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Paper Citation Record · LEDGER

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers

As of 23 August 2026, this Paper Citation Record lists 76 of 76 outbound references and 2 inbound Pith citation observations for arXiv:2505.15239.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.15239 v1

Coverage vector

measured 76 of 76 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:29:36.563390Z

measured 78 of 78 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T05:14:07.208255Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-04T13:29:50.955298Z

Reference resolution

76 of 76 outbound references displayed

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  • unresolved23
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9846464d-742d-4d8e-b572-876656df8420 · outbound

This paper cites The prevalence of neural collapse in neural multivariate regression.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers The prevalence of neural collapse in neural multivariate regression

Reference 1

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Observation 7ccc5928-e426-4889-954a-e48127cac92e · outbound

This paper cites Intrinsic dimension of data representa- tions in deep neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Intrinsic dimension of data representa- tions in deep neural networks

Reference 2

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Observation 2dd94fbe-02ae-4e18-b570-83b3d498e3a3 · outbound

This paper cites Average gradient outer product as a mechanism for deep neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Average gradient outer product as a mechanism for deep neural collapse

Reference 3

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Observation 9620f95c-5bdf-4ab2-9d11-a3478b435982 · outbound

This paper cites On the inductive bias of infinite-depth ResNets and the bottleneck rank.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers On the inductive bias of infinite-depth ResNets and the bottleneck rank

Reference 4

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Observation e03e6101-0f75-4b05-90d9-6549e8c98b52 · outbound

This paper cites Prevalence of simplex compression in adversarial deep neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Prevalence of simplex compression in adversarial deep neural networks

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 2a3bc718-4c7b-4cf3-9e52-d922c78dd334 · outbound

This paper cites Perfectly balanced: Improving transfer and robustness of supervised contrastive learning.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Perfectly balanced: Improving transfer and robustness of supervised contrastive learning

Reference 6

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Source-reported events for the cited work

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Observation 21334e3b-ce2f-4d37-9a51-11da4400e550 · outbound

This paper cites Neural collapse for cross-entropy class-imbalanced learning with unconstrained relu features model.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse for cross-entropy class-imbalanced learning with unconstrained relu features model

Reference 7

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Observation 3e379a38-d6b1-44ec-aa9e-521da9868734 · outbound

This paper cites Neural collapse in deep linear network: From balanced to imbalanced data.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse in deep linear network: From balanced to imbalanced data

Reference 8

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Source-reported events for the cited work

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Observation 4394543c-c6e3-4542-a0c6-a9fb201253b0 · outbound

This paper cites Improving self-supervised learning by characterizing idealized representations.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Improving self-supervised learning by characterizing idealized representations

Reference 9

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Source-reported events for the cited work

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Observation 7cdb0dad-37b9-492e-a2bb-97d8d73f8b59 · outbound

This paper cites Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training

Reference 10

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Observation 5e8a58ee-250e-42b0-a617-bf6aed21d6be · outbound

This paper cites On the Implicit Bias Towards Minimal Depth of Deep Neural Networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers On the Implicit Bias Towards Minimal Depth of Deep Neural Networks

Reference 11

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Observation db528e66-e94e-4242-bc36-c18ebbe0ea26 · outbound

This paper cites Improved generalization bounds for transfer learning via neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Improved generalization bounds for transfer learning via neural collapse

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation dfaa063c-7b16-4752-aa7d-a13bf43e6b92 · outbound

This paper cites The persistence of neural collapse despite low-rank bias: An analytic perspective through unconstrained features.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers The persistence of neural collapse despite low-rank bias: An analytic perspective through unconstrained features

Reference 13

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Observation f832f40e-fc36-4df6-bc58-200ebd890fdc · outbound

This paper cites Unifying Low Dimensional Spectra in Deep Learning.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unifying Low Dimensional Spectra in Deep Learning

Reference 14

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Observation ccba16ae-256f-47d9-8c63-53f1619abacd · outbound

This paper cites Linking neural collapse and l2 normalization with improved out-of-distribution detection in deep neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Linking neural collapse and l2 normalization with improved out-of-distribution detection in deep neural networks

