{"as_of":"2026-07-31T14:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7e0fff1476dd9c571dcf5f1408b69574ace0dba3c076e034a392fd414fc7a6da","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-22T04:38:51.773377Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-07-31T06:34:12.847434+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.21933/citation-record","integrity":"/paper/2605.21933/integrity","json":"/paper/2605.21933/citation-record.json","paper":"/paper/2605.21933"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1902.06015","last_updated":"2019-02-16T00:01:01Z","snapshot_observed_at":"2026-07-06T07:33:25.489427Z","submitted_at":"2019-02-16T00:01:01Z","title":"Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit","version":1},"cited_work":{"arxiv_id":"1902.06015","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.06015","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit","venue":"stat.ML","work_id":"8838a655-5d95-4f3f-a0a3-d1f90245fec3","year":2019},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/1902.06015","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:ad054e9b8b884e4c3266b2ccb46b71d8ced4fa9dc09175a5592de8d08a4e0d34","observation_id":"f60164b5-8377-466a-b445-7e4e45a9c936","resolution":{"observed_at":"2026-05-22T04:41:04.241477Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Halverson, A","venue":null,"work_id":"80051c6d-0666-4625-96f6-4698ef32bd90","year":2021},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:596d8930a27b2bf7d38706850e1fb42f5bf5cff48120362fd7c73ed29170ebfa","observation_id":"f1c76b03-535f-4cbe-b6fa-aabcc8b14ef0","resolution":{"observed_at":"2026-05-22T04:41:04.695336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Rotskoff and E","venue":null,"work_id":"5baaf2e4-91a6-42b1-a1ba-f767b81b4176","year":2022},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:81808c7f4b504c7c76d0e8dc9a35ac1e62e3c47eeb1414fbeaf307949a97c32b","observation_id":"7d65ebdf-4267-4f81-8d8e-38858bf0b995","resolution":{"observed_at":"2026-05-22T04:41:04.683904Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2510.25553","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6cd6bb7a-ef5a-4506-a19b-562052cf2e90","year":2025},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:951fa6666befafd55360c52c565169121926d608e017ef55aad30363cf9ba3c9","observation_id":"c9babf64-7776-47a8-9cc1-f5a82a91f1b2","resolution":{"observed_at":"2026-05-22T04:41:04.274914Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.03495","last_updated":"2021-01-15T14:57:46Z","snapshot_observed_at":"2026-07-06T08:55:58.482745Z","submitted_at":"2020-02-10T02:04:49Z","title":"A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima","version":14},"cited_work":{"arxiv_id":"2002.03495","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2002.03495","snapshot_observed_at":"2026-07-02T16:47:10.361461Z","title":"A diffusion theory for deep learning dynamics: Stochastic gradient descent exponentially favors flat minima","venue":null,"work_id":"1c1ac655-d127-43e9-ab9c-a16d9c68df53","year":2002},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/2002.03495","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:51219e6c7355e798b5d42cd63fdb50e1e495fead16d5293fef35d13440ee933e","observation_id":"16e5f64e-e377-4fe1-9fde-d22be7d914d5","resolution":{"observed_at":"2026-05-22T04:41:04.270581Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Prigogine and R","venue":null,"work_id":"0f045933-5481-4d7a-be41-42d44ddd671a","year":1973},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:bbc87025b02458e7c79813cc58ca5d4546bf70d24b375fdf25ad38b0a182bd42","observation_id":"d615f377-7eb8-468e-8886-837221cd03c0","resolution":{"observed_at":"2026-05-22T04:41:04.764921Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Seifert, The European Physical Journal B64, 423 (2008)","venue":null,"work_id":"c39186bc-cfdc-4dfe-ace1-cf5a056afa20","year":2008},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:022109f7b9812b8ba0b0aeb27a65d6cc28766ded118a3652a8f0186cea790f79","observation_id":"c0541980-2bd8-4e59-9091-72839d8cae24","resolution":{"observed_at":"2026-05-22T04:41:04.758215Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"O’Byrne, Y","venue":null,"work_id":"97bc23c5-6362-4226-9a7f-4bff70201df7","year":2022},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:fdc06c86d9c8aaec98967a098ad27e455eedf72093b03cb6b4543cde64ab0a70","observation_id":"c5b6a752-e98d-4984-b861-575b4addd5a9","resolution":{"observed_at":"2026-05-22T04:41:04.751875Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a83f538d-465c-4157-87bd-23a45bc22386","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:bccfccc45d1b8edde4156ad579a8b78d251492704dc7d3c74bd6c993e2cecaa1","observation_id":"3f6da75b-828a-4876-bbee-c4ae31967ffe","resolution":{"observed_at":"2026-05-22T04:41:04.749060Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":"1412.6980","doi":"10.1002/mrm.28086","metadata_source":"pith","pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"Adam: A Method for Stochastic Optimization","venue":"cs.LG","work_id":"1910796d-9b52-4683-bf5c-de9632c1028b","year":2014},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:9df3f9829cbd70cf55245d71d1c4faa46015cc01c938e5f0910c6fc5c099dd55","observation_id":"d7fbb36c-9575-468e-b9de-6f2090fe635e","resolution":{"observed_at":"2026-05-22T04:41:04.255779Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Tieleman and G","venue":null,"work_id":"d12457ae-1c52-489f-9cbd-2f24230b4b58","year":2012},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:cd7f2827137db1216ae6678ece984c0505238dc81ebe562dad4756ac96a6f739","observation_id":"76d1af30-087b-456c-9ede-2e813c64c710","resolution":{"observed_at":"2026-05-22T04:41:04.746064Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T22:30:10.536235Z","title":null,"venue":null,"work_id":"7ce15c46-67a6-4740-b6f7-eb3072400809","year":1976},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:a07f5482a8d43047440206867fbbd8136c7d84a44d89a9a4e9c6f0d37c43963e","observation_id":"85e60875-b36c-4936-b336-428e6bdd9a45","resolution":{"observed_at":"2026-05-22T04:41:04.743130Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hairer, M","venue":null,"work_id":"e500358f-b945-43a8-833d-aa9fca86cfcd","year":2006},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:4f95f8351635220029bea48909ae6b0039299b7b38a7a6722fa59607ace166ca","observation_id":"0f48fb44-ebb0-4173-ae34-17abc7ee215e","resolution":{"observed_at":"2026-05-22T04:41:04.674103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.12176","last_updated":"2021-01-28T18:32:14Z","snapshot_observed_at":"2026-07-06T10:36:34.713016Z","submitted_at":"2021-01-28T18:32:14Z","title":"On the Origin of Implicit Regularization in Stochastic Gradient Descent","version":1},"cited_work":{"arxiv_id":"2101.12176","doi":null,"metadata_source":"pith","pith_arxiv_id":"2101.12176","snapshot_observed_at":"2026-07-09T07:56:04.664291Z","title":"arXiv preprint arXiv:2101.12176 , year=","venue":"cs.LG","work_id":"5c35f243-a7e6-4541-ab92-8182eaf513fe","year":2021},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/2101.12176","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:fa2d131f755845400cdc7e7f3ca87afc05fc7f7587dac118439a02a7038a4382","observation_id":"b66cfb7d-6808-4888-a784-2e0447680fd7","resolution":{"observed_at":"2026-05-22T04:41:04.236302Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.11162","last_updated":"2022-07-18T20:57:25Z","snapshot_observed_at":"2026-07-06T09:58:08.880543Z","submitted_at":"2020-09-23T14:17:53Z","title":"Implicit Gradient Regularization","version":3},"cited_work":{"arxiv_id":"2009.11162","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.11162","snapshot_observed_at":"2026-07-09T07:56:04.666556Z","title":"Implicit gradient regularization","venue":"cs.LG","work_id":"86014c80-8dfc-43e6-a1d0-77279d545f37","year":2020},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/2009.11162","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:e99740a34c0c991b48161a2ac9738f2d4d532f78b46f911b1ac414fe68172cf4","observation_id":"3152b507-0779-4e32-82ad-fa339ef32253","resolution":{"observed_at":"2026-05-22T04:41:04.218335Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ziyin, H","venue":null,"work_id":"d595a50a-bcb1-4ca1-9672-386dff833a20","year":2025},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:70aa110ed8cc442477c3e84a474a858c7c77b37703d8a9f67b5b2e60dc3242f3","observation_id":"bd6d1732-4dea-4ce3-9b02-e851238d21dd","resolution":{"observed_at":"2026-05-22T04:41:04.701184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"0649fe72-a411-4d7e-8d1d-443bb118e774","year":1971},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:dad972508b0b567d594278bb83107bad65911488ee8496e1ba5fdceb79dff132","observation_id":"7147e5a4-0978-4823-89e8-3caea8e312c3","resolution":{"observed_at":"2026-05-22T04:41:04.686447Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ziyin