{"as_of":"2026-08-09T20:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:93493537c56a72ba01dc38be44c1c6d9e949d3f68d6a1c1b313f2c97ac9d26f4","coverage":[{"denominator":146,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:58:40.750257Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-03T04:24:13.569884Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T04:27:36.143568Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"cited_work":{"arxiv_id":"2506.12493","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.12493","snapshot_observed_at":"2026-07-03T04:27:36.143568Z","title":"Symmetry-preserving neural net- works in lattice field theories,","venue":null,"work_id":"72f46aa0-24f7-4534-8234-55453ff2f835","year":2025},"citing_paper":{"arxiv_id":"2607.01731","last_updated":"2026-07-02T05:38:55Z","snapshot_observed_at":"2026-08-07T16:42:29.556469Z","submitted_at":"2026-07-02T05:38:55Z","title":"Quantum-Inspired Vision: Leveraging Wave-Particle Duality for Low-Illumination Enhancement","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-03T04:24:13.569884Z"},"links":{"cited_paper":"/paper/2506.12493","citing_paper":"/paper/2607.01731"},"observation_digest":"sha256:9200c007ad8ada19eb59f20f877cfae911edb3f9995a25ed97b3590725370467","observation_id":"0717c9e9-9b8f-402b-958b-ab9354c56281","resolution":{"observed_at":"2026-07-03T04:27:36.145348Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.12493/citation-record","integrity":"/paper/2506.12493/integrity","json":"/paper/2506.12493/citation-record.json","paper":"/paper/2506.12493"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2103.14686","last_updated":"2021-10-11T14:38:26Z","snapshot_observed_at":"2026-08-09T04:49:29.661012Z","submitted_at":"2021-03-26T18:53:36Z","title":"Generalization capabilities of translationally equivariant neural networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.14686","snapshot_observed_at":"2026-08-07T00:58:28.793137Z","title":"Bulusu, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:28.793137Z"},"links":{"cited_paper":"/paper/2103.14686","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b20621771c49a8e44f6c1210ede7565b58178b5f7181da0ebfed056de1e2a27a","observation_id":"0f5e69d0-6038-4a89-a508-0a1abadd28dc","resolution":{"observed_at":"2026-08-07T00:58:28.793137Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.12901","last_updated":"2021-11-22T15:51:06Z","snapshot_observed_at":"2026-08-09T14:38:19.912747Z","submitted_at":"2020-12-23T19:00:01Z","title":"Lattice gauge equivariant convolutional neural networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.12901","snapshot_observed_at":"2026-08-07T00:58:28.900626Z","title":"Favoni, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:28.900626Z"},"links":{"cited_paper":"/paper/2012.12901","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:2369e556b906aaad39bb4a9be443425aa0fc54e1e242cadbe643e56674cedb25","observation_id":"490dfe16-8ae4-4ef3-8c08-24cd9507ff99","resolution":{"observed_at":"2026-08-07T00:58:28.900626Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2212.00832","last_updated":"2022-12-01T19:32:42Z","snapshot_observed_at":"2026-07-06T14:25:53.416758Z","submitted_at":"2022-12-01T19:32:42Z","title":"Applications of Lattice Gauge Equivariant Neural Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2212.00832","snapshot_observed_at":"2026-08-07T00:58:29.069057Z","title":"Favoni, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.069057Z"},"links":{"cited_paper":"/paper/2212.00832","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:fa30a867f58bb44efb2ab7d2478a0f09191c7337db951c48c3f771a925b5330e","observation_id":"913926da-69ec-4ed9-b7ac-05219c412ce5","resolution":{"observed_at":"2026-08-07T00:58:29.069057Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.184100Z","title":"Weinberg, A Model of Leptons , Phys","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.184100Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5c32debb8457205c36fff2dd92948f9602d68a43eeca09a1e09c00dd69ba16c8","observation_id":"7e237a4c-345b-480d-8779-1e6a74848aeb","resolution":{"observed_at":"2026-08-07T00:58:29.184100Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.297324Z","title":"Salam, Weak and Electromagnetic Interactions , Conf","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.297324Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:9f996da021414e0f42ded7d462dfaa0b94814ae825c61e8c43dc5b10fe61219c","observation_id":"875148e4-8971-48a8-b66b-03883fb89dfd","resolution":{"observed_at":"2026-08-07T00:58:29.297324Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.437623Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.437623Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:e0a2efe3c1d1c17dfd2da074d8ecf7ca223404248e09a35fb951627582151ac7","observation_id":"51a3a91f-dcad-41dd-9ddd-cc0a7d74e213","resolution":{"observed_at":"2026-08-07T00:58:29.437623Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.04822","last_updated":"2020-11-13T12:36:28Z","snapshot_observed_at":"2026-07-06T09:27:06.824048Z","submitted_at":"2020-06-08T18:00:04Z","title":"The anomalous magnetic moment of the muon in the Standard Model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.04822","snapshot_observed_at":"2026-08-07T00:58:29.573631Z","title":"Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model , Phys","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.573631Z"},"links":{"cited_paper":"/paper/2006.04822","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:e3c1b78109b0ca6b9d33dee44136f1cb32c4310e6314a482edd777b7c7468c94","observation_id":"f067a44e-875c-4d04-986c-1d363d96e595","resolution":{"observed_at":"2026-08-07T00:58:29.573631Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.713635Z","title":"Metropolis and S","venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.713635Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:98dc8eac750dd070a3cd02dfde59486a7b84ff8e5cefbd2a8f5d3a6340a6d01a","observation_id":"7854c8bf-3740-4f64-baf9-d920c085bbe5","resolution":{"observed_at":"2026-08-07T00:58:29.713635Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.825941Z","title":"Sokal, Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms , Springer US, Boston, MA (1997), 10.1007/978-1-4899-0319-8 6","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.825941Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:c01057f27ac805c5ee7c832bac7131ed9c5532d6e686c7cf818ece4efe4a5f5f","observation_id":"56c20967-23f1-42bd-9d0f-761fabb55cb5","resolution":{"observed_at":"2026-08-07T00:58:29.825941Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:29.950773Z","title":"Aarts, Introductory lectures on lattice QCD at nonzero baryon number, Journal of Physics: Conference Series 706 (2016) 022004","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:29.950773Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:df6281518a4b089a2cfbd6c42f69a3e3f6c6f941f6c48e8d8de4113c3c3750d6","observation_id":"bc84b37e-c689-443d-8403-8d524f8724d7","resolution":{"observed_at":"2026-08-07T00:58:29.950773Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1603.09517","last_updated":"2016-03-31T10:30:29Z","snapshot_observed_at":"2026-07-06T04:51:16.652993Z","submitted_at":"2016-03-31T10:30:29Z","title":"Approaches to the sign problem in lattice field theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1603.09517","snapshot_observed_at":"2026-08-07T00:58:30.070692Z","title":"Gattringer and K","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.070692Z"},"links":{"cited_paper":"/paper/1603.09517","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b8149b930e6cd950145542976f94086121effc5139dd306846d7a7d5fb12bf90","observation_id":"3875f6e0-e4c9-4b0f-9f64-fc830c44b169","resolution":{"observed_at":"2026-08-07T00:58:30.070692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1409.0575","last_updated":"2015-01-30T01:23:59Z","snapshot_observed_at":"2026-07-06T03:53:12.119259Z","submitted_at":"2014-09-01T22:29:38Z","title":"ImageNet Large Scale Visual Recognition Challenge","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1409.0575","snapshot_observed_at":"2026-08-07T00:58:30.192258Z","title":"Russakovsky, J","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.192258Z"},"links":{"cited_paper":"/paper/1409.0575","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:f8f6309293a1e2de9ae032b6a756959da189be28f58f70e66cc399c3b471849c","observation_id":"c78f62b6-ef41-49b6-868c-0983e5acf47f","resolution":{"observed_at":"2026-08-07T00:58:30.192258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.08774","last_updated":"2024-03-04T06:01:33Z","snapshot_observed_at":"2026-08-07T07:30:12.213965Z","submitted_at":"2023-03-15T17:15:04Z","title":"GPT-4 