Reference 15

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Source-reported events for the cited work

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Observation 2c64da8d-02ff-49c3-8590-4e3b215436dc · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 16

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Observation 7429ce08-b440-4031-8366-43f723dd8ad2 · outbound

This paper cites A law of data separation in deep learning.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers A law of data separation in deep learning

Reference 17

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Observation 6293ab33-46e6-4194-813d-fce01fd003a3 · outbound

This paper cites Deep residual learning for image recognition.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Deep residual learning for image recognition

Reference 18

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Observation 3db3b0c3-f332-40ad-a562-a0a2703b1ff9 · outbound

This paper cites Beyond Unconstrained Features: Neural Collapse for Shallow Neural Networks with General Data.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Beyond Unconstrained Features: Neural Collapse for Shallow Neural Networks with General Data

Reference 19

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Observation d16c4d09-0784-4eff-ac3c-85571b240f34 · outbound

This paper cites Neural collapse for unconstrained feature model under cross-entropy loss with imbalanced data.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse for unconstrained feature model under cross-entropy loss with imbalanced data

Reference 20

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Observation 939b386f-89f5-4701-a54f-98a2be89a145 · outbound

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Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 21

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Observation eebb8d6c-bf21-47dd-b826-7b500aa00e97 · outbound

This paper cites Limitations of Neural Collapse for Understanding Generalization in Deep Learning.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Limitations of Neural Collapse for Understanding Generalization in Deep Learning

Reference 22

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Observation 31d5559e-af1d-4483-a192-12518140dd09 · outbound

This paper cites Wide neural networks trained with weight decay provably exhibit neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Wide neural networks trained with weight decay provably exhibit neural collapse

Reference 23

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation dd2a58c7-d577-4790-bd14-983b0c63d1af · outbound

This paper cites An unconstrained layer-peeled perspective on neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers An unconstrained layer-peeled perspective on neural collapse

Reference 24

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 95e9506b-2a56-4f2b-a797-f58c7535ab7b · outbound

This paper cites Generalized neural collapse for a large number of classes.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Generalized neural collapse for a large number of classes

Reference 25

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 3de5d767-7767-468f-bd23-5e7dcac32d66 · outbound

This paper cites How does information bottleneck help deep learning? In International Conference on Machine Learning (ICML), 2023.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers How does information bottleneck help deep learning? In International Conference on Machine Learning (ICML), 2023

Reference 26

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Observation e77066bc-5b65-4700-8835-0da8deb74e0c · outbound

This paper cites Kernel vs.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Kernel vs

Reference 27

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Observation 6eb0f9a2-9621-4155-baf9-f04d2b268e2f · outbound

This paper cites A neural collapse perspective on feature evolution in graph neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers A neural collapse perspective on feature evolution in graph neural networks

Reference 28

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 3fc860bb-6aff-4521-b125-7a851facb8c4 · outbound

This paper cites Learning multiple layers of features from tiny images.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Learning multiple layers of features from tiny images

Reference 29

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Source-reported events for the cited work

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Observation ca3f7dae-353b-425e-adec-ff1c975b5a52 · outbound

This paper cites The asymmetric maximum margin bias of quasi-homogeneous neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers The asymmetric maximum margin bias of quasi-homogeneous neural networks

Reference 30

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation a02fe1e5-383b-47f1-acb0-51ba6dfd1a38 · outbound

This paper cites Gradient-based learning applied to document recognition.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Gradient-based learning applied to document recognition

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 14c29c2a-36af-41f1-930e-040e2d07a75d · outbound

This paper cites Principled and efficient transfer learning of deep models via neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Principled and efficient transfer learning of deep models via neural collapse

Reference 32

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation a6b8e422-77a0-433e-9b69-b297c99e40b0 · outbound

This paper cites No fear of classifier biases: Neural collapse inspired federated learning with synthetic and fixed classifier.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers No fear of classifier biases: Neural collapse inspired federated learning with synthetic and fixed classifier

Reference 33

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation e8ceb907-d959-4c83-84ae-6ee15baf072c · outbound

