{"as_of":"2026-08-17T04:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3f8cff194d52d1f3a75ff30d47a193b689a02f80476b36d96569d853cb3e2caf","coverage":[{"denominator":73,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":73,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T14:39:45.825618Z","state":"measured"},{"denominator":73,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":73,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.06597/citation-record","integrity":"/paper/2608.06597/integrity","json":"/paper/2608.06597/citation-record.json","paper":"/paper/2608.06597"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:45.314649Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.314649Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:b8a3bdd722cdda28b7defe806c70434e1e28badfae554e0b742be3a8a38bc5ea","observation_id":"d34842cd-5624-4bc7-8f50-fa3d5fc3134f","resolution":{"observed_at":"2026-08-15T14:39:45.314649Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.192456Z","title":"Mehta, M","venue":null,"work_id":"f49e1fc5-8b0f-49e2-a7b3-488962eed297","year":2019},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.366378Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:71ff85eb81f2ce20188923ce57a262be96e77033f2b6bc02b8752baa323a7d54","observation_id":"21278375-a6a3-49f2-a5b2-0796d38871e0","resolution":{"observed_at":"2026-08-15T14:39:47.197227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.375409Z","title":"Bahri, J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.375409Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:d03a4b77ed8533a9552e03062f7653603f744c119b40901a487f4836b3a17554","observation_id":"62e44537-b8b3-4f04-a6a1-c177077b1ba4","resolution":{"observed_at":"2026-08-15T14:39:45.375409Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.166171Z","title":null,"venue":null,"work_id":"c6ae2f4a-347b-417a-b309-9cd433e722f2","year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.409345Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:fc66213c06cba613ec96640eef70334a9865f732d4190493f0768a2b8a871778","observation_id":"bbbb36a0-f814-496f-b61a-a6484b653f3a","resolution":{"observed_at":"2026-08-15T14:39:47.171245Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.149587Z","title":"Seroussi, G","venue":null,"work_id":"a2861343-40a4-4eb4-858d-5cb678e39afd","year":2023},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.430766Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:5e2c6e22bd788d8cb2c90004b73e09f81313d3d2d96169c20be109ae0bf9b533","observation_id":"497eab47-0f08-4ee5-9f55-8ce8af3e3ea8","resolution":{"observed_at":"2026-08-15T14:39:47.154136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.133662Z","title":null,"venue":null,"work_id":"ff2c8b94-a6fb-4917-ac37-73f45ba7b7d0","year":2014},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.436355Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e109fc91e3b762fb24d6513b1b8456e3194468b40b69ef7cf6c1efcc212010e7","observation_id":"2328092d-abaf-4aac-a713-35590dc02187","resolution":{"observed_at":"2026-08-15T14:39:47.138560Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.15933","last_updated":"2022-01-31T12:58:39Z","snapshot_observed_at":"2026-08-16T18:13:22.960012Z","submitted_at":"2021-06-30T09:34:05Z","title":"Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.15933","snapshot_observed_at":"2026-08-15T14:39:45.442391Z","title":"Jacot, F","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.442391Z"},"links":{"cited_paper":"/paper/2106.15933","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:1763cbc566e8f4c4e14c4ffc7c6ffbb4402ab5668dda65e40e14d8495bb10d52","observation_id":"0d0d25c7-4df3-4299-9acb-9663ea62ff25","resolution":{"observed_at":"2026-08-15T14:39:45.442391Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.117655Z","title":"Menon, The geometry of the deep linear network, inXIV Symposium on Probability and Stochastic Pro- cesses, edited by