{"as_of":"2026-08-08T23:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:368db7ea5d25ff6bb68bd9ea0001aba7770f05b84e2a358ba77cc04e8db6bb25","coverage":[{"denominator":76,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":76,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:29:36.563390Z","state":"measured"},{"denominator":78,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":78,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T05:14:07.208255Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T13:29:50.955298Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"cited_work":{"arxiv_id":"2505.15239","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.15239","snapshot_observed_at":"2026-07-04T13:29:50.955298Z","title":"Neural collapse is globally optimal in deep regularized resnets and transformers.arXiv preprint arXiv:2505.15239","venue":null,"work_id":"0bbfb8e3-4d05-4e75-a9c8-ef068458a859","year":null},"citing_paper":{"arxiv_id":"2510.01105","last_updated":"2026-05-08T13:22:44Z","snapshot_observed_at":"2026-07-06T22:31:24.978726Z","submitted_at":"2025-10-01T16:50:57Z","title":"Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-18T10:22:28.096542Z"},"links":{"cited_paper":"/paper/2505.15239","citing_paper":"/paper/2510.01105"},"observation_digest":"sha256:ab577b6639307ce1fb70f549886f1c761e03827e4f79787bb1c8235d7f2f1d5b","observation_id":"78cb20d8-3a16-480d-ae28-4153551ad9f7","resolution":{"observed_at":"2026-05-18T10:22:33.217125Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"cited_work":{"arxiv_id":"2505.15239","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.15239","snapshot_observed_at":"2026-07-04T13:29:50.955298Z","title":"Neural collapse is globally optimal in deep regularized resnets and transformers.arXiv preprint arXiv:2505.15239","venue":null,"work_id":"0bbfb8e3-4d05-4e75-a9c8-ef068458a859","year":null},"citing_paper":{"arxiv_id":"2606.26749","last_updated":"2026-06-25T08:33:34Z","snapshot_observed_at":"2026-08-01T16:00:20.311664Z","submitted_at":"2026-06-25T08:33:34Z","title":"Structure Before Collapse: Transient semantic geometry in next-token prediction","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-26T05:14:07.208255Z"},"links":{"cited_paper":"/paper/2505.15239","citing_paper":"/paper/2606.26749"},"observation_digest":"sha256:33c8ee542676abf9cc9cb2edf1e59ade70886c06f3de59d3a5ba3139a1fd0d6d","observation_id":"1ec783da-1013-460e-92c7-5ee46817e75b","resolution":{"observed_at":"2026-07-04T13:29:50.957179Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.15239/citation-record","integrity":"/paper/2505.15239/integrity","json":"/paper/2505.15239/citation-record.json","paper":"/paper/2505.15239"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:29:47.463470Z","title":"The prevalence of neural collapse in neural multivariate regression","venue":null,"work_id":"2ef4e9d0-6ea8-434e-bba1-091b78f45b03","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.064592Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b70966db645fa67d810c4dcfcb8cc286c1378e722471e835b63e8d0234222ea2","observation_id":"9846464d-742d-4d8e-b572-876656df8420","resolution":{"observed_at":"2026-08-07T15:29:47.556506Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:47.238820Z","title":"Intrinsic dimension of data representa- tions in deep neural networks","venue":null,"work_id":"afe04cb0-8fb2-4e71-89cf-a575c14fd17d","year":2019},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.113110Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:bce5b2e379af47b6b8616ba57858f0324b3d40e6d39d889d95852800433c8e73","observation_id":"7ccc5928-e426-4889-954a-e48127cac92e","resolution":{"observed_at":"2026-08-07T15:29:47.334484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:47.001777Z","title":"Average gradient outer product as a mechanism for deep neural collapse","venue":null,"work_id":"2a92e57c-50d6-4215-a4ed-7cc2ab2bd65e","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.176334Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b9d00fa6be82f705524f2636540b069a7f418af3e601a6a3c8fd8683b122cb51","observation_id":"2dd94fbe-02ae-4e18-b570-83b3d498e3a3","resolution":{"observed_at":"2026-08-07T15:29:47.121085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.19149","last_updated":"2025-01-31T14:06:13Z","snapshot_observed_at":"2026-08-01T07:35:49.992812Z","submitted_at":"2025-01-31T14:06:13Z","title":"On the inductive bias of infinite-depth ResNets and the bottleneck rank","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.19149","snapshot_observed_at":"2026-08-07T15:29:29.224880Z","title":"On the inductive bias of infinite-depth resnets and the bottleneck rank","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.224880Z"},"links":{"cited_paper":"/paper/2501.19149","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:1755c523ea6609e4565feb9ff672d69315582774a4edabcb4f614c68556bb441","observation_id":"9620f95c-5bdf-4ab2-9d11-a3478b435982","resolution":{"observed_at":"2026-08-07T15:29:29.224880Z","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":"2026-08-07T15:29:46.802858Z","title":"Prevalence of simplex compression in adversarial deep neural networks","venue":null,"work_id":"966cf995-9deb-4090-a204-b8d8873a534e","year":2025},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.290473Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:7db53cd2778aa77a23217ccf9856e858efeb303a4174e0c143bbb4151ddddc2e","observation_id":"e03e6101-0f75-4b05-90d9-6549e8c98b52","resolution":{"observed_at":"2026-08-07T15:29:46.903816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:46.575505Z","title":"Perfectly