Technical Report","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.08774","snapshot_observed_at":"2026-08-07T00:58:30.298709Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.298709Z"},"links":{"cited_paper":"/paper/2303.08774","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:bb1d25c5f7cd60ea926b01c92a51bd0c5bb81a6df8e188c1ba358bcd7672b6c3","observation_id":"62b8aae8-26a6-422f-a7d9-ef4b5b011025","resolution":{"observed_at":"2026-08-07T00:58:30.298709Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:30.400270Z","title":"Silver, T","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.400270Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:7b80420f82ec282d812566df5b45590eb1d13222dbaf054fa625c43f2c7b5fe4","observation_id":"40b64969-1dd1-4768-8ed5-7d1c082b4878","resolution":{"observed_at":"2026-08-07T00:58:30.400270Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:30.562493Z","title":"Jumper, R","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.562493Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:9752ae61be029d430ab13fb07fc3f2e3befc785c87eed5add749fcaf1acfcf1b","observation_id":"e28914b2-4897-4660-b5d7-b10916517027","resolution":{"observed_at":"2026-08-07T00:58:30.562493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:30.680815Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.680815Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5dcb10eef9e3dd053a20de09301fe119edccdce57a6b424016fed7e190b8c11f","observation_id":"50a3e8a9-cf77-4f8e-b79b-b15587bfe3c8","resolution":{"observed_at":"2026-08-07T00:58:30.680815Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:30.795103Z","title":"Dubey, S.K","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.795103Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:0af0578fe6efccae64ce2b93d53dc0c4a70a1c315f35f5d4db9ab9bd4595e9e2","observation_id":"4a5ac0fc-72f5-4e9b-b20d-67a6bec6609b","resolution":{"observed_at":"2026-08-07T00:58:30.795103Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:30.997043Z","title":"Rosenblatt, The perceptron - A perceiving and recognizing automaton, Tech","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:30.997043Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:4580ada679d9d93370074f72aff0855cae211432fe8dda8c408ad0cea760290a","observation_id":"4afbb541-20de-4c8c-99ba-848d1364e0f5","resolution":{"observed_at":"2026-08-07T00:58:30.997043Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:31.092160Z","title":"Rosenblatt, The perceptron: A probabilistic model for information storage and organization in the brain","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.092160Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:d448184e3701b6629d07dea670c769536320b3779137d88607ad83c19dd5a3ca","observation_id":"6be14b57-7546-4cca-9942-c4a661a5a441","resolution":{"observed_at":"2026-08-07T00:58:31.092160Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:31.175213Z","title":"LeCun, Y","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.175213Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:d8c1b2b944c0e86445448b818e9b1adddca3c86f942f614b055cd13777264014","observation_id":"3a0421fb-0507-4afc-bece-e78f944bd638","resolution":{"observed_at":"2026-08-07T00:58:31.175213Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.04747","last_updated":"2017-06-15T13:21:04Z","snapshot_observed_at":"2026-08-04T02:05:40.539691Z","submitted_at":"2016-09-15T17:32:34Z","title":"An overview of gradient descent optimization algorithms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.04747","snapshot_observed_at":"2026-08-07T00:58:31.247227Z","title":"Ruder, An overview of gradient descent optimization algorithms , 1609.04747","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.247227Z"},"links":{"cited_paper":"/paper/1609.04747","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5689d7a76a00ad522fe0c9c5275de82098558af42cb67728fe932fe4e4fc303f","observation_id":"b3d4c2f6-5f9b-46f1-8a10-a89c9ee83d90","resolution":{"observed_at":"2026-08-07T00:58:31.247227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:31.371680Z","title":"Ying, An Overview of Overfitting and its Solutions , Journal of Physics: Conference Series 1168 (2019) 022022","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.371680Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:bb68763ff1c61cda1d8ea2f55fc38d5842a2fc41c022991ca9405e6776448a6a","observation_id":"01a5430b-a086-4331-a366-96bc51d7e950","resolution":{"observed_at":"2026-08-07T00:58:31.371680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:31.506362Z","title":"Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems 2 (1989) 303","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.506362Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:4e1a21e6d94e6f0e32ab31f9b11397fa102aafc38894f9b842e6f8c600d146d9","observation_id":"956af411-2724-4c82-adfe-43ea1f2ddf7f","resolution":{"observed_at":"2026-08-07T00:58:31.506362Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.02540","last_updated":"2017-11-01T08:50:32Z","snapshot_observed_at":"2026-07-06T05:58:41.847458Z","submitted_at":"2017-09-08T05:00:20Z","title":"The Expressive Power of Neural Networks: A View from the Width","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1709.02540","snapshot_observed_at":"2026-08-07T00:58:31.633515Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.633515Z"},"links":{"cited_paper":"/paper/1709.02540","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:9d91b9c763e95c6383938642d206a1e422b2deb190efa7196922ee988cfae6e7","observation_id":"ad3ac98e-28c5-4448-b785-85bc2457a9a9","resolution":{"observed_at":"2026-08-07T00:58:31.633515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:31.737681Z","title":"Carrasquilla and R.G","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.737681Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:52a73cd8fc95a796e5326bd0b4fec8c12be11eb730b3afa298cf35cac48d7a92","observation_id":"c92dfba0-6aba-44e9-8ac4-67e1edbee45d","resolution":{"observed_at":"2026-08-07T00:58:31.737681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.12879","last_updated":"2019-03-15T09:18:40Z","snapshot_observed_at":"2026-08-07T20:12:57.045299Z","submitted_at":"2018-10-30T17:22:57Z","title":"Regressive and generative neural networks for scalar field theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.12879","snapshot_observed_at":"2026-08-07T00:58:31.820940Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.820940Z"},"links":{"cited_paper":"/paper/1810.12879","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:f3b21c994471948c1390008a8395c8263a4323274c68e5a1e1bc59b643d24ea7","observation_id":"0cabe103-4889-4c11-ba78-6b9bbcc28047","resolution":{"observed_at":"2026-08-07T00:58:31.820940Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.04857","last_updated":"2020-09-15T16:24:46Z","snapshot_observed_at":"2026-08-06T07:19:22.822506Z","submitted_at":"2020-05-11T04:28:51Z","title":"Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.04857","snapshot_observed_at":"2026-08-07T00:58:31.910974Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:31.910974Z"},"links":{"cited_paper":"/paper/2005.04857","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:1813677d0452145524085785f26ec30d88897e64998baab41fa7f3a9fdb7ce7a","observation_id":"3c5e00cc-7fe1-4f10-8de5-eca4b8179ee8","resolution":{"observed_at":"2026-08-07T00:58:31.910974Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.00355","last_updated":"2020-11-16T16:08:14Z","snapshot_observed_at":"2026-08-09T07:48:39.568128Z","submitted_at":"2020-07-01T09:46:05Z","title":"Mapping distinct phase transitions to a neural network","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.00355","snapshot_observed_at":"2026-08-07T00:58:32.024975Z","title":"Bachtis, G","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.024975Z"},"links":{"cited_paper":"/paper/2007.00355","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:967e611edb1c638bb7225b2b827b8000a12071435b8189c83226851858a64c51","observation_id":"907745fb-7231-447f-9408-ba3dfc32a860","resolution":{"observed_at":"2026-08-07T00:58:32.024975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.01504","last_updated":"2020-05-18T14:04:18Z","snapshot_observed_at":"2026-08-05T15:50:17.453188Z","submitted_at":"2020-03-03T13:56:58Z","title":"Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.01504","snapshot_observed_at":"2026-08-07T00:58:32.167791Z","title":"Bl¨ ucher, L","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.167791Z"},"links":{"cited_paper":"/paper/2003.01504","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:58b38135a00025c79d6696c433cfb251a33f2b1aeb062e892613f19894cc8727","observation_id":"5054dc24-4fff-4584-b6e7-036311faac09","resolution":{"observed_at":"2026-08-07T00:58:32.167791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1801.05784","last_updated":"2018-01-17T18:26:38Z","snapshot_observed_at":"2026-07-06T06:19:07.703067Z","submitted_at":"2018-01-17T18:26:38Z","title":"Machine learning action parameters in lattice quantum chromodynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1801.05784","snapshot_observed_at":"2026-08-07T00:58:32.279658Z","title":"Shanahan, D","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.279658Z"},"links":{"cited_paper":"/paper/1801.05784","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:a00d765017e1f5eb92055007e51929b4f0c4b1c56159394cc04ae31949b22c07","observation_id":"e3413906-ae8c-4eec-9fcc-7368e369745b","resolution":{"observed_at":"2026-08-07T00:58:32.279658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.07115","last_updated":"2021-01-05T09:42:26Z","snapshot_observed_at":"2026-07-06T09:38:08.796339Z","submitted_at":"2020-07-14T15:31:05Z","title":"Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.07115","snapshot_observed_at":"2026-08-07T00:58:32.381079Z","title":"Nicoli, C.J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.381079Z"},"links":{"cited_paper":"/paper/2007.07115","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5836217a9710b0ade97db4afa377165208f72749a783fe41a1a0b86b20e8ec82","observation_id":"03636e2f-c3d9-4472-97e6-83c6323a8439","resolution":{"observed_at":"2026-08-07T00:58:32.381079Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.05436","last_updated":"2020-07-10T15:17:07Z","snapshot_observed_at":"2026-08-03T18:40:00.303447Z","submitted_at":"2020-07-10T15:17:07Z","title":"Complex Paths Around The Sign Problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.05436","snapshot_observed_at":"2026-08-07T00:58:32.476675Z","title":"Alexandru, G","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.476675Z"},"links":{"cited_paper":"/paper/2007.05436","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:912701bd82f4c03e727000bba5cf0ef8039aee6669b6b2fe53ace794bee7c764","observation_id":"245472e5-7fe0-4577-bc79-d9c3598f5774","resolution":{"observed_at":"2026-08-07T00:58:32.476675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.15625","last_updated":"2023-04-18T12:49:06Z","snapshot_observed_at":"2026-07-06T14:24:05.948664Z","submitted_at":"2022-11-28T18:26:49Z","title":"Towards learning optimized kernels for complex Langevin","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.15625","snapshot_observed_at":"2026-08-07T00:58:32.605341Z","title":"Alvestad, R","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.605341Z"},"links":{"cited_paper":"/paper/2211.15625","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:6b886b3cc151a99a57e364ad822799e14c8b121da2950c0c755a2f2ed296617d","observation_id":"439989d9-0f85-4b30-9a26-d51a8e95fe21","resolution":{"observed_at":"2026-08-07T00:58:32.605341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.08053","last_updated":"2023-10-12T06:01:01Z","snapshot_observed_at":"2026-08-02T19:50:26.173814Z","submitted_at":"2023-10-12T06:01:01Z","title":"Lattice real-time simulations with learned optimal kernels","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.08053","snapshot_observed_at":"2026-08-07T00:58:32.779611Z","title":"Alvestad, A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.779611Z"},"links":{"cited_paper":"/paper/2310.08053","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:cb00264f8de7bf8a1a50130eedb92ba5066ccd73dd1ad9a3ed78da5473122bdd","observation_id":"a9e91b95-ddcc-413c-aa1d-41f495f4a234","resolution":{"observed_at":"2026-08-07T00:58:32.779611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.03229","last_updated":"2023-04-06T17:04:24Z","snapshot_observed_at":"2026-07-06T15:13:06.155585Z","submitted_at":"2023-04-06T17:04:24Z","title":"Mitigating Green's function Monte Carlo signal-to-noise problems using contour deformations","version":1},"cited_work":{"arxiv_id":"2304.03229","doi":null,"metadata_source":"pith","pith_arxiv_id":"2304.03229","snapshot_observed_at":"2026-08-07T00:58:51.356444Z","title":"Mitigating Green's function Monte Carlo signal-to-noise problems using contour deformations","venue":"nucl-th","work_id":"4ad6dd22-9204-4be6-8f82-24ca0d84c154","year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:32.905593Z"},"links":{"cited_paper":"/paper/2304.03229","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:89fbb3b7b11b4b403df0f9d597efa76a3bf11fb43663e9371ad146a4b5b62f65","observation_id":"98be4f62-9996-4feb-9a6a-6d0f0f526989","resolution":{"observed_at":"2026-08-07T00:58:51.451713Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.00804","last_updated":"2019-08-29T20:24:11Z","snapshot_observed_at":"2026-08-08T21:37:01.530994Z","submitted_at":"2019-03-03T01:11:20Z","title":"Machine Learning Holographic Mapping by Neural Network Renormalization Group","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.00804","snapshot_observed_at":"2026-08-07T00:58:33.028515Z","title":"Hu, S.-H","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.028515Z"},"links":{"cited_paper":"/paper/1903.00804","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:692384521fec3c85aeee9061f64de404242a15ac83f8fae1081a41673f15052e","observation_id":"0da7ad59-3cdb-4079-8ce3-4cfdf130f0e0","resolution":{"observed_at":"2026-08-07T00:58:33.028515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.00466","last_updated":"2022-02-23T19:28:31Z","snapshot_observed_at":"2026-08-03T23:38:37.661843Z","submitted_at":"2021-07-01T14:17:51Z","title":"Inverse Renormalization Group in Quantum Field Theory","version":2},"cited_work":{"arxiv_id":"2107.00466","doi":null,"metadata_source":"pith","pith_arxiv_id":"2107.00466","snapshot_observed_at":"2026-08-07T00:58:51.137485Z","title":"Inverse Renormalization Group in Quantum Field Theory","venue":"hep-lat","work_id":"3c28219c-2cde-47ff-a69c-301801d57314","year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.158399Z"},"links":{"cited_paper":"/paper/2107.00466","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:9e1c39e692ea7a5c50f77b0e1da6e95732c689696ba81f1b14d063a53fda1ab8","observation_id":"620ef128-042f-4f38-8a49-f25567b11968","resolution":{"observed_at":"2026-08-07T00:58:51.213377Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.00054","last_updated":"2021-02-10T16:52:48Z","snapshot_observed_at":"2026-07-06T10:00:19.927711Z","submitted_at":"2020-09-30T18:44:18Z","title":"Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.00054","snapshot_observed_at":"2026-08-07T00:58:33.317149Z","title":"Bachtis, G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.317149Z"},"links":{"cited_paper":"/paper/2010.00054","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:edfdb5bcd3932be31a8c4e846a44eae1c06e4995b528278d202e0b0a78fd3304","observation_id":"741c05bc-359e-46d9-a546-be10b0c355d9","resolution":{"observed_at":"2026-08-07T00:58:33.317149Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.03533","last_updated":"2021-12-23T13:15:53Z","snapshot_observed_at":"2026-08-02T10:08:00.994948Z","submitted_at":"2018-11-08T16:26:15Z","title":"Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.03533","snapshot_observed_at":"2026-08-07T00:58:33.467235Z","title":"Pawlowski and J.M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.467235Z"},"links":{"cited_paper":"/paper/1811.03533","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:120a2e04bdc8f5cfc47f2f1c758fecc7f52137bc39ac9d58544ea75d79a5cec6","observation_id":"8fceb8d3-533b-4d8b-a6af-ad0aa19663ac","resolution":{"observed_at":"2026-08-07T00:58:33.467235Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.03578","last_updated":"2023-11-06T22:24:28Z","snapshot_observed_at":"2026-07-06T16:43:54.752924Z","submitted_at":"2023-11-06T22:24:28Z","title":"Generative Diffusion Models for Lattice Field Theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.03578","snapshot_observed_at":"2026-08-07T00:58:33.632085Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.632085Z"},"links":{"cited_paper":"/paper/2311.03578","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:0f18f8b3308a305cc96548b567ea8b96a4fa486fef8cc8d6a203a7a0fceae5e7","observation_id":"ac5c7eba-1143-451f-8159-06ac5acfa3e5","resolution":{"observed_at":"2026-08-07T00:58:33.632085Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.06707","last_updated":"2020-10-26T11:28:47Z","snapshot_observed_at":"2026-08-05T12:33:19.589808Z","submitted_at":"2020-02-16T23:29:32Z","title":"Stochastic Normalizing Flows","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.06707","snapshot_observed_at":"2026-08-07T00:58:33.760555Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.760555Z"},"links":{"cited_paper":"/paper/2002.06707","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:ee5edf11a2388c6d42f9b6cdd4931a23ceaf75a2da398a89b817b4e2e181c73e","observation_id":"e296c230-c761-4ea4-9e8b-c1a2eb6b01e4","resolution":{"observed_at":"2026-08-07T00:58:33.760555Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.08862","last_updated":"2022-07-06T15:59:22Z","snapshot_observed_at":"2026-08-07T17:48:23.344599Z","submitted_at":"2022-01-21T19:00:18Z","title":"Stochastic normalizing flows as non-equilibrium transformations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.08862","snapshot_observed_at":"2026-08-07T00:58:33.889217Z","title":"Caselle, E","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:33.889217Z"},"links":{"cited_paper":"/paper/2201.08862","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b5b1d4330f20d957c7bdfa147812475109833bf4a890074f028b16b0b5684bf1","observation_id":"3f37507f-6683-4a7e-b32c-5551564ab7ad","resolution":{"observed_at":"2026-08-07T00:58:33.889217Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06561","last_updated":"2024-04-29T15:38:39Z","snapshot_observed_at":"2026-08-05T07:24:52.172354Z","submitted_at":"2024-02-09T17:21:04Z","title":"Mitigating topological freezing using out-of-equilibrium simulations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.06561","snapshot_observed_at":"2026-08-07T00:58:34.003489Z","title":"Bonanno, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.003489Z"},"links":{"cited_paper":"/paper/2402.06561","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:015107f0df3cb605ee36a48720699872d566084f2fc194fc976bdba00531d61f","observation_id":"e2b2d704-e01a-4274-96c5-cab974efb82b","resolution":{"observed_at":"2026-08-07T00:58:34.003489Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.01107","last_updated":"2024-02-12T10:03:28Z","snapshot_observed_at":"2026-08-08T11:35:22.588120Z","submitted_at":"2023-07-03T15:34:36Z","title":"Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.01107","snapshot_observed_at":"2026-08-07T00:58:34.125151Z","title":"Caselle, E","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.125151Z"},"links":{"cited_paper":"/paper/2307.01107","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:24a334a9991ebc13718bd79711a3123076b904f84f5abaaae7d41a7e623ebe83","observation_id":"f77cd1a5-475a-4b78-951b-389f8e5a22bf","resolution":{"observed_at":"2026-08-07T00:58:34.125151Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:34.282738Z","title":"Noether, Invariante Variationsprobleme, Nachrichten von der Gesellschaft der Wissenschaften zu G¨ ottingen, Mathematisch-Physikalische Klasse 1918 (1918) 235","venue":null,"work_id":null,"year":1918},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.282738Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:847b3e2c9e1ab5763ddb2df75bd87a60214c212235bf254feadffced2eab672c","observation_id":"da759037-5da0-480b-a583-2bb17dcdbde5","resolution":{"observed_at":"2026-08-07T00:58:34.282738Z","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":"10.1088/0957-0233/13/9/711","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:46.484883Z","title":"J¨ ahne,Digital Image Processing, 5th revised and extended edition , Berlin: Springer-Verlag (2002), 10.1088/0957-0233/13/9/711","venue":null,"work_id":"defc53ad-27fe-4121-82ff-d59e47d28a65","year":2002},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.401117Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b0aa5541ecbdba5db8410c6f7f555b9b46a6d7c24750ffee39fa73d35742114e","observation_id":"559207c0-ab19-4da3-8ad6-78ac5c1d06b5","resolution":{"observed_at":"2026-08-07T00:58:46.598143Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:34.551263Z","title":"Yarotsky, Universal Approximations of Invariant Maps by Neural Networks, Constructive Approximation 55 (2022) 407","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.551263Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:cdc841ea205e8aee9133378daee5e03288a893cdb5ef7db17ec52175030aeb85","observation_id":"32b492b6-a49d-483c-a94f-681e06f81986","resolution":{"observed_at":"2026-08-07T00:58:34.551263Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:34.679671Z","title":"Zhou, Universality of deep convolutional neural networks , Applied and Computational Harmonic Analysis 48 (2020) 787","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.679671Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:80860dea12468efde4c1453fd162ea21b83ab87dc6c18f4cd6cc9d08dd07dd21","observation_id":"8dd83a8d-85fc-402d-b6a4-1659c39f301d","resolution":{"observed_at":"2026-08-07T00:58:34.679671Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:34.824742Z","title":"Fukushima, Neocognitron: A Self-organizing Neural Network Model for a Mechanism of Pattern Recognition Unaffected by Shift in Position, Biological Cybernetics 36 (1980) 193","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.824742Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:8e892726cc73915207b77852533e49d8f3049aeb9c239d9a28cbefd5e2c908e2","observation_id":"673f2168-705f-4203-b4f0-104a6993d96c","resolution":{"observed_at":"2026-08-07T00:58:34.824742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:34.928536Z","title":"Krizhevsky, I","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:34.928536Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:959ee51ddde4911b2cd2d1eba9c6f7a2f0ae0b0bc064c070aaadbbf88c442220","observation_id":"ee7d0ea0-1f45-4c70-ae85-5d7bf27291ac","resolution":{"observed_at":"2026-08-07T00:58:34.928536Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1312.4400","last_updated":"2014-03-04T05:15:42Z","snapshot_observed_at":"2026-08-02T17:47:13.893077Z","submitted_at":"2013-12-16T15:34:13Z","title":"Network In Network","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1312.4400","snapshot_observed_at":"2026-08-07T00:58:35.093299Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.093299Z"},"links":{"cited_paper":"/paper/1312.4400","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:1bbf726a06030f1b3d7c4cb99a7da532ca5926c118c0ef82ccae5b3b7165ed68","observation_id":"2114cddb-4e27-4efa-bedd-3ef4319261c0","resolution":{"observed_at":"2026-08-07T00:58:35.093299Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:35.197113Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.197113Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5ecd1b6240976a14d0b9fdfc703eaa57e7b3549ea0f4bc224d867e972255ff4c","observation_id":"7ec491da-6fee-4415-a6f8-4639989c1379","resolution":{"observed_at":"2026-08-07T00:58:35.197113Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1705.05582","last_updated":"2017-05-16T08:26:14Z","snapshot_observed_at":"2026-07-06T05:42:48.879600Z","submitted_at":"2017-05-16T08:26:14Z","title":"Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1705.05582","snapshot_observed_at":"2026-08-07T00:58:35.330614Z","title":"Wetzel and M","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.330614Z"},"links":{"cited_paper":"/paper/1705.05582","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:2d59272e17fa70eda2024db63f0c072136f9b5084306b41535278d52c67bbd6d","observation_id":"3af39853-6264-465c-b76a-8a3663719808","resolution":{"observed_at":"2026-08-07T00:58:35.330614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2102.03006","last_updated":"2021-05-24T11:39:18Z","snapshot_observed_at":"2026-08-09T12:09:26.769457Z","submitted_at":"2021-02-05T05:33:32Z","title":"Machine Learned Phase Transitions in a System of Anisotropic Particles on a Square Lattice","version":4},"cited_work":{"arxiv_id":"2102.03006","doi":null,"metadata_source":"pith","pith_arxiv_id":"2102.03006","snapshot_observed_at":"2026-08-07T00:58:50.792002Z","title":"Machine Learned Phase Transitions