382bfedb58af4830743d1961ecfced","observation_id":"c9a8da62-3b7e-45fd-80e9-91b5c3100dee","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of machine learning research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:3d43e3147ff951bc3c0e2db22bcb3870ae340ff046265277f13a02f04a66c841","observation_id":"1b109f5c-1eaf-4ed9-8065-6dea6e8f7605","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:6ca7341db9a6c8cfc78aca610dead3f0008961a6397f17946839f379c9bb7dc8","observation_id":"0c0e1bfd-0f98-4bd2-8e6d-8e65acb2c0f8","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.14954","last_updated":"2026-07-24T17:40:12Z","snapshot_observed_at":"2026-08-15T05:09:39.058828Z","submitted_at":"2026-06-12T20:57:05Z","title":"Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.14954","snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:2606.14954 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"cited_paper":"/paper/2606.14954","citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:176cf6ed6342d6d61c4cb3875c0537fb2e1d36dd63177d58b64688f4fd498f8d","observation_id":"e3592864-bdbe-4499-b54c-ef130c9fad4f","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:47d87a51ef829b3d06c94b3429da2f64fcc8afa5bcb70c69f91f0ba4ad07370f","observation_id":"99e2569b-fd00-4ae1-aa6d-989fc7b185f8","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"1991 , publisher=","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2d8231f6e67d1451b94f61ed84444d5cd3df61aa8bef038b2f991c5d68eb63d7","observation_id":"42efefe4-93e2-4920-8949-97a188d37104","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Bulletin of the American Mathematical Society , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:85b28523c63eadb5ee785f1ce0321f3e580a9255fe8f18cbc052d1b9763e3d81","observation_id":"4ee781c1-d31c-4f9d-8cd8-62d0d7d68900","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2021 , publisher=","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:81b45bca94a8c622344dad1e6b60f46d63a2ad154557fd8a8c554b63cca048c4","observation_id":"e7d6d876-fa4a-44aa-967d-a03f33353d30","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Studia Mathematica , volume=","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:89f0eb119c4524e41af9eac597869a3669f1489f3e2cee06a27acae4289b1f3b","observation_id":"541c80ae-15f6-442e-8c26-40209a238de1","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:c22e3dba5323970972680aae7a9e95038adfe2c343f279e35df16e58e709acc6","observation_id":"8960531c-9249-419c-9f59-6561c6bc1bb9","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Proceedings of the American Mathematical Society , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2d0a7001f434f7565b75dac504d4f1c20c9c9e9389f16d1bab75b27424aa3ffb","observation_id":"55c14eef-ea4a-4435-a165-5ed31051534e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on Learning Theory , pages=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:ee7b88cf579ab869d2a90997eec09e51fc242731005009b7ec46cc072f7e5d65","observation_id":"a8110cfd-6f99-41e8-9e5f-2e2b9ac88d07","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"International Conference on Learning Representations , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:16133fe95733ba3cf4c0977e28a18154f93c1c7833b53678e4c0a94cff329a02","observation_id":"19af0853-2a9d-482b-a437-d9641840c7b4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:4ad404b01e95acf8836abcb300462deaee07a7f6753072f7bbc61efe3f702327","observation_id":"cb573edf-c063-46fc-aa05-24e0054962f9","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2009 , publisher=","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:9bea4b59f5a66f66883e8ea5d2c121dba55983467d4deb2e53c6e80cd87c3aa8","observation_id":"6dc8c452-291c-4f34-b9ee-66accc680963","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:89f84647ddb2cb266261f04484a57708f1fd53320b01f0c3f0963bb0050ec0ab","observation_id":"9872ebe0-dbd3-4c16-aea5-88115e30f2d0","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing , pages=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:15709076dcc31778bbcc8973f8b44a90553be70fe6f6d6cbb75e49ae1dbcd933","observation_id":"8534a89a-0f78-4ef3-a106-e855d14e279c","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Acta numerica , volume=","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:15e3cd8feaf7fa204978b9ff9372da999eee52c775ee59179a169fa51ca19f52","observation_id":"d1a61ce7-b351-438c-8f18-9e02ebd98a5d","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Neural networks , volume=","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:eeb3a570e7e49644f99e1c6b46558f1949317f46bcec1b8b7cde4176b37d6389","observation_id":"70cfd5a0-1a46-48e9-9d87-fbf821c98dc8","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:9645df490e854f08925cdbecb13b676e481e5e4ca46c49f4ce894d2d088a2b04","observation_id":"dd8500f0-5f99-4294-86df-bab4f259f002","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:cf5b69ca50cb97b237da3cf468d8e9d3d5852861ee1c11d04f1889dd67b4c45a","observation_id":"72d52335-dc48-4a7c-bacb-30758d6d120e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Applied and Computational Harmonic Analysis , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:1293da85060e5e12f3fbad8f3f35d2c86ffdc969d84c43e85d244a648be114d6","observation_id":"144ce489-757a-419d-be0d-684e448db3c4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:8fe92a3bb525cf6344193e3b426a0b562525a4f21a5e0245a87255f546ee3920","observation_id":"a94012b6-722c-4a0e-9f27-1001b017f2c4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:83ecc132d65af81e2d7d2c68fcb315f6e82b98dc97bad9fce6d9101234dd5364","observation_id":"3e36f815-523f-4367-b739-521306feacd4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"International Conference on Computational Learning Theory , pages=","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:a677182a206b661196663ab46551091f3da6bfbf13b64196d7d23f82420a444f","observation_id":"15938f9c-4598-4ce1-9ee5-3356423d092c","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of machine learning research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:f24f36cd72cb0d71ac9468a3fb08c9a4032a90ae21913303ed9b35889ccd6dd3","observation_id":"563ab211-6b6e-429f-b77a-24911b5debd6","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"1977 , publisher=","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:dc2080d15fe39be2e92ff03322ac2fdd952829440db690790e7915950ff3327b","observation_id":"a7891f06-2c62-4688-90c3-4edd660ac00f","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":", publisher =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:fe90e4bbbc16a4653336e2c19db81f9189a78d444f029d42925238edc25f8bae","observation_id":"2c12cfc9-e5a0-4689-9ba5-998509f82032","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"IEEE Transactions on Information Theory , volume=","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:8d2e6a1b1b45c23ec7156bfe3f7e16654f6c06771e565a7079e4a68055729368","observation_id":"63bf2d9a-2716-4181-8dc8-a8abba376e7a","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Computer Intensive Methods in Control and Signal Processing: The Curse of Dimensionality , pages=","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2e409446ead810fb3b77e582a260c536a10133ae9dd989c7c61e96da57cd8809","observation_id":"f8689e3c-93eb-40f0-8602-6c141ad8602e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:1a295f026cb13164c9d2195aeda1e4bd26185cf9bfdffd1855fc41ca3a3f3099","observation_id":"7856a3e6-00ab-405b-8994-d76b7c39e048","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Neural networks , volume=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:7d3a291a65e2d70b2c3af0246cda409d583d0401144c266a736bef8546917f65","observation_id":"0aa0b29d-db0b-45ca-ad3a-0737b412f6fe","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:aaeda07744e1eb60e46b2aecaa52a519f52dacb92fa9b40ef7b48ee07a327cc9","observation_id":"ca06c092-fec3-4367-8b89-e86adb6ba55c","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Acta Mathematica , volume=","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:f4b7acb01b4e29a47689b275b2f3be0e06a2998e1afbffe1bccfe1dbfd69f93b","observation_id":"a5de0f85-70bd-4b88-b394-0cf3f3e8aa43","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"International Conference on Learning Representations (ICLR 2020) , year=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2b3d20e850a704f775ff5356afdf97b3c51ca78c79e19d2b04f5f1966072b131","observation_id":"571c2a77-2269-4b45-bdfe-3ef41fdc6a0e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"IEEE Transactions on Information Theory , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:52c760f7ac7115fa3f2e6fe6ac69c8e95580c77958e812bd0930859512696057","observation_id":"e5a74f3e-8799-43e3-ab9a-c2897362bb42","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:964e408c429980324c7347e0cebf170c1e7effbf0502d9f3fcc18800c963a0c0","observation_id":"916d646b-d79e-4bf0-8078-8cb7d017a4e4","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Foundations of Computational Mathematics , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:a0ccdcbe4681108bddb6d54248248d898f08cb5dc894f46fe5896e7408ead0d2","observation_id":"6251b240-1b6f-497d-a9a2-a51b0f11ad3e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:382df96ff50587f87c6cd598003c86a1f1ede7eade81a29fe2369a921f8993c9","observation_id":"c9e132a0-b529-4362-ad97-bdfbe56e25ea","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.00800","last_updated":"2019-02-06T20:16:55Z","snapshot_observed_at":"2026-08-14T17:21:51.184811Z","submitted_at":"2019-02-02T21:41:49Z","title":"Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using Total Path Variation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.00800","snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:1902.00800 , year=","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"cited_paper":"/paper/1902.00800","citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:e524981fc60f8f2c1e25fa6c064ee04bade2f1eae0917a703a7f4fac74723c0b","observation_id":"e4019ca5-f9eb-439e-8b09-2f22cdad39cd","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:2410.06378 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:7c144ca87b3a974610586a9dabe7b37ef9d65c913b609ba4121ac6c6e0bb4e30","observation_id":"3377b92f-5be4-4b2f-8f71-4b7bee2199c1","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.08750","last_updated":"2025-08-21T08:54:47Z","snapshot_observed_at":"2026-08-16T14:10:04.841913Z","submitted_at":"2024-03-13T17:51:02Z","title":"Neural reproducing kernel Banach spaces and representer theorems for deep networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.08750","snapshot_observed_at":"2026-07-11T06:01:25.773672Z","title":"arXiv preprint arXiv:2403.08750 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"cited_paper":"/paper/2403.08750","citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:096a0954c0c67645750847e747ba5c6569b44b7787c04b2f6b51e0894e423e53","observation_id":"c18fac96-d452-4741-8bfd-48ec34ea1a2e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Functional Analysis , volume=","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:bbba0f58e5e4abc2208194dac2a29da4177b67d127c96da83cf793461e3e4217","observation_id":"254fd966-c088-47b1-8d98-72b925f29fa0","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Neural Networks , volume=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:9aa628dd3986d6508ca3de5f074cd8417dd721a74453e75415733d6100c4efba","observation_id":"654fb494-1356-42f8-a06a-c49f1e603e3d","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Constructive Approximation , volume=","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2db965b637c43638f084b7dccc69be6172811224fa08da376ff2625872cdc9ca","observation_id":"b36b7310-bf0b-4291-a968-11eb82af75a9","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"1999 , publisher=","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:8dccb9a669308a32828d8a819f0fd75c39f3445316ea62edd506254f80deb74f","observation_id":"b90e73dc-cc07-424b-95cd-c99286254fef","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Oracle inequalities in empirical risk minimization and sparse recovery problems: Ecole D’Et","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:1d13e9becfd6d14131c37ecd5c7230c15c56890571f0768686ea3772481820e0","observation_id":"3bc68c82-a4bd-4b5e-a106-69934270d58d","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Conference on learning theory , pages=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2e3066083adecaf6cf97a11a01c55078f22aa7c7aa807f767a6279489dc71440","observation_id":"a632cd9b-2830-4ffb-a2d1-ae6df6f21148","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Bulletin of the American Mathematical Society , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:ad8df11df8734afbb7f290cca04a215edbb591bfcc5ebfa9b271358b46411789","observation_id":"506716e7-f981-42d1-8be6-95adbdacfb29","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2014 , publisher=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:6ef6c9dfa665742b7057aec602525a81b71909b05ed3c51effaf94622a4cb793","observation_id":"770c1317-4b5c-4bac-9c51-9145fb5fe058","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of the London Mathematical Society , volume=","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:de7513fdf51d179cb64e16757b16022e9930d1f7a62d2b271ce697ba2dee1a11","observation_id":"14068184-168a-4073-8b51-cd5a4512173e","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Annals of Statistics , pages=","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:1779d68e5c781b558baf1013b8f2aa2096b9741b2a7ec79eb9ecd6e13c2b462f","observation_id":"f265706c-5e4c-4fc5-9fde-39f9e471e7ed","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Israel Journal of Mathematics , volume=","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:505c0807afcd52944e9158a93a4607b8d93f656a17b864ec4e5fa02087b70797","observation_id":"a87b2c85-c26b-4085-99b8-2cbdcdb5e52f","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"1981 , publisher=","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:1d28fbc83033a54b03716e3d7cc765c24d526319db24dd0a60a0c6a73aedbd2d","observation_id":"c79b2ee1-d31b-4334-b9ca-6640bfcaa738","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Approximation Theory , volume=","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:019a4ae292cbb649d82d7781108f7cb1bf73dc0044c17cee35cf69b1414ad2d7","observation_id":"3fdbb005-b728-4218-985f-a98a644fd8ce","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"1999 , publisher=","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:0dfd45d87a8cde72888308f685de01b56ab2696c091db9a56c77e025dc81030b","observation_id":"f5578a20-06fb-4461-a493-be28ebe3d336","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":", year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:87ba571e847827d5c50ded143b3cf84836470393b43db0bcdf523701c64160e9","observation_id":"23a6b8b2-d564-42a9-b903-5b4a9dc1c7b9","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2018 , publisher=","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:fabb1b7df91cf4f5277b73af1ae8063c014967e271f016e832a99cc7307a722b","observation_id":"63ebbd19-bee6-42eb-a6d9-fe658e9dae68","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2005 , publisher=","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:9f138bcc427a556e0267880182375d201a0a632982bf023b2d5d847784b1502c","observation_id":"1c803686-665b-48c7-bb07-bcf85aed08f0","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2006 , publisher=","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:f700f33224ea360c18f1db1f589f761b755a9140cf62980a2a9cfeb0e86f5b6e","observation_id":"aa8584ca-cfec-403d-889f-ab0a9cd22850","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":81,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:776d2cf180aba205eea9375cdfa3450ba3c680b3170f53c11655ef0529257661","observation_id":"e79048e5-451f-47a3-bf1e-27f33b3b7e84","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Approximation Theory , volume=","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":82,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:2632dbaef60d4102de638bb42f68fda37802339f1a34546777516e279c5dd128","observation_id":"6913b2d9-2e28-4b04-bc89-547930ff2e01","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2000 , publisher=","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":83,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:3dfca58fee4d09e4d574f2ede70fcca2a074b064d8ea0c51fbdf84848398e68c","observation_id":"2045f070-0aee-46c8-be4a-24feb367f319","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2007 , publisher=","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:d3f9c0a745c3622fd4d5c4490c9c54abebf66004f419ffdcb740f41fa65efcda","observation_id":"c19a0d79-96ff-42a7-b124-619c3f8a9e29","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"2017 , publisher=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:148474adcadcf146daba909ff1a1041ab2ec888791b8b1bc937ac4925d9d655a","observation_id":"d93c01ec-4548-4f9d-9bb7-e532d65c59aa","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Advances in neural information processing systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":86,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:519ae9ef9bb689477b6e6684f5b9ae23c4541d5628abff7b61b5aa61810cad1a","observation_id":"8b2a1e9d-ac4c-4099-b75c-0714678dd05c","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","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":"2026-07-11T06:01:25.773672Z","title":"Journal of Complexity , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity","version":1},"reference_index":87,"source":"arxiv_source","source_observed_at":"2026-07-11T06:01:25.773672Z"},"links":{"citing_paper":"/paper/2607.05546"},"observation_digest":"sha256:73b003531840a3b4d23a80fb15bc2d13b3cb0fa4e9337a5665f3b3c7caa1340d","observation_id":"29132d20-2c76-4628-9c5d-c8ae478fa1af","resolution":{"observed_at":"2026-07-11T06:01:25.773672Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.05546","last_updated":"2026-07-06T18:29:35Z","latest_version":1,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-17T20:51:08.692001Z","submitted_at":"2026-07-06T18:29:35Z","title":"Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity"},"reference_resolution":{"displayed":87,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":87,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":87},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 87 of 87 outbound references and 0 inbound Pith citation observations for arXiv:2607.05546."}