C","venue":null,"work_id":"f24c2f1e-92ab-4e66-986f-3596a56f6052","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.448166Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:d91690b29d23845d05203c06da2f7294a37dde5aee5caecaa1a6d479d5012a08","observation_id":"7888bb80-9364-464f-85e4-7037372ca744","resolution":{"observed_at":"2026-08-15T14:39:47.122718Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.100988Z","title":"Zhang, A","venue":null,"work_id":"8f45e477-e331-47e2-8f0f-fad62aac4e84","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.453641Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:83cc2fe87117145aadc135e6167de6b282c695d50066a5e2295dc3b5984d02c9","observation_id":"e0ffecf6-ec6d-431c-af36-79e9fe50e64e","resolution":{"observed_at":"2026-08-15T14:39:47.106998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.084703Z","title":"Kunin, G","venue":null,"work_id":"15a06eb8-3c75-48fd-bab4-512bd6c4d1d1","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.458777Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:38497061324c41716917448031950e197fb3f5d28831f412bffd2006329bf1a4","observation_id":"c3350b88-92e1-4d61-976e-0757fd14396c","resolution":{"observed_at":"2026-08-15T14:39:47.090299Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.487576Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.487576Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:d15fbcb568f0d8604fe9687f72fee5ad9e8f24f11d99b41cefc61e2d0cfab88e","observation_id":"d72a592e-d681-47a9-a598-38f89bc6023c","resolution":{"observed_at":"2026-08-15T14:39:45.487576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.059710Z","title":"Zhang, Z","venue":null,"work_id":"e6b5b27b-514a-4a7a-b595-485b88f16916","year":2021},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.508462Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:0d76c8a1ae5db113c4eb9423114aadec6cd68c4a53db1a638ec67ed9faac3df2","observation_id":"b080839a-c185-4626-b421-da6ba2a3f4ec","resolution":{"observed_at":"2026-08-15T14:39:47.064497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.043675Z","title":null,"venue":null,"work_id":"77d5a335-1262-48ea-95ea-2801c8fc0b9d","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.513815Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:3df1586ee062ae6ede188dc75629e558e6809e53a6ca81a138581ceede39f90d","observation_id":"a23e4b1c-c909-487b-8504-f49d75c0797b","resolution":{"observed_at":"2026-08-15T14:39:47.048827Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.05300","last_updated":"2025-05-23T17:22:54Z","snapshot_observed_at":"2026-08-15T18:42:58.655522Z","submitted_at":"2025-02-07T20:10:05Z","title":"Parameter Symmetry Potentially Unifies Deep Learning Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.05300","snapshot_observed_at":"2026-08-15T14:39:45.519471Z","title":"Ziyin, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.519471Z"},"links":{"cited_paper":"/paper/2502.05300","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:85fce1568fbb7bdd679782de01abbccb2d706a3846e985077eb122c78b969978","observation_id":"036721bb-2fbb-40e3-b939-fedb3118a6fc","resolution":{"observed_at":"2026-08-15T14:39:45.519471Z","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":"2026-08-15T14:39:45.524700Z","title":"Goldenfeld,Lectures On Phase Transitions And The Renormalization Group(CRC Press, 1992)","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.524700Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:bde5f98847da5b524b0daa7bbcd13eec715637748dd676b6cce0539c50435a41","observation_id":"64a5a947-df04-4773-bc31-4c512fb1809e","resolution":{"observed_at":"2026-08-15T14:39:45.524700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.018724Z","title":null,"venue":null,"work_id":"573d12a9-1427-4640-9f83-e661a71a145a","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.532783Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:1bcc3484abd6cfe2bf951a9e92fe11e67053e1392630438c6d46fe77faab017e","observation_id":"c6631cc5-b54e-4fd0-b52e-81c679443e53","resolution":{"observed_at":"2026-08-15T14:39:47.023468Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:47.003402Z","title":null,"venue":null,"work_id":"1e6b31f2-bbea-4c58-8447-640e675459d0","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.538755Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:439297f26a19f66ffe2a1d5a8a9168ad0d6d5520c6c623cee7b1c045a5cc2aee","observation_id":"655adea4-44f8-41c9-9bae-b05799331350","resolution":{"observed_at":"2026-08-15T14:39:47.007850Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.987625Z","title":"Ziyin, B","venue":null,"work_id":"8468eaab-370f-4308-9661-cbd9b417960d","year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.544166Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:0a5075361e1df180c07ac38ed213a22607c047477178e5dc19b2367e06a7733d","observation_id":"3ba266a9-475f-4dee-8e48-761a72c1714b","resolution":{"observed_at":"2026-08-15T14:39:46.992219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.970986Z","title":"Ziyin and