in a System of Anisotropic Particles on a Square Lattice","venue":"cond-mat.stat-mech","work_id":"85866a9a-2a97-4cf2-a1d6-fff75d735ad0","year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.459064Z"},"links":{"cited_paper":"/paper/2102.03006","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:cfed0e437dc045a1407a1d2ca70bb0099c4fd7551b71138be997dd984213505f","observation_id":"b312d348-720b-487c-9a1e-02f9837e0ea0","resolution":{"observed_at":"2026-08-07T00:58:50.877389Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.07399","last_updated":"2021-02-09T05:03:18Z","snapshot_observed_at":"2026-07-06T10:33:36.814570Z","submitted_at":"2021-01-19T01:24:18Z","title":"Deep Reinforcement Learning Optimizes Graphene Nanopores for Efficient Desalination","version":2},"cited_work":{"arxiv_id":"2101.07399","doi":null,"metadata_source":"pith","pith_arxiv_id":"2101.07399","snapshot_observed_at":"2026-08-07T00:58:50.627175Z","title":"Deep Reinforcement Learning Optimizes Graphene Nanopores for Efficient Desalination","venue":"cs.LG","work_id":"0d1b7930-c14b-4cdd-8c4f-037cd500e45b","year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.601422Z"},"links":{"cited_paper":"/paper/2101.07399","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:7024b1b6204c36f2009f78a1b68583b7fb60be4bc0023a7603a04fb67ed0044a","observation_id":"0f7eaa36-3ac2-4f3b-8e92-153e90d16656","resolution":{"observed_at":"2026-08-07T00:58:50.678385Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:35.740103Z","title":"Karniadakis, I.G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.740103Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:4d768f48fc188364533e9646c09b624a738a031b32b7ff19fdb2587d662f903b","observation_id":"eef887d7-b54f-4118-82c7-c479b1fa7d3b","resolution":{"observed_at":"2026-08-07T00:58:35.740103Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.01563","last_updated":"2019-09-05T04:20:28Z","snapshot_observed_at":"2026-08-02T00:19:27.415872Z","submitted_at":"2019-06-04T16:27:55Z","title":"Hamiltonian Neural Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.01563","snapshot_observed_at":"2026-08-07T00:58:35.856533Z","title":"Greydanus, M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.856533Z"},"links":{"cited_paper":"/paper/1906.01563","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5f011f2a4c71c8db494d81ff6c7e01eb71b407ba3ec17b6c9f492783c3e110e5","observation_id":"267ce6c6-dc3c-4786-a56f-4d3d639dd0cc","resolution":{"observed_at":"2026-08-07T00:58:35.856533Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.04630","last_updated":"2020-07-30T05:22:58Z","snapshot_observed_at":"2026-08-04T10:05:44.957260Z","submitted_at":"2020-03-10T10:55:25Z","title":"Lagrangian Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.04630","snapshot_observed_at":"2026-08-07T00:58:35.953422Z","title":"Cranmer, S","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:35.953422Z"},"links":{"cited_paper":"/paper/2003.04630","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:27c07ce5484dd823129fb5e7945defee4de613e6561ecfa5ed3309667214471b","observation_id":"2b4dfeac-babb-4072-a533-2cf50c7ad473","resolution":{"observed_at":"2026-08-07T00:58:35.953422Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:36.047396Z","title":"M¨ uller,Exact conservation laws for neural network integrators of dynamical systems , Journal of Computational Physics 488 (2023) 112234","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.047396Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:6a0982d5c9b2fdc98f297b31611130e88c2e7a101ec1ef84bba0f2629c53806b","observation_id":"27acd6f3-b03a-4969-be02-613888bbaf71","resolution":{"observed_at":"2026-08-07T00:58:36.047396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.07576","last_updated":"2016-06-03T10:54:16Z","snapshot_observed_at":"2026-07-06T04:47:14.492719Z","submitted_at":"2016-02-24T16:17:15Z","title":"Group Equivariant Convolutional Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1602.07576","snapshot_observed_at":"2026-08-07T00:58:36.200164Z","title":"Cohen and M","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.200164Z"},"links":{"cited_paper":"/paper/1602.07576","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b02dc49ef431fe66c811a80284aa1020d0bff03d34d251bd2d0eabec492d20f3","observation_id":"a725f05d-ba25-4c98-8ead-d870c8bd3d7b","resolution":{"observed_at":"2026-08-07T00:58:36.200164Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.08498","last_updated":"2016-12-27T04:38:28Z","snapshot_observed_at":"2026-08-03T09:34:12.086195Z","submitted_at":"2016-12-27T04:38:28Z","title":"Steerable CNNs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.08498","snapshot_observed_at":"2026-08-07T00:58:36.289416Z","title":"Cohen and M","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.289416Z"},"links":{"cited_paper":"/paper/1612.08498","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:34cd9f2a223ea04bfae675369ca376e6a9f9ea9d7c6a5330dd18c35504a5f3ca","observation_id":"5e96cee4-6250-4f62-94fd-71de449ddd36","resolution":{"observed_at":"2026-08-07T00:58:36.289416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.04642","last_updated":"2017-04-11T13:34:17Z","snapshot_observed_at":"2026-07-06T05:22:39.584532Z","submitted_at":"2016-12-14T14:01:11Z","title":"Harmonic Networks: Deep Translation and Rotation Equivariance","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1612.04642","snapshot_observed_at":"2026-08-07T00:58:36.372277Z","title":"Worrall, S.J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.372277Z"},"links":{"cited_paper":"/paper/1612.04642","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:26c3783bc39fb99d30419449e2634e21f5adc8dc061d300b5dfc66c9e543e3fb","observation_id":"b815964e-7a45-4cbf-a309-ba7fbd123dce","resolution":{"observed_at":"2026-08-07T00:58:36.372277Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1804.04458","last_updated":"2018-04-12T12:14:18Z","snapshot_observed_at":"2026-07-06T06:33:06.588416Z","submitted_at":"2018-04-12T12:14:18Z","title":"CubeNet: Equivariance to 3D Rotation and Translation","version":1},"cited_work":{"arxiv_id":"1804.04458","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.04458","snapshot_observed_at":"2026-08-07T00:58:50.343658Z","title":"CubeNet: Equivariance to 3D Rotation and Translation","venue":"cs.CV","work_id":"83b95f23-6e52-4807-a8a5-918224c18f71","year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.477054Z"},"links":{"cited_paper":"/paper/1804.04458","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:195f3e2595ac910525733fac06dc99ccba7d5a453a5cf28c636f4aea3ccda047","observation_id":"2bee4283-698f-438a-9090-2662b52140cd","resolution":{"observed_at":"2026-08-07T00:58:50.445101Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1809.10504","last_updated":"2018-09-27T13:16:37Z","snapshot_observed_at":"2026-08-08T06:43:39.877825Z","submitted_at":"2018-09-27T13:16:37Z","title":"A rotation-equivariant convolutional neural network model of primary visual cortex","version":1},"cited_work":{"arxiv_id":"1809.10504","doi":null,"metadata_source":"pith","pith_arxiv_id":"1809.10504","snapshot_observed_at":"2026-08-07T00:58:50.133705Z","title":"A rotation-equivariant convolutional neural network model of primary visual cortex","venue":"q-bio.NC","work_id":"7c4e7f06-80bb-4d7b-9848-3fc5ccc94fe6","year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.563770Z"},"links":{"cited_paper":"/paper/1809.10504","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:4d398ca355579f5d0ce7f1f5a40d72a82dd0dd9f55ef0b5755561ce209114c8f","observation_id":"2997f42e-2144-4e73-8953-b8f96c98be92","resolution":{"observed_at":"2026-08-07T00:58:50.181374Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1806.03962","last_updated":"2018-06-08T12:13:37Z","snapshot_observed_at":"2026-08-04T22:07:19.105018Z","submitted_at":"2018-06-08T12:13:37Z","title":"Rotation Equivariant CNNs for Digital