balanced: Improving transfer and robustness of supervised contrastive learning","venue":null,"work_id":"4995cf60-1546-4923-8254-15c9d467dbc9","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.387395Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:0276f77bcf56f106496d418915e31883ed7ae9b3cd816274e77d3d56a9f9868b","observation_id":"2a3bc718-4c7b-4cf3-9e52-d922c78dd334","resolution":{"observed_at":"2026-08-07T15:29:46.666628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:46.469777Z","title":"Neural collapse for cross-entropy class-imbalanced learning with unconstrained relu features model","venue":null,"work_id":"5a7b86f7-f674-4555-9641-2e5b5406f004","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.444031Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b37dca7a72b0d2164c104012ab953b0e227e336588ad7c6fc3edba5e09150bce","observation_id":"21334e3b-ce2f-4d37-9a51-11da4400e550","resolution":{"observed_at":"2026-08-07T15:29:46.514568Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:46.356347Z","title":"Neural collapse in deep linear network: From balanced to imbalanced data","venue":null,"work_id":"ee10c312-0877-457a-a971-923d087c6319","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.509111Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:e1fa0d5aacd8c44e736cbbd84f48c700e62400f4d59cca2605094c88c5867daf","observation_id":"3e379a38-d6b1-44ec-aa9e-521da9868734","resolution":{"observed_at":"2026-08-07T15:29:46.411659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:46.228048Z","title":"Improving self-supervised learning by characterizing idealized representations","venue":null,"work_id":"309a6038-74c4-4e4b-827a-bfba1aa37c3c","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.559945Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:0b07b17801cd3a3d1e0a308645e5715d12f331aab92af2b6c893652e7d961d50","observation_id":"4394543c-c6e3-4542-a0c6-a9fb201253b0","resolution":{"observed_at":"2026-08-07T15:29:46.287477Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:46.090173Z","title":"Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training","venue":null,"work_id":"de533161-2dbb-4520-9b19-6e5895b7146a","year":2021},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.641400Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:13676d777d3c4847f436d8133b8019b2b0530da5a9d9f5a4d6ffaeaac1e49552","observation_id":"7cdb0dad-37b9-492e-a2bb-97d8d73f8b59","resolution":{"observed_at":"2026-08-07T15:29:46.164607Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.09028","last_updated":"2022-09-28T00:10:02Z","snapshot_observed_at":"2026-07-06T12:39:02.767876Z","submitted_at":"2022-02-18T05:21:28Z","title":"On the Implicit Bias Towards Minimal Depth of Deep Neural Networks","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.09028","snapshot_observed_at":"2026-08-07T15:29:29.712149Z","title":"On the implicit bias towards minimal depth of deep neural networks","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.712149Z"},"links":{"cited_paper":"/paper/2202.09028","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:26372c49d8b9adbdc753eb83eacd6bd8b53467ece3469985ad597e2fc4fbace1","observation_id":"5e8a58ee-250e-42b0-a617-bf6aed21d6be","resolution":{"observed_at":"2026-08-07T15:29:29.712149Z","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":"2026-08-07T15:29:45.843330Z","title":"Improved generalization bounds for transfer learning via neural collapse","venue":null,"work_id":"163f8e9e-8baf-4bcc-9bad-70ed6ee26495","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.775724Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:0963f2e5abf4799cf6af47a5634cb256530f216afe7bf4d8f7502a2d8a777844","observation_id":"db528e66-e94e-4242-bc36-c18ebbe0ea26","resolution":{"observed_at":"2026-08-07T15:29:45.954980Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:29.831436Z","title":"The persistence of neural collapse despite low-rank bias: An analytic perspective through unconstrained features","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.831436Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:1ba25d5dfa821e5fbcc4deb813c1e38c9e694e13648aad51141db410ebab744f","observation_id":"dfaa063c-7b16-4752-aa7d-a13bf43e6b92","resolution":{"observed_at":"2026-08-07T15:29:29.831436Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.06106","last_updated":"2026-05-26T21:31:31Z","snapshot_observed_at":"2026-07-06T17:57:35.831578Z","submitted_at":"2024-04-09T08:17:32Z","title":"Unifying Low Dimensional Spectra in Deep Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.06106","snapshot_observed_at":"2026-08-07T15:29:29.876998Z","title":"Unifying low dimensional observations in deep learning through the deep linear unconstrained feature model","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.876998Z"},"links":{"cited_paper":"/paper/2404.06106","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b13dd455996bde1ff272f99ffaf5ace5a8f2d612eda7122c8c1edbebfba3b502","observation_id":"f832f40e-fc36-4df6-bc58-200ebd890fdc","resolution":{"observed_at":"2026-08-07T15:29:29.876998Z","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":"2026-08-07T15:29:45.590165Z","title":"Linking neural collapse and l2 normalization with improved out-of-distribution detection in deep neural