and M","venue":null,"work_id":"d0ce4798-7fc0-471a-bf25-e7cbe647d715","year":2023},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:8835e310d69881aa6c2a1413f0983d46035c6c6847264e14df09863225565863","observation_id":"629d5f67-c9f6-4aa7-8ded-a65550d522d6","resolution":{"observed_at":"2026-05-22T04:41:04.739681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1912.11797","last_updated":"2020-08-03T06:36:23Z","snapshot_observed_at":"2026-07-06T08:47:02.129339Z","submitted_at":"2019-12-26T08:05:35Z","title":"Thermodynamic Uncertainty Relation for Arbitrary Initial States","version":2},"cited_work":{"arxiv_id":"1912.11797","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1912.11797","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9c857648-cce1-44ce-8c1f-c8ab616f667a","year":1912},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/1912.11797","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:a4cda79047222dc954c125c5a2f19f5e9000c1f17192bdb8dbb83dfe7589fafd","observation_id":"653a38f6-7960-4a47-a6da-8c82d32c3fb7","resolution":{"observed_at":"2026-05-22T04:41:04.246630Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Goldt and U","venue":null,"work_id":"ef44503e-46e8-46b1-aac8-6e1a01106d71","year":2017},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:b262f6befdaa8a961da7d99bea4f36efb189bd9be0c38eee5fcf15f414c5f61b","observation_id":"7ba0233d-0ddf-4cdd-a2bd-cfd6bb4ed877","resolution":{"observed_at":"2026-05-22T04:41:04.773976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Murashita, K","venue":null,"work_id":"0ae31a74-e1bf-4590-bf9b-ee344b53b950","year":2014},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:6dce1f6dcaf28bf5a31cca6e29f45cb4e957af2ea790dd27ac99454d063d7dea","observation_id":"29d4c86a-5da5-46d1-b28e-8b2957e1b33f","resolution":{"observed_at":"2026-05-22T04:41:04.777122Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"38d191b1-ce9a-4ef9-994c-89bbbf00a28b","year":2021},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:d56c81ac56ccf63b8190493b0a633cef2aaab5616821e26d943e050be1f1af12","observation_id":"10c88cfd-b70c-4b3e-b802-c1d85bdcfa87","resolution":{"observed_at":"2026-05-22T04:41:04.768138Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"40c7e817-a7c7-450b-8ad1-6e584b3fc283","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:b3af87041d2713e7e1c1745c2cced6510c9d234bb15a1e6c3c64a1861df17b8a","observation_id":"e2acecba-54d4-4490-b820-4d4e50c88b57","resolution":{"observed_at":"2026-05-22T04:41:04.771012Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.05300","last_updated":"2025-05-23T17:22:54Z","snapshot_observed_at":"2026-07-06T20:33:06.406223Z","submitted_at":"2025-02-07T20:10:05Z","title":"Parameter Symmetry Potentially Unifies Deep Learning Theory","version":2},"cited_work":{"arxiv_id":"2502.05300","doi":"10.48550/arxiv.2502.05300","metadata_source":"arxiv_reference","pith_arxiv_id":"2502.05300","snapshot_observed_at":"2026-07-10T12:15:01.137692Z","title":"Ziyin, Y","venue":null,"work_id":"8e11bd7e-9d06-4c6c-b342-bbbdf465dd00","year":2025},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/2502.05300","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:8da876aba88f34061012e91ab51e4e7db4550b33c383d11f2ff9867336e754bf","observation_id":"fb451b88-15e2-4900-b577-343e509179c3","resolution":{"observed_at":"2026-05-22T04:41:04.261521Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1810.00004","last_updated":"2018-12-21T16:09:27Z","snapshot_observed_at":"2026-07-06T07:04:59.871975Z","submitted_at":"2018-09-28T18:00:00Z","title":"Fluctuation-dissipation relations for stochastic gradient descent","version":2},"cited_work":{"arxiv_id":"1810.00004","doi":null,"metadata_source":"pith","pith_arxiv_id":"1810.00004","snapshot_observed_at":"2026-07-01T15:35:47.573383Z","title":"Fluctuation-dissipation relations for stochastic gradient