Pathology","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.03962","snapshot_observed_at":"2026-08-07T00:58:36.715649Z","title":"Veeling, J","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.715649Z"},"links":{"cited_paper":"/paper/1806.03962","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:09edf4626ac8599f6f7940aec560474ed94b3d78aeeb7633f5c7aac57578a2cf","observation_id":"a74d1b8d-6cd3-4985-96fa-b26acc262f21","resolution":{"observed_at":"2026-08-07T00:58:36.715649Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.08725","last_updated":"2020-02-20T13:44:29Z","snapshot_observed_at":"2026-08-07T19:24:47.471695Z","submitted_at":"2020-02-20T13:44:29Z","title":"Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis","version":1},"cited_work":{"arxiv_id":"2002.08725","doi":null,"metadata_source":"pith","pith_arxiv_id":"2002.08725","snapshot_observed_at":"2026-08-07T00:58:49.933060Z","title":"Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis","venue":"cs.CV","work_id":"75cf7c37-58eb-4a5e-baba-0ddac5428b03","year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.850216Z"},"links":{"cited_paper":"/paper/2002.08725","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:496bb429b7d3b44d9bde43482f88b09c3a060a595694143c21fe434ad2cf2ee0","observation_id":"accbe9f4-e101-43e5-a6ff-edeed870b061","resolution":{"observed_at":"2026-08-07T00:58:50.012050Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2005.03924","last_updated":"2020-05-08T09:36:50Z","snapshot_observed_at":"2026-08-09T19:13:38.268607Z","submitted_at":"2020-05-08T09:36:50Z","title":"Beyond CNNs: Exploiting Further Inherent Symmetries in Medical Images for Segmentation","version":1},"cited_work":{"arxiv_id":"2005.03924","doi":null,"metadata_source":"pith","pith_arxiv_id":"2005.03924","snapshot_observed_at":"2026-08-07T00:58:49.758662Z","title":"Beyond CNNs: Exploiting Further Inherent Symmetries in Medical Images for Segmentation","venue":"eess.IV","work_id":"e8be9e26-5971-4a61-81eb-66e5398b79a4","year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:36.967900Z"},"links":{"cited_paper":"/paper/2005.03924","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:fb05b924c77303ddf522261fc2b5c54959b83b10f16bbea12e7c25cb0d99fb17","observation_id":"2d480661-f0e8-49ae-a067-a5c033f8eeb2","resolution":{"observed_at":"2026-08-07T00:58:49.844399Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2102.08252","last_updated":"2021-02-18T13:18:00Z","snapshot_observed_at":"2026-08-09T10:17:57.104499Z","submitted_at":"2021-02-16T16:17:14Z","title":"Fanaroff-Riley classification of radio galaxies using group-equivariant convolutional neural networks","version":2},"cited_work":{"arxiv_id":"2102.08252","doi":null,"metadata_source":"pith","pith_arxiv_id":"2102.08252","snapshot_observed_at":"2026-08-07T00:58:49.622268Z","title":"Fanaroff-Riley classification of radio galaxies using group-equivariant convolutional neural networks","venue":"astro-ph.IM","work_id":"f86be9d6-36ca-4010-84a9-83aba491a4f6","year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.076834Z"},"links":{"cited_paper":"/paper/2102.08252","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:f8b0473edb00a087503c1207e5249b8f108bafcd080aef5cd8e3e4b752108557","observation_id":"8af01af8-55c8-4e05-b92d-9d902b2b6a5d","resolution":{"observed_at":"2026-08-07T00:58:49.701517Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.03690","last_updated":"2018-11-10T23:20:43Z","snapshot_observed_at":"2026-07-06T06:22:45.639530Z","submitted_at":"2018-02-11T04:32:33Z","title":"On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1802.03690","snapshot_observed_at":"2026-08-07T00:58:37.199994Z","title":"Kondor and S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.199994Z"},"links":{"cited_paper":"/paper/1802.03690","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:544a180818e87758560de2e83da5eb5358134115fae38dce52c32ec36604e140","observation_id":"29e012bb-adc1-429d-b0c5-ae014c616bab","resolution":{"observed_at":"2026-08-07T00:58:37.199994Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.02481","last_updated":"2019-06-06T08:51:50Z","snapshot_observed_at":"2026-07-06T07:58:24.206559Z","submitted_at":"2019-06-06T08:51:50Z","title":"Covariance in Physics and Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":"1906.02481","doi":null,"metadata_source":"pith","pith_arxiv_id":"1906.02481","snapshot_observed_at":"2026-08-07T00:58:49.387938Z","title":"Covariance in Physics and Convolutional Neural Networks","venue":"cs.LG","work_id":"2b4cadcd-fe77-4161-8fe1-dece674c4ab4","year":2019},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.348370Z"},"links":{"cited_paper":"/paper/1906.02481","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:bf56bcbc1a8059f068be1c22c4ab46a7261cbf6d8dd52e3cbddb54eeb3366394","observation_id":"d30ea498-0796-497f-9872-792d4f8238ab","resolution":{"observed_at":"2026-08-07T00:58:49.492821Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2004.05154","last_updated":"2020-04-30T02:10:51Z","snapshot_observed_at":"2026-08-09T18:21:34.036117Z","submitted_at":"2020-04-10T17:57:27Z","title":"Theoretical Aspects of Group Equivariant Neural Networks","version":2},"cited_work":{"arxiv_id":"2004.05154","doi":null,"metadata_source":"pith","pith_arxiv_id":"2004.05154","snapshot_observed_at":"2026-08-07T00:58:49.221362Z","title":"Theoretical Aspects of Group Equivariant Neural Networks","venue":"cs.LG","work_id":"811c4c9f-fde5-424d-980b-818450165295","year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.523954Z"},"links":{"cited_paper":"/paper/2004.05154","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:56a4d951b15fe7acd910f049dd8f33952cc223ac074a1bde2a17e7f51de9f1bb","observation_id":"df285526-dd37-4060-bb1e-bcaedd286087","resolution":{"observed_at":"2026-08-07T00:58:49.286596Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.16867","last_updated":"2023-03-03T15:36:34Z","snapshot_observed_at":"2026-08-05T10:25:31.426480Z","submitted_at":"2020-06-30T14:56:05Z","title":"Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey","version":2},"cited_work":{"arxiv_id":"2006.16867","doi":null,"metadata_source":"pith","pith_arxiv_id":"2006.16867","snapshot_observed_at":"2026-08-07T00:58:49.066189Z","title":"Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey","venue":"cs.CV","work_id":"10f1bae1-0c97-4dac-811d-d15e1bed0f96","year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.651999Z"},"links":{"cited_paper":"/paper/2006.16867","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:2dc73845da74eb9ff229a9bbb2f97168a06beca12aa373ada7cfa9017cf4c12c","observation_id":"3c89c460-bbbe-4788-9c83-15a3fa9306a4","resolution":{"observed_at":"2026-08-07T00:58:49.158611Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2105.13926","last_updated":"2021-05-28T15:41:52Z","snapshot_observed_at":"2026-08-03T23:51:57.733307Z","submitted_at":"2021-05-28T15:41:52Z","title":"Geometric Deep Learning and Equivariant Neural Networks","version":1},"cited_work":{"arxiv_id":"2105.13926","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.13926","snapshot_observed_at":"2026-08-07T00:58:48.873412Z","title":"Geometric Deep Learning and Equivariant Neural Networks","venue":"cs.LG","work_id":"4867aa3c-c267-4a04-8d8a-776f4bd7f916","year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.737413Z"},"links":{"cited_paper":"/paper/2105.13926","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:832dae4c4025d10a06981d44c618b87d5456eb4a658d88775cbae323397e3694","observation_id":"5bb847ee-aff7-44e7-8101-60b8b8ab65d2","resolution":{"observed_at":"2026-08-07T00:58:48.945466Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:37.830157Z","title":"Celledoni, M.J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.830157Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:30783dd4e74003bde9237d901c55f9482e3cf9f077253f12f8e12737cab4680e","observation_id":"fdb902a9-dfd8-4dc9-9151-632c96718464","resolution":{"observed_at":"2026-08-07T00:58:37.830157Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:37.974704Z","title":"Aronsson, Homogeneous vector bundles and G-equivariant convolutional neural networks , Sampling Theory, Signal Processing, and Data Analysis 20 (2022) 10","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:37.974704Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:23c2abb4364a38f84779c5a9366a97cd43a8516591b5b4e475c598ff31dddf8b","observation_id":"874723e4-83ff-4f9f-b68a-3491c1525023","resolution":{"observed_at":"2026-08-07T00:58:37.974704Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2212.06096","last_updated":"2023-10-27T14:31:32Z","snapshot_observed_at":"2026-08-09T18:40:04.086318Z","submitted_at":"2022-12-12T18:10:33Z","title":"Implicit Convolutional Kernels for Steerable CNNs","version":3},"cited_work":{"arxiv_id":"2212.06096","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.06096","snapshot_observed_at":"2026-08-07T00:58:48.648768Z","title":"Implicit Convolutional Kernels for Steerable