networks","venue":null,"work_id":"15e7ff77-c5fe-442d-8756-6b399b7420e5","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.908467Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:661bd04163beb381cc0af46d17972ba80105f3406774f78fc4132954f356e2f6","observation_id":"ccba16ae-256f-47d9-8c63-53f1619abacd","resolution":{"observed_at":"2026-08-07T15:29:45.711747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:45.407558Z","title":null,"venue":null,"work_id":"a169e7f0-e395-4d03-a2cd-3ca15a8119bc","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:29.947527Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:e4240302feb9e0e378cba64ad19922b38180c8c50fee8b39c1a7bfebd85676ee","observation_id":"2c64da8d-02ff-49c3-8590-4e3b215436dc","resolution":{"observed_at":"2026-08-07T15:29:45.491309Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:45.232446Z","title":"A law of data separation in deep learning","venue":null,"work_id":"9dcf03fe-6495-4a71-af2f-df019142dc85","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.066059Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:479ee7b408883620528340643a16f077910ee4ca044a11e1090a955ec7e855e7","observation_id":"7429ce08-b440-4031-8366-43f723dd8ad2","resolution":{"observed_at":"2026-08-07T15:29:45.307511Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:30.175606Z","title":"Deep residual learning for image recognition","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.175606Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:4a5918cb2def0f245b1180df2306a7d484ecdab9e1c83d95bb7948c580b0d04d","observation_id":"6293ab33-46e6-4194-813d-fce01fd003a3","resolution":{"observed_at":"2026-08-07T15:29:30.175606Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.01832","last_updated":"2024-09-06T03:13:22Z","snapshot_observed_at":"2026-08-06T14:26:23.175703Z","submitted_at":"2024-09-03T12:30:21Z","title":"Beyond Unconstrained Features: Neural Collapse for Shallow Neural Networks with General Data","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.01832","snapshot_observed_at":"2026-08-07T15:29:30.299550Z","title":"Beyond unconstrained features: Neural collapse for shallow neural networks with general data","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.299550Z"},"links":{"cited_paper":"/paper/2409.01832","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:6b62dabcfb761c63e9e6a50b17ec5f6d47f5c0b2b759b5b3587c22b89312d73f","observation_id":"3db3b0c3-f332-40ad-a562-a0a2703b1ff9","resolution":{"observed_at":"2026-08-07T15:29:30.299550Z","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":"2026-08-07T15:29:44.981789Z","title":"Neural collapse for unconstrained feature model under cross-entropy loss with imbalanced data","venue":null,"work_id":"594fde00-1ca9-4692-8bc2-215b3f702a8a","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.464264Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:f9b5218bdac8656279ddb9699cc5d231facbad268f8f5c5e010b3d4c691cf8c5","observation_id":"d16c4d09-0784-4eff-ac3c-85571b240f34","resolution":{"observed_at":"2026-08-07T15:29:45.119526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:44.754451Z","title":null,"venue":null,"work_id":"c0baa79b-2859-4c79-95c0-f5841caba935","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.590534Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:40f955b23882604e7c5ff203f7a8cf1ce7874a9313a341e35a05dc3b9e6afbad","observation_id":"939b386f-89f5-4701-a54f-98a2be89a145","resolution":{"observed_at":"2026-08-07T15:29:44.877279Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.08384","last_updated":"2022-02-17T00:20:12Z","snapshot_observed_at":"2026-07-06T12:38:37.285432Z","submitted_at":"2022-02-17T00:20:12Z","title":"Limitations of Neural Collapse for Understanding Generalization in Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.08384","snapshot_observed_at":"2026-08-07T15:29:30.744223Z","title":"Limitations of neural collapse for understanding generalization in deep learning","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.744223Z"},"links":{"cited_paper":"/paper/2202.08384","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:6eef0fc28a4d69a37b6e2067ca565a19c832b5c54f251d73a62ce9bd84a89656","observation_id":"eebb8d6c-bf21-47dd-b826-7b500aa00e97","resolution":{"observed_at":"2026-08-07T15:29:30.744223Z","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":"2026-08-07T15:29:44.457470Z","title":"Wide neural networks trained with weight decay provably exhibit neural collapse","venue":null,"work_id":"fcf766f3-283b-4033-b028-ba347127a064","year":2025},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.866331Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:cbfbe0a771947a3014283a714d5f1abcd1ed1786fca915f06215890462b591ad","observation_id":"31d5559e-af1d-4483-a192-12518140dd09","resolution":{"observed_at":"2026-08-07T15:29:44.584104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:44.223524Z","title":"An unconstrained layer-peeled perspective on neural collapse","venue":null,"work_id":"b0921bb3-293a-447f-b20e-33f69859ab41","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:30.974018Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:6fcbc245e74142565f444366200fa3a868d013690e34c555aa8babc650e0f92e","observation_id":"dd2a58c7-d577-4790-bd14-983b0c63d1af","resolution":{"observed_at":"2026-08-07T15:29:44.359893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:44.086205Z","title":"Generalized neural collapse for a large number of classes","venue":null,"work_id":"745e1507-41c5-44e0-96da-8f1993d2115b","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.139944Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:7f7dd0cd7038e61a8c6729dadc919695d73684a79059eabb0d5d7e535561f85b","observation_id":"95e9506b-2a56-4f2b-a797-f58c7535ab7b","resolution":{"observed_at":"2026-08-07T15:29:44.135518Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.957265Z","title":"How does information bottleneck help deep learning? In International Conference on Machine Learning (ICML), 2023","venue":null,"work_id":"ec5452f9-3e62-4461-ab45-9177034e92e5","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.329097Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:219a740169e9fcf37aaa2dfa3425c1fee0f4e7aab61a42234dca984d08412095","observation_id":"3de5d767-7767-468f-bd23-5e7dcac32d66","resolution":{"observed_at":"2026-08-07T15:29:44.011827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.809509Z","title":"Kernel vs","venue":null,"work_id":"e7717fd5-4708-44ec-9f63-40a00bbc4ecc","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.475978Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:e51a40c025cf3f9041cb2aed4b3f8fc98b580d0cd1cfd5283df3a82bb6a6e84d","observation_id":"e77066bc-5b65-4700-8835-0da8deb74e0c","resolution":{"observed_at":"2026-08-07T15:29:43.876796Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.678470Z","title":"A neural collapse perspective on feature evolution in graph neural networks","venue":null,"work_id":"53fce46b-ac2d-4c7c-b57d-0b57120db04a","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.632591Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:5f0abbaca1b5168b25147b31ac231330d336745309323cc2a7077931366a97c7","observation_id":"6eb0f9a2-9621-4155-baf9-f04d2b268e2f","resolution":{"observed_at":"2026-08-07T15:29:43.728014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:31.824940Z","title":"Learning multiple layers of features from tiny images","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.824940Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:2b509b8186b02be0843535fcb75e5089b32650ae408194f7fdfc1f5a76ed9076","observation_id":"3fc860bb-6aff-4521-b125-7a851facb8c4","resolution":{"observed_at":"2026-08-07T15:29:31.824940Z","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":"2026-08-07T15:29:43.543388Z","title":"The asymmetric maximum margin bias of quasi-homogeneous neural networks","venue":null,"work_id":"223b3d81-3bd9-490d-8d9a-bbb3fe2cd325","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:31.963051Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:303415cef011a6de751e6113e658d4a551698023c6d13ccdb938e507385ac8c8","observation_id":"ca3f7dae-353b-425e-adec-ff1c975b5a52","resolution":{"observed_at":"2026-08-07T15:29:43.606136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.382998Z","title":"Gradient-based learning applied to document recognition","venue":null,"work_id":"a69d6e5c-080f-4725-ad2b-a614325284f4","year":1998},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.143546Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b734391e824be810c446b36b120612f31f3f93ee2eba3d5e9f381ad77323b7a3","observation_id":"a02fe1e5-383b-47f1-acb0-51ba6dfd1a38","resolution":{"observed_at":"2026-08-07T15:29:43.459075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.255482Z","title":"Principled and efficient transfer learning of deep models via neural collapse","venue":null,"work_id":"09d1d6a9-4ca3-4988-a80d-c242d39118e4","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.248103Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:d7c004c0fdf5f5585eb171105ff22fe7fe08a64c7f1b1d56a56ee76f9aac4081","observation_id":"14c29c2a-36af-41f1-930e-040e2d07a75d","resolution":{"observed_at":"2026-08-07T15:29:43.303949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:43.098136Z","title":"No fear of classifier biases: Neural collapse inspired federated learning with synthetic and fixed classifier","venue":null,"work_id":"34c2983c-5c3a-4d69-bb1c-feddc0751f57","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.405422Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:8e5af4872cc8ca0bd53e64f6623448a385b6487c8af1076e0056739aba701827","observation_id":"a6b8e422-77a0-433e-9b69-b297c99e40b0","resolution":{"observed_at":"2026-08-07T15:29:43.170078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.959030Z","title":"Inducing neural collapse to a fixed hierarchy-aware frame for reducing mistake severity","venue":null,"work_id":"c5202d5b-264c-473a-99d8-a7e837a97444","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.509972Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:866d5713a0563512c241d75fe22f8d5bd76571af63b34bd9f022de61e062cad4","observation_id":"e8ceb907-d959-4c83-84ae-6ee15baf072c","resolution":{"observed_at":"2026-08-07T15:29:43.031231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.815265Z","title":"Spurious feature diversification improves out-of-distribution generalization","venue":null,"work_id":"52415778-0bbf-43bc-b337-a83205ce5f72","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.666662Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:c1dc4cfa76b87c74c2f8efc38f84fed4c93d315a18daade6f0ec0cabb60bdda2","observation_id":"d6d92af6-f3c9-474d-aba8-bdb631de011b","resolution":{"observed_at":"2026-08-07T15:29:42.888402Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.17278","last_updated":"2024-11-26T09:59:34Z","snapshot_observed_at":"2026-07-06T19:57:10.411888Z","submitted_at":"2024-11-26T09:59:34Z","title":"The Exploration of Neural Collapse under Imbalanced