M","venue":null,"work_id":"b7b408ef-9de3-494a-96f8-8929d4cacdf2","year":2023},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.549427Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:424f5bdf5c8fd646bff080685b7ca477066bb8d3e9a351c9a45b4299e0ed6545","observation_id":"964df118-aa60-4c1f-969b-cc402ed808a6","resolution":{"observed_at":"2026-08-15T14:39:46.976603Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.955443Z","title":"Ziyin, Symmetry induces structure and constraint of learning, inForty-first International Conference on Ma- chine Learning(2024)","venue":null,"work_id":"fc3441e5-2b15-457e-b58a-455b70b0fb4c","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.553842Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:70a1cbfca003936f7720a1dde48cd56e89b19c169269f90888d6d43664bcc8e0","observation_id":"eb3a68f7-c8c3-47d2-8881-195125e69249","resolution":{"observed_at":"2026-08-15T14:39:46.960276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.939782Z","title":null,"venue":null,"work_id":"dad21d89-8787-4b0b-826c-719cf88548a8","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.559493Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:cfef9ea090c9e536582bb902fb99c8f0080698fe68ef37a6189a8819c5441985","observation_id":"f219d60f-60cd-40e6-bd01-11870963e1ca","resolution":{"observed_at":"2026-08-15T14:39:46.944758Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.564485Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.564485Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e4e72ebe50541fb504844b69ff8610443910ba4b0a52328ae2fddb36891a6928","observation_id":"9293325a-c622-415c-b507-58402981a625","resolution":{"observed_at":"2026-08-15T14:39:45.564485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.923744Z","title":null,"venue":null,"work_id":"751ddbb9-8b07-4f44-aa85-e5d7addb3159","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.569463Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:9791fbe22f14a5e296519c2246c258cc83a2dc21c9c9b21c16232e2a05f18c69","observation_id":"e95f146b-9c22-4936-8ed5-d01f51e9a9f8","resolution":{"observed_at":"2026-08-15T14:39:46.928685Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.18553","last_updated":"2025-04-17T07:48:20Z","snapshot_observed_at":"2026-08-16T12:55:16.346140Z","submitted_at":"2025-02-25T18:19:06Z","title":"Applications of Statistical Field Theory in Deep Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.18553","snapshot_observed_at":"2026-08-15T14:39:45.574183Z","title":"Ringel, N","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.574183Z"},"links":{"cited_paper":"/paper/2502.18553","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:ef0abe2dc41a9c8ca3150746eafdde5165c21ecdf57493728713fa055f60baa2","observation_id":"5e9414df-a6e2-4634-a117-ad9976ddcd57","resolution":{"observed_at":"2026-08-15T14:39:45.574183Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.21691","last_updated":"2026-04-23T13:58:12Z","snapshot_observed_at":"2026-08-02T12:48:50.592713Z","submitted_at":"2026-04-23T13:58:12Z","title":"There Will Be a Scientific Theory of Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.21691","snapshot_observed_at":"2026-08-15T14:39:45.580227Z","title":"Simon, D","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.580227Z"},"links":{"cited_paper":"/paper/2604.21691","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:c10553b6a93af9f320b4765be22baf3783139b821d903cd33b901ff2ddb29b71","observation_id":"5d5406d7-03b3-4a4a-ba38-101144727dcd","resolution":{"observed_at":"2026-08-15T14:39:45.580227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.907502Z","title":"Baldi and K","venue":null,"work_id":"62ae2879-1f19-40f4-bada-8d4f84ac0b79","year":1989},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.585858Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:cfbb3f28c1ae4fb092bd2c30d4c9926a76e450e0453b11668c6d8e2f71b807f3","observation_id":"d052cbd6-0837-4d61-9dea-97c35cdfd222","resolution":{"observed_at":"2026-08-15T14:39:46.912959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.892295Z","title":"Fukumizu, Dynamics of Batch Learning in Multilayer Neural Networks, inICANN 98, edited by L","venue":null,"work_id":"2b2dbb33-8865-4bb2-9480-c5dd37668494","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.591229Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:5730a219e91fb6d3a50be9d08515e1bbd5e906a63d2e25a3ec50f667b2e0fa5f","observation_id":"af17e4f2-2d4e-4794-b778-2c0ddb62d540","resolution":{"observed_at":"2026-08-15T14:39:46.897271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.876599Z","title":"Kawaguchi, Deep