CNNs","venue":"cs.LG","work_id":"89e955d8-528a-48ad-a796-da376a60bc42","year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.082000Z"},"links":{"cited_paper":"/paper/2212.06096","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:35c3de627fac6a7e35d6ef468b7cee564a8d2109d5ac07b68c86c4fc50bb7777","observation_id":"2c1e9e36-9237-425c-980e-82b4ba703c4c","resolution":{"observed_at":"2026-08-07T00:58:48.749597Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:38.202852Z","title":"Hossain, S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.202852Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:f8936a2f32ed74a7bf025812094a67fc56661bbde1deba5b40b2feeb0953c935","observation_id":"a9d22d46-24bb-443a-91cb-050fef95cd04","resolution":{"observed_at":"2026-08-07T00:58:38.202852Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:38.310581Z","title":"Edixhoven, A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.310581Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:8d820d0d09a1cac0be0087dde049501e9df0e08c7009b21186a21b290e7acfbd","observation_id":"c5167c25-72ff-4665-b17b-a5b812c7f66b","resolution":{"observed_at":"2026-08-07T00:58:38.310581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.04615","last_updated":"2019-05-13T23:03:52Z","snapshot_observed_at":"2026-08-09T17:17:13.630798Z","submitted_at":"2019-02-11T17:01:05Z","title":"Gauge Equivariant Convolutional Networks and the Icosahedral CNN","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.04615","snapshot_observed_at":"2026-08-07T00:58:38.413877Z","title":"Cohen, M","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.413877Z"},"links":{"cited_paper":"/paper/1902.04615","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:c507b282c28a1449fb444ac52c1affba3d718d23581bce6ff88b576ec4b878e2","observation_id":"4a37f704-b90f-478a-932a-a6cca03ffb7b","resolution":{"observed_at":"2026-08-07T00:58:38.413877Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.05232","last_updated":"2022-05-11T23:38:50Z","snapshot_observed_at":"2026-07-06T10:22:18.963385Z","submitted_at":"2020-12-09T18:57:02Z","title":"Gauge equivariant neural networks for quantum lattice gauge theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.05232","snapshot_observed_at":"2026-08-07T00:58:38.511943Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.511943Z"},"links":{"cited_paper":"/paper/2012.05232","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:254ff8aeb3c7135c572b9ee76387f1bc6288fe094fb151e53d01c234751bd5f6","observation_id":"8fd83f4f-0234-462c-8143-2198470cd760","resolution":{"observed_at":"2026-08-07T00:58:38.511943Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.12880","last_updated":"2020-09-24T15:08:36Z","snapshot_observed_at":"2026-08-04T21:17:08.888463Z","submitted_at":"2020-02-25T17:40:38Z","title":"Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.12880","snapshot_observed_at":"2026-08-07T00:58:38.627300Z","title":"Finzi, S","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.627300Z"},"links":{"cited_paper":"/paper/2002.12880","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:d8f9d2778f1764bc7331533fcd3c0c0b74f167b0009cfc5d68f8d5f3bedc3956","observation_id":"d5564258-a6d8-453f-b747-83a7863a8c00","resolution":{"observed_at":"2026-08-07T00:58:38.627300Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2103.11965","last_updated":"2024-10-29T13:03:56Z","snapshot_observed_at":"2026-08-03T22:56:59.365268Z","submitted_at":"2021-03-22T16:14:09Z","title":"Gauge covariant neural network for quarks and gluons","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.11965","snapshot_observed_at":"2026-08-07T00:58:38.742479Z","title":"Nagai and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.742479Z"},"links":{"cited_paper":"/paper/2103.11965","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:c9e4494d7929c38da721fa72d3669a5f583e86e4b605563447cbc10b2a325921","observation_id":"54b21998-f4ee-46f9-a468-272ce22d9648","resolution":{"observed_at":"2026-08-07T00:58:38.742479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.11448","last_updated":"2023-03-20T20:49:08Z","snapshot_observed_at":"2026-07-06T15:05:53.556198Z","submitted_at":"2023-03-20T20:49:08Z","title":"Geometrical aspects of lattice gauge equivariant convolutional neural networks","version":1},"cited_work":{"arxiv_id":"2303.11448","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.11448","snapshot_observed_at":"2026-08-07T00:58:48.370863Z","title":"Geometrical aspects of lattice gauge equivariant convolutional neural networks","venue":"hep-lat","work_id":"a063e503-04a8-4465-a807-093c0bd81c46","year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.860519Z"},"links":{"cited_paper":"/paper/2303.11448","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:15edf97b76eaa234ceb21f4d98d783432e406cd2ca9c8d37b1ce1ace97d3c984","observation_id":"fe9fcd2d-e8b2-4b80-b215-6e34b64cd9bf","resolution":{"observed_at":"2026-08-07T00:58:48.433396Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2302.05419","last_updated":"2023-02-10T18:34:54Z","snapshot_observed_at":"2026-07-06T14:50:33.453443Z","submitted_at":"2023-02-10T18:34:54Z","title":"Gauge-equivariant neural networks as preconditioners in lattice QCD","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.05419","snapshot_observed_at":"2026-08-07T00:58:38.966083Z","title":"Lehner and T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:38.966083Z"},"links":{"cited_paper":"/paper/2302.05419","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:e1316a72735511218549564622a688d8369175cbf6266373ef9149a941194ca4","observation_id":"2f35d0df-3e3a-4361-83b3-6b128bd7ca97","resolution":{"observed_at":"2026-08-07T00:58:38.966083Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.10438","last_updated":"2023-04-20T16:30:37Z","snapshot_observed_at":"2026-08-02T11:40:30.840316Z","submitted_at":"2023-04-20T16:30:37Z","title":"Gauge-equivariant pooling layers for preconditioners in lattice QCD","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.10438","snapshot_observed_at":"2026-08-07T00:58:39.066099Z","title":"Lehner and T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.066099Z"},"links":{"cited_paper":"/paper/2304.10438","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:958f0c5ffbc680fa1fdbe75ba968fd3a470fb531399a21bff492bd68048392ba","observation_id":"6687f949-d2c8-45e9-9818-d912e7c8efca","resolution":{"observed_at":"2026-08-07T00:58:39.066099Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.06481","last_updated":"2024-10-02T22:51:02Z","snapshot_observed_at":"2026-08-01T18:45:22.570957Z","submitted_at":"2024-01-12T10:03:00Z","title":"Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.06481","snapshot_observed_at":"2026-08-07T00:58:39.161490Z","title":"Holland, A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.161490Z"},"links":{"cited_paper":"/paper/2401.06481","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:bf0685c12e651e22896001e1cd51792a05ca7cd2fc132990b0e47cf4f0139c61","observation_id":"ad41b40e-5761-496d-8c4e-76d2402bf201","resolution":{"observed_at":"2026-08-07T00:58:39.161490Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2306.11527","last_updated":"2024-07-02T05:10:18Z","snapshot_observed_at":"2026-07-06T15:44:35.147343Z","submitted_at":"2023-06-20T13:30:01Z","title":"Self-learning Monte Carlo with equivariant Transformer","version":3},"cited_work":{"arxiv_id":"2306.11527","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.11527","snapshot_observed_at":"2026-08-07T00:58:48.157390Z","title":"Self-learning Monte Carlo with equivariant Transformer","venue":"cond-mat.str-el","work_id":"e7a14b7c-d4f3-40d5-9707-7eef5d26e281","year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.264522Z"},"links":{"cited_paper":"/paper/2306.11527","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:a757bb5035188ab990a85012f81c1f2de6aee4464d593e508fc5fb9fa98d47bb","observation_id":"61d0d7e6-eb6b-40d1-afcc-37543ed99ffe","resolution":{"observed_at":"2026-08-07T00:58:48.228936Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.13222","last_updated":"2023-10-20T01:57:03Z","snapshot_observed_at":"2026-08-09T19:44:18.814178Z","submitted_at":"2023-10-20T01:57:03Z","title":"Equivariant Transformer is all you need","version":1},"cited_work":{"arxiv_id":"2310.13222","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.13222","snapshot_observed_at":"2026-08-07T00:58:47.956433Z","title":"Equivariant Transformer is all you