Data","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.17278","snapshot_observed_at":"2026-08-07T15:29:32.821539Z","title":"The exploration of neural collapse under imbalanced data","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.821539Z"},"links":{"cited_paper":"/paper/2411.17278","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:05fb6b74906d05848ccec458cde1335987158d933dae7162e7b72fd406d64425","observation_id":"523d4705-37f1-4040-bbad-0a13b2eec36d","resolution":{"observed_at":"2026-08-07T15:29:32.821539Z","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":"2026-08-07T15:29:42.662125Z","title":"Gen: Pushing the limits of softmax-based out-of-distribution detection","venue":null,"work_id":"26982c1b-aa6f-4473-a122-ff841ea895b1","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:32.927621Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:93563b211b4402616fd888d80a4d5828745b7622badd5d98f0a79490029fa512","observation_id":"3f5ddd31-a05b-4848-ae09-16254c80dae8","resolution":{"observed_at":"2026-08-07T15:29:42.745762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.486407Z","title":"Inducing neural collapse in deep long-tailed learning","venue":null,"work_id":"3bae619d-bb64-4de6-8810-608116ea3125","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.055826Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:ac6e971235f1520b9b7337c17b6949bc0f0a9a08af5d7499e737cbc44e4f4748","observation_id":"a152b90a-039d-47f3-9e2a-1987590ecd8b","resolution":{"observed_at":"2026-08-07T15:29:42.550085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.323187Z","title":"Neural collapse under cross-entropy loss","venue":null,"work_id":"aa3f35ed-908d-416a-b0fe-2dea3df14ae9","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.142770Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:9391714b8199b63e5969cafd4349cc640e05e408675eab95e87628bf713ef3a6","observation_id":"abac31a4-a14c-4c81-a43d-3f40f25d32e0","resolution":{"observed_at":"2026-08-07T15:29:42.394658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.175112Z","title":"Do we need neural collapse? Learning diverse features for fine-grained and long-tail classification","venue":null,"work_id":"b23ba04f-bba0-4408-8706-404927eee64e","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.219860Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:77e6a167b9feb4181c61df07ffe43a8b567ef67e4eb2a2b0beb18e5810fe6b2c","observation_id":"e1d32ba0-df8b-4c4e-a1fd-4ce29b4c8092","resolution":{"observed_at":"2026-08-07T15:29:42.244077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:42.062791Z","title":"The tunnel effect: Building data representations in deep neural networks","venue":null,"work_id":"5bd301fd-f105-407a-b5ce-f14aac73e632","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.306908Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:cd02903f67f7aadaf2977cdc50131d6dcd723d1d8ec77198a160e851b600b925","observation_id":"b99f69e4-ed57-429c-9eae-797d5c8a9728","resolution":{"observed_at":"2026-08-07T15:29:42.109245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:33.405386Z","title":"Neural collapse with unconstrained features","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.405386Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:94172849931115ce09e3c313360f06ab5cd6f1ef25c7aa9bd8d1ec4a14e787be","observation_id":"a629c04d-22a1-41a1-b59d-de5905eeb709","resolution":{"observed_at":"2026-08-07T15:29:33.405386Z","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":"2026-08-07T15:29:41.900867Z","title":null,"venue":null,"work_id":"f173f722-a5e2-403d-9373-286c8d2db3cc","year":2020},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.497099Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:94d7e8e17ce1216820bf1e66e4e14e156849db36f08ecf8e4ad7bad443661f06","observation_id":"ab7ba2b4-ffb4-4ad1-aead-06618ab8d8c5","resolution":{"observed_at":"2026-08-07T15:29:41.983244Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.799539Z","title":"Neural collapse in deep homogeneous classifiers and the role of weight decay","venue":null,"work_id":"9a3ce9a3-3d3c-4edc-ae7c-776a25a0980a","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.603044Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:5edb4aae529961ee9dfbbdff36557d47e1233115695bb759adc69d5d7e8fbe8c","observation_id":"8d6ba635-3af8-4687-9108-886f564e3c55","resolution":{"observed_at":"2026-08-07T15:29:41.846414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.686786Z","title":"Feature learning in deep classifiers through intermediate neural collapse","venue":null,"work_id":"e1f2d38f-b09c-4ace-8b86-105999cfa9dd","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.684784Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:c41307db95e24d614b2c698b6075f1c8ef00a7a45e8af8af89cf8f688febf6cc","observation_id":"91431ad9-9f58-409b-80d1-eec46cf3dacd","resolution":{"observed_at":"2026-08-07T15:29:41.754223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.531766Z","title":"Neural (tangent kernel) collapse","venue":null,"work_id":"b43bd14d-4385-481b-9977-addde3090efa","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.778875Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:32c01d9c191dfb14d02062461e243f6a3e0a324f4507e5538b3924365fbbacb0","observation_id":"fc0e9a81-895a-48b6-bd0c-e95cc383b3b5","resolution":{"observed_at":"2026-08-07T15:29:41.608509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.410043Z","title":"On the robustness of neural collapse and the neural collapse of