Learning without Poor Local Min- ima, inAdvances in Neural Information Processing Systems, Vol","venue":null,"work_id":"2604caa4-3513-43ae-bc7a-5905f6611904","year":2016},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.596255Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:d1a9ea862e7ffa4837e0e82a281d8d25abb586d127d410edf969a567bbeb5610","observation_id":"0742cb1c-957b-4d42-9b9f-1ba3e8f63dfa","resolution":{"observed_at":"2026-08-15T14:39:46.881601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.861399Z","title":null,"venue":null,"work_id":"2ad72413-c134-48e7-a0a5-63333c933199","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.601194Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:1082fdaaefca4c7f5498389c91fa7af7576ea4e283b18fda4e7327ed60faa765","observation_id":"676f24eb-7bd3-46bd-b5a0-ef9b47c95201","resolution":{"observed_at":"2026-08-15T14:39:46.866253Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.846034Z","title":"Wendin and C","venue":null,"work_id":"2310f670-b619-47de-afa9-7ce82ae52c7a","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.606981Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e07773c0e97bd14ded47c597cff09544e424714b0d1cebc2a94d62d0910ffebf","observation_id":"3f0201db-ab5b-4022-b0dd-186ecf317680","resolution":{"observed_at":"2026-08-15T14:39:46.851101Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.830271Z","title":null,"venue":null,"work_id":"a52531de-7d55-475d-8524-4679221d64db","year":2021},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.612481Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:f976966a98c4b779bd67bf47233763ec6df28f022e18506aae5442038ffe310d","observation_id":"9c89ed91-6ef3-4266-a3dc-fba1abf85134","resolution":{"observed_at":"2026-08-15T14:39:46.835835Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.815532Z","title":null,"venue":null,"work_id":"bd412cc1-5790-478a-9f50-a9e5aeef6ae8","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.617023Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:8abc626f08b082193e6d7c4c5a37c02e66fb959ce91a61bb0a3f1db8afa647ca","observation_id":"b886bfa3-41f8-49ac-9ba6-cc54c80a580a","resolution":{"observed_at":"2026-08-15T14:39:46.820182Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.622132Z","title":"Lindsey and G","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.622132Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:197d6634bbe4d30142f6bad261eadbebb6e408baa1ad076a307756d78e0f9eca","observation_id":"f1c01f05-59cc-4fa8-a6ff-47b54e5691d3","resolution":{"observed_at":"2026-08-15T14:39:45.622132Z","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":"2512.06137","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.026193Z","title":null,"venue":null,"work_id":"24480264-2d77-46e5-8d22-8845d5f222c4","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.626878Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e2d8c55932c92ba43adf2ee19f51a8b905d2b8839cd2d45af1908df4e8f3fc2c","observation_id":"7bd74f28-b6cd-47ec-a599-adf396bb6996","resolution":{"observed_at":"2026-08-15T14:39:46.035030Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.09088","last_updated":"2026-05-20T19:22:45Z","snapshot_observed_at":"2026-07-06T22:28:33.382363Z","submitted_at":"2025-09-11T01:40:46Z","title":"An entropy formula for the Deep Linear Network","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.09088","snapshot_observed_at":"2026-08-15T14:39:45.631808Z","title":"Menon and T","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.631808Z"},"links":{"cited_paper":"/paper/2509.09088","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:0b985a3cb1b01ad05a962d9adacad07ceeef8c89d8c657eeba41bdfb842327d6","observation_id":"89b09ace-119e-4da9-8fe0-28e0c6a52411","resolution":{"observed_at":"2026-08-15T14:39:45.631808Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.799252Z","title":null,"venue":null,"work_id":"59d8932d-40a4-4c60-868f-9558d69ebca9","year":2010},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.636851Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:f095be69d94f4203555557fdd504f4b62657c0ac2e5668a3875126a67303d3b9","observation_id":"7c4cc7fb-8c05-4ff4-94a0-4ad774c8fb9f","resolution":{"observed_at":"2026-08-15T14:39:46.804935Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.784559Z","title":null,"venue":null,"work_id":"90743d33-cd5f-4370-bb84-0050e2c41353","year":2005},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.642049Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:9e260f1a3bcf0b8b0dc4cb1b78c4233fb8f956ed64a7db4d5050a16b9c0c1509","observation_id":"c05906d3-4be2-4b46-9c84-35b2e6d1f1be","resolution":{"observed_at":"2026-08-15T14:39:46.789162Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.768682Z","title":"Scarvelis