descent","venue":"stat.ML","work_id":"88750898-9e79-464b-bf56-16604a3c5652","year":2018},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/1810.00004","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:72cd57bc49c9a39c1c77526e68f92d3517307f4438615d0dfa2cbbe796508757","observation_id":"64503291-11bf-43a8-aae2-0ba0d53bdb47","resolution":{"observed_at":"2026-05-22T04:41:04.251165Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ziyin, Y","venue":null,"work_id":"a45acb39-91c5-4cda-af32-5b43899fa63f","year":2025},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:322900d41a7f3cad9f6b754b9ef070c306fc84c420a10256d504d3399c6b2a37","observation_id":"7d2b96b4-2b2b-4aa7-946a-b69aae0ea03d","resolution":{"observed_at":"2026-05-22T04:41:04.761649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.05065","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"4be30e6c-dd76-4d08-815e-28f48765a0d7","year":2026},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:6375f6c96d91c22128fa108a650f9e98305ee7295dd7084823d3c8f2401bc2f8","observation_id":"4aa122e1-216d-4e62-b755-bd5200da4a36","resolution":{"observed_at":"2026-05-22T04:41:04.266323Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Poggio, R","venue":null,"work_id":"013d6f2d-380c-440f-a980-73ef8f02c336","year":2004},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:be48fd35de8bfd5de267ee1c8608f90e970263691bc361a60d12d2ea9ffb99f8","observation_id":"e883348a-4936-437c-9519-a75cbf7a69bf","resolution":{"observed_at":"2026-05-22T04:41:04.754845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.01558","last_updated":"2018-11-05T09:00:29Z","snapshot_observed_at":"2026-07-06T07:12:36.518166Z","submitted_at":"2018-11-05T09:00:29Z","title":"Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations","version":1},"cited_work":{"arxiv_id":"1811.01558","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.01558","snapshot_observed_at":"2026-07-02T17:37:13.879256Z","title":"Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations","venue":"cs.LG","work_id":"119b1002-f3db-437c-9036-401a4196fe0a","year":2018},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"cited_paper":"/paper/1811.01558","citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:accaa2c4d0a2a002160083dd5bc8a518d8930b25a66002d1d8ba1e24b886f2b5","observation_id":"397c6b61-4d87-47cb-95e8-88a2e12d5a22","resolution":{"observed_at":"2026-05-22T04:41:04.213211Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"d730664e-bfbc-45d9-a5e8-ba5d42c4372c","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:d1645ddaf311b38bd3fe32c74664ed440d20b6ce41acb764335f1ecbf162a28f","observation_id":"a83c4d37-d675-49d9-ae22-2005861f09ca","resolution":{"observed_at":"2026-05-22T04:41:04.670939Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"symmetry","venue":null,"work_id":"0f09af08-5b5a-4242-be3a-b520a38b2798","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:57022ef6257b269ed1672eb04b77d05569edd98be9b00c3062c89962487cc492","observation_id":"eabbc429-9939-4532-a041-cd7d9d45276c","resolution":{"observed_at":"2026-05-22T04:41:04.736700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Theorem 6(Continuous Symmetry Breaking).Let K(θ, λ) =θ+λQ(θ) +O(λ 2)be a continuous symmetry generated byQ(θ)","venue":null,"work_id":"a9f892f5-51b8-42e3-ba50-e316a6f72a86","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:af35194f2df79dcbce676775e66f0b1909acfb5bfea001cf83b79625db58a746","observation_id":"e3d1d1c3-6a07-43cb-884b-28e1825982a6","resolution":{"observed_at":"2026-05-22T04:41:04.724667Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Theorem 7(Discrete Symmetry Preservation).Let the transformation beK(θ) =Oθ, whereOis an orthogonal matrix (O T O=I)","venue":null,"work_id":"96a881aa-a59a-4392-9a6e-9f493342fc22","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:da6283026c4bf469d87868166bb10367942b7498d9ab95aaf798fcdd1e1a7116","observation_id":"71860016-78f6-4143-b1d9-6fa08b2cbf25","resolution":{"observed_at":"2026-05-22T04:41:04.721383Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"f1c1b633-0287-445f-bf62-ec687b310f32","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:54aa2eaf3532768a8c5f9cb7d913bab0a0705f74f178b8340405f84d48dec8e2","observation_id":"3a20a6df-7a52-4ca3-9151-9892159ec15c","resolution":{"observed_at":"2026-05-22T04:41:04.677635Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Define Θcoarse(θ;η) =θ−ηU(θ),(G10) and Θfine(θ;η) = Θ η/2 ◦Θ η/2(θ),Θ η/2(θ) =θ− η 2 