This paper cites Inducing neural collapse to a fixed hierarchy-aware frame for reducing mistake severity.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Inducing neural collapse to a fixed hierarchy-aware frame for reducing mistake severity

Reference 34

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation d6d92af6-f3c9-474d-aba8-bdb631de011b · outbound

This paper cites Spurious feature diversification improves out-of-distribution generalization.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Spurious feature diversification improves out-of-distribution generalization

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.888402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:32.666662Z digest=sha256:feeff2a16b0076065661cef226920ba1b6ea57468b900d038dc383d2061bcb79

Observation 523d4705-37f1-4040-bbad-0a13b2eec36d · outbound

This paper cites The Exploration of Neural Collapse under Imbalanced Data.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers The Exploration of Neural Collapse under Imbalanced Data

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:32.821539Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:32.821539Z digest=sha256:bffda3b2487ca9bf5eeec9d5bd05ff5597e48fb5f852bd951a3407621d511802

Observation 3f5ddd31-a05b-4848-ae09-16254c80dae8 · outbound

This paper cites Gen: Pushing the limits of softmax-based out-of-distribution detection.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Gen: Pushing the limits of softmax-based out-of-distribution detection

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.745762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:32.927621Z digest=sha256:0a54837d3c4c6021421e01f36a28530efd6d9e7f74f472cb3bca962e19a6197b

Observation a152b90a-039d-47f3-9e2a-1987590ecd8b · outbound

This paper cites Inducing neural collapse in deep long-tailed learning.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Inducing neural collapse in deep long-tailed learning

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.550085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.055826Z digest=sha256:5e600f372c86d0a1318ec6c807d2ad8e38c74230d7bdc33ebfedde83a9cc4158

Observation abac31a4-a14c-4c81-a43d-3f40f25d32e0 · outbound

This paper cites Neural collapse under cross-entropy loss.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse under cross-entropy loss

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.394658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.142770Z digest=sha256:bc7df58b34bd11668bf9f93446d621543e2cbb6d5591935aec6a111fa09eeaee

Observation e1d32ba0-df8b-4c4e-a1fd-4ce29b4c8092 · outbound

This paper cites Do we need neural collapse? Learning diverse features for fine-grained and long-tail classification.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Do we need neural collapse? Learning diverse features for fine-grained and long-tail classification

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.244077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.219860Z digest=sha256:dff3638cdd4a270cac03b4f84b34ffef31c393c415bc3b6246e8569428b182bd

Observation b99f69e4-ed57-429c-9eae-797d5c8a9728 · outbound

This paper cites The tunnel effect: Building data representations in deep neural networks.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers The tunnel effect: Building data representations in deep neural networks

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:42.109245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.306908Z digest=sha256:7dd89f2af133b7fb6d24a20c3047701161439382346827feea1c2be9a3d96e08

Observation a629c04d-22a1-41a1-b59d-de5905eeb709 · outbound

This paper cites Neural collapse with unconstrained features.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse with unconstrained features

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:33.405386Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:33.405386Z digest=sha256:89759aef0c97a5fca8da8bb0161f2f4b808d69bd0df9ce9ad8ab282c8fec9fe9

Observation ab7ba2b4-ffb4-4ad1-aead-06618ab8d8c5 · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:41.983244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.497099Z digest=sha256:0ca31a4fdd907fcae20ef632c105e7e4971ad1b26e024c4abcf34d14aa545b84

Observation 8d6ba635-3af8-4687-9108-886f564e3c55 · outbound

This paper cites Neural collapse in deep homogeneous classifiers and the role of weight decay.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural collapse in deep homogeneous classifiers and the role of weight decay

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:41.846414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.603044Z digest=sha256:241b60641c61b90e3bf958d6451ab6c19bdd157a2bf5b1569936c53853fc94d7

Observation 91431ad9-9f58-409b-80d1-eec46cf3dacd · outbound

This paper cites Feature learning in deep classifiers through intermediate neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Feature learning in deep classifiers through intermediate neural collapse