robustness","venue":null,"work_id":"5a4b5643-824e-4cb7-929a-b7aafe5af79b","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.876027Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:836dd71c5a7257a28fa15696d96c3a92411a54d7448fcc1a939f708573095ffe","observation_id":"a5cc1223-59e6-4f3d-83c2-d896ddca5169","resolution":{"observed_at":"2026-08-07T15:29:41.464450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.225263Z","title":null,"venue":null,"work_id":"23266e95-466d-4b46-aaf2-7b17e255ebad","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:33.942285Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:f5c011df51af295b4a1b8f4bba1063f60e0748b0b74332a2aa9eb6a077c91b02","observation_id":"2eda8b2e-1948-45ec-a9ed-aa93fb6ed219","resolution":{"observed_at":"2026-08-07T15:29:41.320640Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:41.035767Z","title":null,"venue":null,"work_id":"91551861-d7a6-4f00-95e0-7350fcef4085","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.022436Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:27df076cdaef9616838547242cbe26ad1966b743239fa58435193f1a2403c0ff","observation_id":"9598fe2e-6b3b-488d-8d2c-ab62680dec1b","resolution":{"observed_at":"2026-08-07T15:29:41.126773Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:40.854493Z","title":"Implicit optimization bias of next-token prediction in linear models","venue":null,"work_id":"bbffb1bc-1652-419d-8fad-00478785c096","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.129677Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:bbbc4dd25de607f696e7238dc0b1b6d548734b2c931562e42950a5fba25ae2e9","observation_id":"1c4acdcb-92a1-4d99-844b-3e4145b0f3e3","resolution":{"observed_at":"2026-08-07T15:29:40.938642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:40.624099Z","title":"Imbalance trouble: Revisiting neural-collapse geometry","venue":null,"work_id":"e6d31cf9-e7fb-4f29-a258-361a6e0e8610","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.249417Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:a10ce699f9a70dab89d17435c92e995aa9fc91df4569986f6ba4f4dab928f855","observation_id":"9ef041ce-71ba-4135-9215-a139eff8728e","resolution":{"observed_at":"2026-08-07T15:29:40.699177Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:40.462179Z","title":"Extended unconstrained features model for exploring deep neural collapse","venue":null,"work_id":"c478e914-cfc9-4d38-9a16-168fcfd2b585","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.323975Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:880a88f0533e4cd4da25036c72e9c553bdf0f4dcc53032174d42bc6837944189","observation_id":"e8653096-01da-4baa-9bae-646bea903968","resolution":{"observed_at":"2026-08-07T15:29:40.548188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:40.198302Z","title":"Perturbation analysis of neural collapse","venue":null,"work_id":"18513132-9784-4cfc-b32c-dd641deb4871","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.388455Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:1104e8043efaa1528ee4e0a72ee72dda7f9638d52d9752c32c0dade356cb38eb","observation_id":"75e278c2-258f-4911-b8e7-aa0410bfdecd","resolution":{"observed_at":"2026-08-07T15:29:40.349583Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:34.510160Z","title":"Attention is all you need","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.510160Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:57eb99ff913e229d5dc66a96b47dca5315c6a5568ca6adf483951ce5b6dc91e3","observation_id":"377d1d83-26d4-4e1b-a30a-1b30163bfd01","resolution":{"observed_at":"2026-08-07T15:29:34.510160Z","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":"2026-08-07T15:29:39.969884Z","title":"Get the best of both worlds: Improving accuracy and transferability by grassmann class representation","venue":null,"work_id":"14c48351-6ae8-4785-a519-7d51c09779ce","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.607527Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:b0262e74cf28c25abb392c340a7aba6c258eda068040099113162016aa3ca55e","observation_id":"03bd2be7-16ee-4a95-bf72-0d35aeb561cb","resolution":{"observed_at":"2026-08-07T15:29:40.073635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.02960","last_updated":"2026-07-02T02:35:50Z","snapshot_observed_at":"2026-07-06T16:43:26.087606Z","submitted_at":"2023-11-06T09:00:38Z","title":"Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.02960","snapshot_observed_at":"2026-08-07T15:29:34.702471Z","title":"Understanding deep representation learning via layerwise feature compression and discrimination","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.702471Z"},"links":{"cited_paper":"/paper/2311.02960","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:d9a95bd44c98398e8de8b0f3eb200c126bafadac2befefc4998d8e5df548ec52","observation_id":"ed2e6243-381c-4482-b988-0fa2f881d8a1","resolution":{"observed_at":"2026-08-07T15:29:34.702471Z","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":"2026-08-07T15:29:39.651193Z","title":"Linear convergence analysis of neural collapse with unconstrained features","venue":null,"work_id":"b8f0ec6f-f124-4a9b-8bd4-8338ab4ae3fe","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.785009Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:3a55e070a7174ee67fd881410aa6e4c5eca5d669f07b0fa6eefe2718e8a6534e","observation_id":"269429fd-5355-45ed-9f28-a1be021c3394","resolution":{"observed_at":"2026-08-07T15:29:39.874408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.00985","last_updated":"2024-05-02T03:48:08Z","snapshot_observed_at":"2026-07-06T18:08:35.173140Z","submitted_at":"2024-05-02T03:48:08Z","title":"Progressive Feedforward Collapse of ResNet Training","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.00985","snapshot_observed_at":"2026-08-07T15:29:34.877392Z","title":"Progressive feedforward collapse of resnet training","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.877392Z"},"links":{"cited_paper":"/paper/2405.00985","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:1b0f583089db5cd8c39a6f72584f79ec1fd438252642f879879e87669592cfb2","observation_id":"d828600a-71d1-4028-bf96-2250adf96c96","resolution":{"observed_at":"2026-08-07T15:29:34.877392Z","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":"2026-08-07T15:29:39.507374Z","title":"How far pre-trained models are from neural collapse on the target dataset informs their transferability","venue":null,"work_id":"6c2fe6ea-a8d4-445f-a46f-9499e157846b","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:34.981607Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:409d578595f693cdca2b3d99aeb4d16825fa36bd7b7d3f349f4cce5719a957a0","observation_id":"90cf3d23-7bd5-4766-a60e-46c694258d50","resolution":{"observed_at":"2026-08-07T15:29:39.583346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:39.294973Z","title":"On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers","venue":null,"work_id":"34f9291f-470d-4d74-916b-b3f601a5d19f","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.078644Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:6da60a9bd04ef4c6ecf83e9e4b19011c335eadab9314e0bd7ae02fd291d08696","observation_id":"6ddbabf0-bac5-40ee-a7e1-46c79286e668","resolution":{"observed_at":"2026-08-07T15:29:39.423883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.19104","last_updated":"2025-02-04T12:16:07Z","snapshot_observed_at":"2026-07-31T04:14:42.479120Z","submitted_at":"2025-01-31T12:57:29Z","title":"Neural Collapse Beyond the Unconstrained Features Model: Landscape, Dynamics, and Generalization in the Mean-Field Regime","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.19104","snapshot_observed_at":"2026-08-07T15:29:35.159012Z","title":"Neural collapse beyond the unconstrainted features model: Landscape, dynamics, and generalization in the mean-field regime","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.159012Z"},"links":{"cited_paper":"/paper/2501.19104","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:46295ff0939c13de995a3e048e3c128d2f9b377d783ebc56e98411aca158ef6c","observation_id":"ab79a979-049e-4d91-bd42-7ffbd27e53ec","resolution":{"observed_at":"2026-08-07T15:29:35.159012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.17767","last_updated":"2024-11-26T03:54:09Z","snapshot_observed_at":"2026-08-08T09:36:21.431403Z","submitted_at":"2024-05-28T02:46:11Z","title":"Linguistic Collapse: Neural Collapse in (Large) Language Models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.17767","snapshot_observed_at":"2026-08-07T15:29:35.247658Z","title":"Linguistic collapse: Neural collapse in (large) language models","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.247658Z"},"links":{"cited_paper":"/paper/2405.17767","citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:aea1bb1b022dbaf6337be0a62eb2144ac572da6856f6ab2ed1cb04818a11ea55","observation_id":"44c17b53-b122-4db6-8b1c-870ed91df133","resolution":{"observed_at":"2026-08-07T15:29:35.247658Z","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":"2026-08-07T15:29:39.053063Z","title":"Pursuing feature separation based on neural collapse for out-of-distribution detection","venue":null,"work_id":"ec7747ad-cb57-4d8f-a76b-0566209e2be3","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.344317Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:ddcb9f305f0ea7f2d3a2f77ff51976fc51169414b52dc2b229a50dcb5e43db41","observation_id":"87e81fca-547a-484c-ab84-06e72231df45","resolution":{"observed_at":"2026-08-07T15:29:39.167053Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:38.867210Z","title":"Dynamics in deep classifiers trained with the square loss: Normalization, low rank, neural collapse, and generalization bounds","venue":null,"work_id":"79c669f5-acb6-463e-b0d5-ac49f1e46905","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.446974Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:55c4bb2685b31d3b9708345d10b93c422bad0b186890f3dd25625cde29eeb71a","observation_id":"f226edc2-3386-4730-98b8-b4c168e48e36","resolution":{"observed_at":"2026-08-07T15:29:38.959030Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:38.703834Z","title":"Epa: Neural collapse inspired robust out-of- distribution detector","venue":null,"work_id":"e5cd40b5-7fc4-45a9-8dd8-8bfcca07bb72","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.508233Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:744dd284924bafc4f790e79a850a3e4afa3e103df7f1b0956948409dcedad379","observation_id":"0d0c3110-66ce-4448-942d-1e106dd0334c","resolution":{"observed_at":"2026-08-07T15:29:38.762058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:38.526605Z","title":"Implicit geometry of next-token prediction: From language sparsity patterns to model representations","venue":null,"work_id":"1b2f3302-d62f-4fab-ad1f-573c2b136a64","year":2024},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.595578Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:2d00c86cac4659e08f0ed2b89b06e03417d60d05e378199f5b88fabf8c487170","observation_id":"66c9f432-3e04-4d93-8cd4-95aab63eeee9","resolution":{"observed_at":"2026-08-07T15:29:38.608768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:38.314033Z","title":"Understand- ing