U(θ)","venue":null,"work_id":"af67f4ef-6ab0-4383-b549-112c6402ee9c","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:0131f3d6228d9291226fe81ee2c417a3e7580dc921cd3a51c72b7707dc35f06f","observation_id":"af932534-2fb2-4dc5-918b-29883eed6af0","resolution":{"observed_at":"2026-05-22T04:41:04.718528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Starting at θt, take one forward step and then one backward step with the sign of the step size reversed: θt+1 =θ t −ηU(θ t), ˜θt =θ t −ηU(θ t) +ηU(θ t+1)","venue":null,"work_id":"fec5076b-19c7-4286-a2bb-c413a0d8fecd","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:470eee6885ac938718570b65521c97eff468625696a3828956b1b7e5f41e271d","observation_id":"e723b048-c0da-4972-ace6-a149224c4910","resolution":{"observed_at":"2026-05-22T04:41:04.715225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"We in- troduce a virtual Gaussian transition kernel pσ(θ′|θ)∝exp − ∥θ′ −θ+ηU(θ)∥ 2 2σ2 ,(G27) whereσ 2 is a small virtual noise variance","venue":null,"work_id":"b3038eb1-5752-4b44-b37b-4665843d49d4","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:fb5228c90e9a04461ab14c8d2239e629b3fd9c358bcc4f907a6b40d3a5fd3b4f","observation_id":"ee432604-30d8-43b5-ab5b-db2daa616ccb","resolution":{"observed_at":"2026-05-22T04:41:04.711791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"(G33) Here bϕTA denotes the normalized quantity defined in Eq","venue":null,"work_id":"f6935f7e-0350-40c8-b36c-0a9d634d86e5","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:8cabe3440c721951b4b33b0113616c2585560da79fd33b95add3ef98575df6ba","observation_id":"7673364d-e4ac-48e6-90d7-bd41b6ed3c61","resolution":{"observed_at":"2026-05-22T04:41:04.708470Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"We consider a quadratic potential E(θ) = 1 2 θ⊤Aθ,(G34) whereA∈R d×d is positive definite","venue":null,"work_id":"206c04e3-2984-48f0-a7b6-cc999791b194","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:0f88ebdb0ab8eb58ffc0f27c6139e6dc5af5fadd8179fc517f13df00c5117b01","observation_id":"af75dcea-bf8a-45a1-8805-610f94e1d060","resolution":{"observed_at":"2026-05-22T04:41:04.705007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The model is a 2- layer causal Transformer (GPT-style) withd model = 128, nhead = 4 attention heads, and a feedforward dimension of 512","venue":null,"work_id":"149a21ae-f088-41d7-be40-119faed0c0e5","year":2000},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:44de3a3a5b20a4207cff7cce79ea41a1887714463953aa8b924f52603f8de61a","observation_id":"52cf208a-3aad-4e51-9331-221d65f366a3","resolution":{"observed_at":"2026-05-22T04:41:04.692394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Our model is a gated recurrent unit (GRU) lan- guage model withL= 2 recurrent layers and hidden size h= 256","venue":null,"work_id":"1f4481b8-6f85-4117-92f4-da3579f2b125","year":2000},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:8e3908579b5b8c985fa112ef2954df744614f412fd2c5aec235d083d72704fb2","observation_id":"2e998348-4f58-4a15-9b63-bd62fbed87e2","resolution":{"observed_at":"2026-05-22T04:41:04.689401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"linear re- gression)","venue":null,"work_id":"714fb02b-630b-469a-bd5b-192b2662e4c9","year":2000},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:1d379024892faf29ce098c892d82901310b1f1d25adf407e197d0fa37354fbbe","observation_id":"b6d02fdc-0ab4-4a6e-8ac1-ec32faf908cb","resolution":{"observed_at":"2026-05-22T04:41:04.697936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ac50f225-7585-43be-b066-f655af2a247b","year":null},"citing_paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-22T04:38:51.773377Z"},"links":{"citing_paper":"/paper/2605.21933"},"observation_digest":"sha256:7c2f243b5f27da981bf721d1995889f0a2a809eb70705bdc64e90e3c8a5dac25","observation_id":"59c88fe2-2661-4da6-bfd5-ea001825d176","resolution":{"observed_at":"2026-05-22T04:41:04.681056Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.21933","last_updated":"2026-05-21T03:04:44Z","latest_version":1,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-07-06T23:32:20.708664Z","submitted_at":"2026-05-21T03:04:44Z","title":"Thermodynamic Irreversibility of Training Algorithms"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":8,"verified_exact":10,"verified_fuzzy":24},"total_outbound_references":43},"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":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"thesis":"As of 31 July 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2605.21933."}