and J","venue":null,"work_id":"b6e4a7fc-9db7-4e15-a0b6-db629105cda9","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.647109Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:740a39a60ace4589ce00365790f04be33cd6dcf690baf4e68fe2bc875db461fe","observation_id":"b5388c26-8ffe-4232-84c8-911eec740062","resolution":{"observed_at":"2026-08-15T14:39:46.773985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.13714","last_updated":"2025-06-16T17:24:07Z","snapshot_observed_at":"2026-08-16T15:41:22.554431Z","submitted_at":"2025-06-16T17:24:07Z","title":"Understanding Learning Invariance in Deep Linear Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.13714","snapshot_observed_at":"2026-08-15T14:39:45.652256Z","title":"Duan and G","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.652256Z"},"links":{"cited_paper":"/paper/2506.13714","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:db9283fc84efe7c6812d1401781179bd0ce06b0a28de92b0d04078bf6ecf1e29","observation_id":"fa90a9f4-9abd-4e91-b010-aa3394eb7fec","resolution":{"observed_at":"2026-08-15T14:39:45.652256Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.753575Z","title":"Wang and A","venue":null,"work_id":"936a02bc-1d1a-4faf-af6b-3eb8e3e1474b","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.657889Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:436f95ac3425834418b70c4c62068c37a2c326ae52d260e677f2b0d0fba1aad0","observation_id":"719511bc-02a7-4846-84db-e0f206628d6f","resolution":{"observed_at":"2026-08-15T14:39:46.758145Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.737047Z","title":"Chechik, A","venue":null,"work_id":"f004f969-7459-4593-892e-700b8ff98f6f","year":2003},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.663018Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:ecf58b37418fd3fa14f98722b9b59432cce02039f22ea451f1085fa1bed8ac51","observation_id":"64d35645-e735-481a-a729-1f3f09ed1f15","resolution":{"observed_at":"2026-08-15T14:39:46.742514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.718559Z","title":"Arora, N","venue":null,"work_id":"31eae554-d25b-4683-b74b-7a69085e13ea","year":2018},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.668258Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:714d28c263b38ebae9c71cceb34502fc1cfa3154aff6bbee1e647b4a5e666b7e","observation_id":"ecad120e-4f92-4eeb-923f-8fef00d1ac90","resolution":{"observed_at":"2026-08-15T14:39:46.725829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.700293Z","title":null,"venue":null,"work_id":"e2010bb1-5fa4-4ac9-9502-64324b0df740","year":2023},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.673424Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:6e81e25a8222b3fefa54d44d2429526907b3d1a3be9188598e8dac3d7006088a","observation_id":"c6d6cbe7-67bd-4e26-bbd8-57cc6f68bff5","resolution":{"observed_at":"2026-08-15T14:39:46.705725Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.684271Z","title":null,"venue":null,"work_id":"0b8f6ea4-f9df-407e-8298-fb690759e102","year":2018},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.678109Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e1a5c000f99b1a237ad5a3058d749f1cbac7ec381d0b54d1b844ef2ad0bda71b","observation_id":"35a30d90-6004-4b2c-b713-65ffefea6e67","resolution":{"observed_at":"2026-08-15T14:39:46.689163Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.667314Z","title":"Trager, K","venue":null,"work_id":"58bbac15-9332-4eec-90af-2a6c3404d50e","year":2020},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.682785Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:f2637fa0df25430d21d76329c86f68cba0ddd926756685438da659ad8297b606","observation_id":"5ffd063e-ea50-47fb-bec8-24b6d8e87eb9","resolution":{"observed_at":"2026-08-15T14:39:46.672027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.650930Z","title":null,"venue":null,"work_id":"cd69ad53-0d05-425c-b2e6-d56fc78fb76c","year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.688404Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:7d1abfc35e3fbf49d9c6e3ecd7805e09862c578a0b20003a50c6fdd55398f243","observation_id":"754ba6b1-f8f6-47d1-9e62-e362a921e108","resolution":{"observed_at":"2026-08-15T14:39:46.656200Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.633800Z","title":"Liang, L","venue":null,"work_id":"c37558f5-f2a6-4752-a0aa-ad18d9d281f2","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.693251Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:603439cd679d795ffbb6696284e997188f1f98200ba99b65b097a8fab2ab182f","observation_id":"717a07b3-a9ca-4f15-94ce-bef59faeaf8e","resolution":{"observed_at":"2026-08-15T14:39:46.638788Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.698366Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.698366Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:7cad9fc8e07273580e3b4b8a19cfe902332cdbc53230e8ba3a92bae6121ec47f","observation_id":"8096d572-71c5-4298-8a24-459ac7f6d2fb","resolution":{"observed_at":"2026-08-15T14:39:45.698366Z","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":"2026-08-15T14:39:45.703263Z","title":"Altland and B","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.703263Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:fc7fd5a0780b4ff73346452423a7bd4dff198d8f63851f384a06516f01ab21b0","observation_id":"86eade46-1443-4371-8a68-4807dc4c160d","resolution":{"observed_at":"2026-08-15T14:39:45.703263Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.607358Z","title":"Braun, C","venue":null,"work_id":"0a7bcc99-2408-40fb-8260-b2ca3248ff7e","year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.707987Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:7129894921d4c5a4d172a9cdf20a8cbb19f3a0101783ab457b4956f74485ae9c","observation_id":"d335d365-c968-4a7e-94ee-1e031e5bf1af","resolution":{"observed_at":"2026-08-15T14:39:46.612703Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.590046Z","title":null,"venue":null,"work_id":"647561f9-cdd2-42cf-a976-dc58b0789d6f","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.712566Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:0624e860a53883249d51788454476ea8f605a8a3d2e71756ebc1ef519c3e5d02","observation_id":"3b690c0f-4668-4b57-8196-c3f83052cba7","resolution":{"observed_at":"2026-08-15T14:39:46.595455Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.573173Z","title":null,"venue":null,"work_id":"5b4a9768-f9b2-4a75-b562-3ee47bab576d","year":2022},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.717539Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:cc5f6c10ce8b303bd807057e61ea62d966b8b88e3bbcbc04fbd8e8638499c0b2","observation_id":"c94b5dcb-62d0-4200-bc06-89da35df9ed6","resolution":{"observed_at":"2026-08-15T14:39:46.578826Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-15T14:39:45.722309Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.722309Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:d4262f1b83049170f9adddda3c3a84ff0ea662ce26de46f54481eb81f7ea6f54","observation_id":"807f4adb-2cad-4295-884b-362f4ea9d60a","resolution":{"observed_at":"2026-08-15T14:39:45.722309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.544005Z","title":"Roy and M","venue":null,"work_id":"35816410-390b-4c45-8c7a-52143024f62d","year":2007},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.726877Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:78ccece7337e4cdb90b8991bc0531c9f27d56a13022bcb38d8d50ef731b8207f","observation_id":"eac0f23d-6029-4713-8329-7a1ae31df62c","resolution":{"observed_at":"2026-08-15T14:39:46.549323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.527058Z","title":"Yunis, K","venue":null,"work_id":"3c16bdaf-1f8d-49f1-9076-a4f4350baf3f","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.732364Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:4edaa48ac935a05bc60cdc71bd9e827b0774ad5fb4f02023afbf9c879061204f","observation_id":"3927575b-c943-4d74-93f8-c20b0d45c5f1","resolution":{"observed_at":"2026-08-15T14:39:46.532556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.509572Z","title":null,"venue":null,"work_id":"98316d58-f24a-4a77-a6c9-5bffe701ef05","year":2024},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.737614Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:17c0d1b6d7f9b81aeaf1187c4d4c3c708ed18e13811a595de1571b4f38cedfd8","observation_id":"97d5d4b8-a2d0-457b-88b2-54dc8a1a6ae4","resolution":{"observed_at":"2026-08-15T14:39:46.514642Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.491381Z","title":"Li and