imbalanced semantic segmentation through neural collapse","venue":null,"work_id":"d4c95c54-d195-4b21-9fcd-d7b24f3c5da6","year":2023},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.698990Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:80b25b325c4ed708c584ce6ceaacb078c327a2b508470090c90637a379528662","observation_id":"9887efea-1e49-4162-9dfe-588245d8425f","resolution":{"observed_at":"2026-08-07T15:29:38.447192Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:38.129746Z","title":"On the optimization landscape of neural collapse under MSE loss: Global optimality with unconstrained features","venue":null,"work_id":"813b48bb-c705-4e50-a761-a175d83ec091","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.795762Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:8e5f85a9667f36bc9e25acaa0898846c852e6235d982c11d6e10f8654e512379","observation_id":"c61d8ba6-55f6-40fd-9d88-df00a533ecd0","resolution":{"observed_at":"2026-08-07T15:29:38.227964Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.974944Z","title":"Are all losses created equal: A neural collapse perspective","venue":null,"work_id":"6eeeab66-003d-4c24-9395-aeca3c80617d","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:35.889103Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:1b237d861f21f121d0a5814e55d7231bc38a135bafde619f573942f852d2a0cd","observation_id":"79accd6d-8faa-4f16-b31e-6d35dd780fef","resolution":{"observed_at":"2026-08-07T15:29:38.032659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.816192Z","title":"Balanced contrastive learning for long-tailed visual recognition","venue":null,"work_id":"2da78169-ed71-42a7-8fd0-fa5f79bef25d","year":2022},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.003232Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:9bce3e349904b59e2c15febb04e084d70ff3c97ba06a02aa989c09d466fbded5","observation_id":"8c71310e-3e41-489b-b6bd-0bf272ab0da8","resolution":{"observed_at":"2026-08-07T15:29:37.888997Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.645366Z","title":"A geometric analysis of neural collapse with unconstrained features","venue":null,"work_id":"8ba21846-e60a-4b4c-94d1-e9627b00ec1a","year":2021},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.085256Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:8e428fc16538988b18e854c77e1f0a282eecc528a1c60bb602a44dd3e9f254c5","observation_id":"2e013ca7-6580-4f40-bba9-14319a1a5f86","resolution":{"observed_at":"2026-08-07T15:29:37.714048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.435195Z","title":null,"venue":null,"work_id":"61f82464-0137-44b3-bb1b-43381667b552","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.170930Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:157690b73f52293ad79eb4ebcf58554d374750a007f36c21dd36de88a2a5d023","observation_id":"a5894bf0-263a-452b-8fe5-f9ae6ed08186","resolution":{"observed_at":"2026-08-07T15:29:37.507633Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.291309Z","title":null,"venue":null,"work_id":"5258efc0-4309-4a95-afb4-27b2cde6f67e","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.251304Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:cc8c1d3731e7f7ffcf923535802d45e9ff818a22413af4abb3d8aa363ac62067","observation_id":"5b281216-730f-4172-afb7-a4fa83dd585a","resolution":{"observed_at":"2026-08-07T15:29:37.357653Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:37.117954Z","title":"Denote ¯Gki as the set of points on Gki between xki and ¯xki","venue":null,"work_id":"59a947b6-f57c-4935-8b71-dc290cfbe39b","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.355317Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:c364c4c701f02f6bba839e6b03357253fbf7d32e4f5001ded38abc09c940378e","observation_id":"b93ca3a1-4317-4bfa-95d0-92fb2ae6fb6a","resolution":{"observed_at":"2026-08-07T15:29:37.217865Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:36.962133Z","title":null,"venue":null,"work_id":"09c74e63-4ff9-42d3-88f3-733339fbea53","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.470034Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:896108e170489bb6fabf77931dc6457a8e7dbf8fb7830a1e1ecfffd23a2ceb9e","observation_id":"504d3e5c-e801-4baf-8d1a-10c881083362","resolution":{"observed_at":"2026-08-07T15:29:37.032452Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-07T15:29:36.794262Z","title":"10cm ≤ (d − max j(ki)̸=j(lp) ¯hT j(ki) ¯hj(lp))/d","venue":null,"work_id":"0ddc65d3-98e9-4ab4-b56a-ea2a7145f9c5","year":null},"citing_paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-07T15:29:36.563390Z"},"links":{"citing_paper":"/paper/2505.15239"},"observation_digest":"sha256:cf8169d8839bdf0b70934881b130b0a50ad121336fb878b4abd46c36ce84d690","observation_id":"aa7dd894-af75-4b6e-a532-d941f3a1f824","resolution":{"observed_at":"2026-08-07T15:29:36.864014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.15239","last_updated":"2025-05-21T08:16:03Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-07T15:19:13.226269Z","submitted_at":"2025-05-21T08:16:03Z","title":"Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers"},"reference_resolution":{"displayed":76,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":23,"verified_exact":0,"verified_fuzzy":53},"total_outbound_references":76},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 76 of 76 outbound references and 2 inbound Pith citation observations for arXiv:2505.15239."}