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:41.754223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.684784Z digest=sha256:1c4de15f517bb0addc493aa5559c99e7ce35f02781ba864838ae8a9eeb45658f

Observation fc0e9a81-895a-48b6-bd0c-e95cc383b3b5 · outbound

This paper cites Neural (tangent kernel) collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural (tangent kernel) collapse

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:41.608509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.778875Z digest=sha256:668838b62294b99c345405fef64fb731f0fe806734668ae22697f6c59eb588f0

Observation a5cc1223-59e6-4f3d-83c2-d896ddca5169 · outbound

This paper cites On the robustness of neural collapse and the neural collapse of robustness.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers On the robustness of neural collapse and the neural collapse of robustness

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:41.464450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.876027Z digest=sha256:a5bdf2ab7c7570bc4df9c8879b7a1f7aeba9af574b2b4cc58431ae7a7b3b5ba1

Observation 2eda8b2e-1948-45ec-a9ed-aa93fb6ed219 · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:41.320640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:33.942285Z digest=sha256:088133624713e83136df554c7c3e5e2c11e5b6488c533203d4991b2368e867af

Observation 9598fe2e-6b3b-488d-8d2c-ab62680dec1b · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:41.126773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.022436Z digest=sha256:cd354eead41351d89a1344fcfbb9c74296b1047fa5768e3c164d747724a9e931

Observation 1c4acdcb-92a1-4d99-844b-3e4145b0f3e3 · outbound

This paper cites Implicit optimization bias of next-token prediction in linear models.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Implicit optimization bias of next-token prediction in linear models

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:40.938642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.129677Z digest=sha256:c9bd2fe4264bec607be60075af32e068d8876ee0cebb0315b9924db176dbce90

Observation 9ef041ce-71ba-4135-9215-a139eff8728e · outbound

This paper cites Imbalance trouble: Revisiting neural-collapse geometry.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Imbalance trouble: Revisiting neural-collapse geometry

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:40.699177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.249417Z digest=sha256:bbed26ff706efb428d15cb2c6e007ac4ed6f901726db3be3a56d8a58b7bbfb75

Observation e8653096-01da-4baa-9bae-646bea903968 · outbound

This paper cites Extended unconstrained features model for exploring deep neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Extended unconstrained features model for exploring deep neural collapse

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:40.548188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.323975Z digest=sha256:8e5bc994e584e1bd303be8fe2524540dc72f27cd1af3ce8c5b3bb9fb42e45fdc

Observation 75e278c2-258f-4911-b8e7-aa0410bfdecd · outbound

This paper cites Perturbation analysis of neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Perturbation analysis of neural collapse

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:40.349583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.388455Z digest=sha256:f851ff44a420fdba8e5697100315bc30cdb5784af80ec7843497ded5ae6c4e20

Observation 377d1d83-26d4-4e1b-a30a-1b30163bfd01 · outbound

This paper cites Attention is all you need.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Attention is all you need

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:34.510160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:34.510160Z digest=sha256:734369f3fd883c8b32af87482a4165d363597555006af420a7992c85dd0e4f1c

Observation 03bd2be7-16ee-4a95-bf72-0d35aeb561cb · outbound

This paper cites Get the best of both worlds: Improving accuracy and transferability by grassmann class representation.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Get the best of both worlds: Improving accuracy and transferability by grassmann class representation

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:40.073635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.607527Z digest=sha256:d8abe63a92a0a93b085c8b74f6602d559f20f44c61892e941e8c3f4c1e4bc324

Observation ed2e6243-381c-4482-b988-0fa2f881d8a1 · outbound

This paper cites Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:34.702471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:34.702471Z digest=sha256:f35a2eb38fb75466b9668461f1140dbb1bb937a88122aaa0882885ee557c2956

Observation 269429fd-5355-45ed-9f28-a1be021c3394 · outbound

This paper cites Linear convergence analysis of neural collapse with unconstrained features.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Linear convergence analysis of neural collapse with unconstrained features

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:39.874408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.785009Z digest=sha256:00420b6352adff4553472efe28bd29542c1d0fff81127353d206b2b2e40473e6