H","venue":null,"work_id":"a4e5a747-e9f0-4333-a90e-621c0e3a0446","year":2021},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.742769Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:c3dcb3bafbc904bad0ebdccc044fadc6d94f770067ee724ff0a3bcb2dfd7eb4f","observation_id":"f690d33b-633e-441b-b260-6707b71c8961","resolution":{"observed_at":"2026-08-15T14:39:46.498027Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.475401Z","title":"Bachtis, G","venue":null,"work_id":"58dfa265-f4e5-4ebd-847f-a8d060756849","year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.747564Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e0c54b517047b8c0c1ed323d45af82e3adbe27de9bf8ae281efbbce72bda465c","observation_id":"bcd2696d-1cdd-47ab-b624-f2d11b025b1c","resolution":{"observed_at":"2026-08-15T14:39:46.480373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.17340","last_updated":"2025-08-20T14:53:28Z","snapshot_observed_at":"2026-08-16T12:55:39.980590Z","submitted_at":"2025-02-24T17:17:00Z","title":"Low-rank bias, weight decay, and model merging in neural networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.17340","snapshot_observed_at":"2026-08-15T14:39:45.753110Z","title":"Kuzborskij and Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.753110Z"},"links":{"cited_paper":"/paper/2502.17340","citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:03cb9d53dcf5bf96a5fcb21deb8ccdd295cc5d23dce01114a7f7178b136a020c","observation_id":"4ae5cb14-3c04-4f06-90d1-2cbfd84ed1c5","resolution":{"observed_at":"2026-08-15T14:39:45.753110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.458524Z","title":null,"venue":null,"work_id":"e2ab35b6-7c62-4ce5-9f10-9fec6d392e06","year":2026},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.759036Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e52962addf0f9b6b465fb1bb8fd3d9fc937f117c264a355ec8bfcbc34e7ea0d8","observation_id":"0b5df035-4abb-4fb0-a391-7098f0e6c3fe","resolution":{"observed_at":"2026-08-15T14:39:46.463749Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.442119Z","title":"Sasagawa, On the finite escape phenomena for ma- trix Riccati equations, IEEE Transactions on Automatic Control27, 977 (1982)","venue":null,"work_id":"cd60f789-00fb-4039-bb8b-16bf962727ef","year":1982},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.764346Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:fce2d862f8a3023717a9fd89c405e6be1866063aa84854f5d3780b961ae4df0d","observation_id":"c731aa5b-b139-459d-ab86-00754f8a2f4c","resolution":{"observed_at":"2026-08-15T14:39:46.447304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.425580Z","title":null,"venue":null,"work_id":"8274853b-2ab3-4f0d-aefc-6ecaad1ce0ff","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.768986Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:6259526f5d580043b3198ced098b7450c634b67c53df49c630f01ef843b324c6","observation_id":"11367d12-b222-47a2-abfa-1e4f8ff4efe4","resolution":{"observed_at":"2026-08-15T14:39:46.430795Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.409508Z","title":null,"venue":null,"work_id":"00de1ed1-7976-49ff-a842-cd851c206a06","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.773695Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:ff489e859fbc7f36a8efeb680b7d7ccb36ec55bb9b309fa1c98a03f0c8c2f908","observation_id":"fa4e983c-f924-453d-a068-2c76af81f81d","resolution":{"observed_at":"2026-08-15T14:39:46.414362Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.392061Z","title":null,"venue":null,"work_id":"09ca007b-da7f-42e8-93b3-6400c0fe3396","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.778927Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:ef945558c40d6ae2368f2dd0e07d4221e92b4109e07094fdade290be9ea9791d","observation_id":"bbdbfd84-c63b-412f-84d1-11971d9b8317","resolution":{"observed_at":"2026-08-15T14:39:46.397952Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.374696Z","title":"Here,Dis a diagonal matrix with entriesκi","venue":null,"work_id":"6f5b53c8-6ad5-4ca7-bd1c-2dbc77075339","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.783804Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:c6e2b0c4c848fe3074529b75cec20b8765532016d18f48a6aa0f8188c0950450","observation_id":"ebc92b39-e78b-48f2-8269-f0dd3557f853","resolution":{"observed_at":"2026-08-15T14:39:46.380218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.357749Z","title":"For 1 hidden layer (n= 2):The first path corresponds to the direction dictated by the leading singular value ofΣyx, which isη 1 with (right) singular vector⃗ r1 =⃗ e1","venue":null,"work_id":"1fad41e1-83c3-4a46-9b5f-5a011765cda2","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.788511Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:fa215d5de42f82404a0ad6ac6b5a059c7ac85ec2ea8d692ede1a2370e17622d8","observation_id":"9398d0a8-2d5e-4f17-86e8-eb81b77bbe5f","resolution":{"observed_at":"2026-08-15T14:39:46.363112Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.339817Z","title":"To analyze the Hessian, we are working with column vectorization, where vecc(W) := (W :,1,W :,2,...), such that the Hessian becomes a matrix","venue":null,"work_id":"542b0043-683c-4252-8699-3cb1aa657779","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.794136Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:a776732982ce353a0f50bebde53831c54ae30080bc108822c2650dd1b3d9548e","observation_id":"ff0f51f5-0f13-40ae-92f6-8c03c895f3a7","resolution":{"observed_at":"2026-08-15T14:39:46.346162Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.321440Z","title":"The rankrof the criticalW (i)’s is crucial to understand the Hessian spectrum","venue":null,"work_id":"b42d7e1c-286b-45d6-af91-80a402a3a3f6","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.799200Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:5571e73b25c799a21b99a9afbe7b757e6df994f462375a395958aee385c1aedf","observation_id":"38a72d20-42f0-4378-9230-403b76989fa6","resolution":{"observed_at":"2026-08-15T14:39:46.327821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.303056Z","title":"The main point is that the flat directions andβ-directions do not depend on the model details as they are associated with (broken) symmetry transformations","venue":null,"work_id":"f370c6a0-fc5d-4b6d-b0f4-827f5cf51813","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.804483Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:156b37916019bd1e37eff396b022c3ebcf1e9fa058bb81bb60c521d349cedb62","observation_id":"ba174b2c-fb75-4534-acb8-067994fff8d0","resolution":{"observed_at":"2026-08-15T14:39:46.309596Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.285999Z","title":"However, we should get access to some of the eigenvectors and eigenvalues (namely those that do not break the0-balance condition)","venue":null,"work_id":"16764487-4341-42c9-8506-73f873e58ac7","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.809779Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:1342d44a420d6ee6ab7d7504073d67dc3f891753f7eedc7d89744c0225cb7b29","observation_id":"7ee51643-098f-4468-be48-c36909b99437","resolution":{"observed_at":"2026-08-15T14:39:46.292152Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.268165Z","title":"The special case of 1 hidden layer (n= 2) instead can also be approached differently by making use of the Riccati equation","venue":null,"work_id":"ac38b307-6277-454d-b1b3-1ce0fa8680ad","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.815275Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:773911d46e21ab2ed22329ec9294ee1cf892b6c2a6ab199ae21e6aa47cb3464b","observation_id":"bed2f43a-46f5-4555-a3a0-d15332ef1605","resolution":{"observed_at":"2026-08-15T14:39:46.273965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.252866Z","title":null,"venue":null,"work_id":"c6e9b538-fc92-4c5b-add1-a72b5878e181","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.820552Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:e1126901103c46b6c3cd6ea006da98099380c98339991e0f51b129dc9d54cae7","observation_id":"9dbfecfc-d20e-4514-abe2-6c60b0c75d44","resolution":{"observed_at":"2026-08-15T14:39:46.257896Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:39:46.237061Z","title":null,"venue":null,"work_id":"266bbcfa-904d-4745-8c17-5864772629c5","year":null},"citing_paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-15T14:39:45.825618Z"},"links":{"citing_paper":"/paper/2608.06597"},"observation_digest":"sha256:01ae6b135ede6fbaa2175703487d126700e77c3de3eab160578be1c999fb920c","observation_id":"f0c55f28-e7c4-41b3-97be-5e999821a51a","resolution":{"observed_at":"2026-08-15T14:39:46.242039Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06597","last_updated":"2026-08-06T21:15:32Z","latest_version":1,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-08-16T17:07:30.079861Z","submitted_at":"2026-08-06T21:15:32Z","title":"Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks"},"reference_resolution":{"displayed":73,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":40,"verified_exact":1,"verified_fuzzy":32},"total_outbound_references":73},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 73 of 73 outbound references and 0 inbound Pith citation observations for arXiv:2608.06597."}