need","venue":"hep-lat","work_id":"a5db0e20-48d3-498d-bd0c-41a092f66401","year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.347255Z"},"links":{"cited_paper":"/paper/2310.13222","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b53a6e6ef859d5f0885c1be1d8fb22af5e8fc59387054e443af35f87b2326502","observation_id":"e78611ab-c050-450a-83dc-983e11c069ff","resolution":{"observed_at":"2026-08-07T00:58:48.055757Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.06413","last_updated":"2020-03-13T17:54:05Z","snapshot_observed_at":"2026-07-06T09:04:34.898649Z","submitted_at":"2020-03-13T17:54:05Z","title":"Equivariant flow-based sampling for lattice gauge theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.06413","snapshot_observed_at":"2026-08-07T00:58:39.474806Z","title":"Kanwar, M.S","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.474806Z"},"links":{"cited_paper":"/paper/2003.06413","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:92f3624f70ec31192d7a37db27394c2ccce4884d1368ae8213fbf714f1c976ab","observation_id":"2dccc692-8348-4d20-bb71-ebb0a971e76a","resolution":{"observed_at":"2026-08-07T00:58:39.474806Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.05456","last_updated":"2020-09-18T18:39:15Z","snapshot_observed_at":"2026-07-06T09:46:42.056120Z","submitted_at":"2020-08-12T17:43:39Z","title":"Sampling using $SU(N)$ gauge equivariant flows","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.05456","snapshot_observed_at":"2026-08-07T00:58:39.563726Z","title":"Boyda, G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.563726Z"},"links":{"cited_paper":"/paper/2008.05456","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:c083128847189894e52d87021456e05e3ad0a67d9c8a736ca2e3fcb59fd26a43","observation_id":"22bbe7c8-951a-414d-83c6-4527af939172","resolution":{"observed_at":"2026-08-07T00:58:39.563726Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.05934","last_updated":"2021-12-28T22:33:50Z","snapshot_observed_at":"2026-08-07T06:49:57.231320Z","submitted_at":"2021-06-10T17:32:47Z","title":"Flow-based sampling for fermionic lattice field theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.05934","snapshot_observed_at":"2026-08-07T00:58:39.653396Z","title":"Albergo, G","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.653396Z"},"links":{"cited_paper":"/paper/2106.05934","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:0ce72894ff111f7eb7bc5a414b84c70448200c5a83d654290d6f8b82c5cea9a9","observation_id":"bee0ecda-749c-45f8-bc96-c439fa356d33","resolution":{"observed_at":"2026-08-07T00:58:39.653396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:39.778568Z","title":"Abbott, M.S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.778568Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:5a03e7aefe97c69bf50b8e874f68af75821ce2a89125639dc03ab042a5190590","observation_id":"8ca5e41b-85de-490f-91ef-67269462b63e","resolution":{"observed_at":"2026-08-07T00:58:39.778568Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.14082","last_updated":"2023-11-03T07:19:53Z","snapshot_observed_at":"2026-08-06T19:54:11.108629Z","submitted_at":"2023-02-27T19:00:22Z","title":"Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.14082","snapshot_observed_at":"2026-08-07T00:58:39.900674Z","title":"Nicoli, C.J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.900674Z"},"links":{"cited_paper":"/paper/2302.14082","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:b37057cf5d577c4f25afa13f99d9ac74cbe699c8b7dbd71e138c0ee08045c27e","observation_id":"f29e81e7-1bbe-4dd9-a07f-1fc3ac3c69fc","resolution":{"observed_at":"2026-08-07T00:58:39.900674Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:39.999839Z","title":"Bacchio, P","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:39.999839Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:fc383d271810f0bc2ed54c0265a0458a3a88023f62488b41c12c7854ea221adf","observation_id":"484cbad4-9966-4769-9dd8-f424d441b0b8","resolution":{"observed_at":"2026-08-07T00:58:39.999839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.08895","last_updated":"2020-09-18T15:38:21Z","snapshot_observed_at":"2026-07-06T09:56:50.303479Z","submitted_at":"2020-09-18T15:38:21Z","title":"Remarks on relativistic scalar models with chemical potential","version":1},"cited_work":{"arxiv_id":"2009.08895","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.08895","snapshot_observed_at":"2026-08-07T00:58:47.715002Z","title":"Remarks on relativistic scalar models with chemical potential","venue":"hep-th","work_id":"811f5e3f-452f-4ba9-8830-62779fe055f7","year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.092090Z"},"links":{"cited_paper":"/paper/2009.08895","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:fa9fd375e9895f412b493a5c2171ce4637c17a8cde622b997e198ad500dbfd00","observation_id":"7e7602ed-126a-443b-8a39-8b85856f6efe","resolution":{"observed_at":"2026-08-07T00:58:47.798748Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1206.2954","last_updated":"2017-02-03T11:28:10Z","snapshot_observed_at":"2026-08-08T21:08:33.503231Z","submitted_at":"2012-06-13T22:15:10Z","title":"Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1206.2954","snapshot_observed_at":"2026-08-07T00:58:40.231523Z","title":"Gattringer and T","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.231523Z"},"links":{"cited_paper":"/paper/1206.2954","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:637254dc140c567e9227a601b7643c3189a604d2616f780b69caf6a1864c2c6d","observation_id":"482383b5-09ab-4a8b-aa41-a39155afff75","resolution":{"observed_at":"2026-08-07T00:58:40.231523Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:40.350656Z","title":"Angulu, J.R","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.350656Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:1c2c7883b77556d326a7217579c5f8ecc21275a2d506f0c265deb41e9df33c4b","observation_id":"bd37881e-4c23-493e-809b-dbfc42af8789","resolution":{"observed_at":"2026-08-07T00:58:40.350656Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.01703","last_updated":"2019-12-03T22:06:05Z","snapshot_observed_at":"2026-07-06T08:41:49.632205Z","submitted_at":"2019-12-03T22:06:05Z","title":"PyTorch: An Imperative Style, High-Performance Deep Learning Library","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.01703","snapshot_observed_at":"2026-08-07T00:58:40.485614Z","title":"Paszke, S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.485614Z"},"links":{"cited_paper":"/paper/1912.01703","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:4f72f4253c0e4871c881f958746a1865a858f2e8c1929e59583d131234f04af8","observation_id":"7e14b243-91c0-4347-b549-4bc8651d8b25","resolution":{"observed_at":"2026-08-07T00:58:40.485614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:58:40.608054Z","title":"Bozinovski, Reminder of the First Paper on Transfer Learning in Neural Networks, 1976 , Informatica (Slovenia) 44 (2020) 291","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.608054Z"},"links":{"citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:1358ed1d73d9c7dd53a38c66994ca2891acf63f2c1a32a75ee09abe3e36db2ef","observation_id":"f9b45110-26b5-4486-a192-81e633426773","resolution":{"observed_at":"2026-08-07T00:58:40.608054Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1511.07122","last_updated":"2016-04-30T18:19:37Z","snapshot_observed_at":"2026-07-06T04:37:24.552839Z","submitted_at":"2015-11-23T07:32:14Z","title":"Multi-Scale Context Aggregation by Dilated Convolutions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.07122","snapshot_observed_at":"2026-08-07T00:58:40.750257Z","title":"Yu and V","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-07T00:58:40.750257Z"},"links":{"cited_paper":"/paper/1511.07122","citing_paper":"/paper/2506.12493"},"observation_digest":"sha256:7897125b938f9b47226cca4f35f392daaf3238145549ad553c56f29fbbb2a7ff","observation_id":"3a66b026-ef51-4c1b-8b54-7abbd4a02adb","resolution":{"observed_at":"2026-08-07T00:58:40.750257Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2506.12493","last_updated":"2025-06-14T13:12:25Z","latest_version":1,"primary_category":"hep-lat","snapshot_observed_at":"2026-08-07T17:48:45.226951Z","submitted_at":"2025-06-14T13:12:25Z","title":"Symmetry-preserving neural networks in lattice field theories"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":81,"verified_exact":19,"verified_fuzzy":0},"total_outbound_references":146},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 100 of 146 outbound references and 1 inbound Pith citation observation for arXiv:2506.12493."}