Observation d828600a-71d1-4028-bf96-2250adf96c96 · outbound

This paper cites Progressive Feedforward Collapse of ResNet Training.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Progressive Feedforward Collapse of ResNet Training

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:34.877392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:34.877392Z digest=sha256:ed393303da326fb080152db00519d9d43b3c30f11a313d26ebf33ccc1de4dd1e

Observation 90cf3d23-7bd5-4766-a60e-46c694258d50 · outbound

This paper cites How far pre-trained models are from neural collapse on the target dataset informs their transferability.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers How far pre-trained models are from neural collapse on the target dataset informs their transferability

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:39.583346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:34.981607Z digest=sha256:42632be89a5e1b219bb642bde069851f7e9688a95c55aa672df4b5a6a77f45d8

Observation 6ddbabf0-bac5-40ee-a7e1-46c79286e668 · outbound

This paper cites On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:39.423883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.078644Z digest=sha256:8a937656529dbe8ab3a474c6d74c520490fec64b2375512be443d947c88f72ab

Observation ab79a979-049e-4d91-bd42-7ffbd27e53ec · outbound

This paper cites Neural Collapse Beyond the Unconstrained Features Model: Landscape, Dynamics, and Generalization in the Mean-Field Regime.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Neural Collapse Beyond the Unconstrained Features Model: Landscape, Dynamics, and Generalization in the Mean-Field Regime

Reference 61

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:35.159012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:35.159012Z digest=sha256:dd68c0e1d76ef2aa358bcb73c57193f2b037e3bea082c1ba988c0c89d7303335

Observation 44c17b53-b122-4db6-8b1c-870ed91df133 · outbound

This paper cites Linguistic Collapse: Neural Collapse in (Large) Language Models.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Linguistic Collapse: Neural Collapse in (Large) Language Models

Reference 62

Resolution
unresolved
no resolver link, observed 2026-08-07T15:29:35.247658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T15:29:35.247658Z digest=sha256:d671b3986c5e3344fc159dceded8b4ed3d21e4e2279dd420a458867380ff34c7

Observation 87e81fca-547a-484c-ab84-06e72231df45 · outbound

This paper cites Pursuing feature separation based on neural collapse for out-of-distribution detection.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Pursuing feature separation based on neural collapse for out-of-distribution detection

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:39.167053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.344317Z digest=sha256:ed21c90e4dbaaf25fe33a666358ba09d217392ee08b862fbff7dd01a6911de39

Observation f226edc2-3386-4730-98b8-b4c168e48e36 · outbound

This paper cites Dynamics in deep classifiers trained with the square loss: Normalization, low rank, neural collapse, and generalization bounds.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Dynamics in deep classifiers trained with the square loss: Normalization, low rank, neural collapse, and generalization bounds

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.959030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.446974Z digest=sha256:b6c6721af07cedcacf012ed7e8840c32610e128aaa4cec1acdd55be6f643047f

Observation 0d0c3110-66ce-4448-942d-1e106dd0334c · outbound

This paper cites Epa: Neural collapse inspired robust out-of- distribution detector.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Epa: Neural collapse inspired robust out-of- distribution detector

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.762058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.508233Z digest=sha256:0f9d6f39088622e9ab7e52329af3980025cbb4a5af326a8189ca3c285dc4c46e

Observation 66c9f432-3e04-4d93-8cd4-95aab63eeee9 · outbound

This paper cites Implicit geometry of next-token prediction: From language sparsity patterns to model representations.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Implicit geometry of next-token prediction: From language sparsity patterns to model representations

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.608768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.595578Z digest=sha256:d77c12cd92296cfbdbd8fb86b6d9405428f6fea7ac96852cbfc696c647bf9266

Observation 9887efea-1e49-4162-9dfe-588245d8425f · outbound

This paper cites Understand- ing imbalanced semantic segmentation through neural collapse.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Understand- ing imbalanced semantic segmentation through neural collapse

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.447192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.698990Z digest=sha256:f5fdfce5f8df51286f355026c936cca20c26ce65b187399d2fcb79e831facb53

Observation c61d8ba6-55f6-40fd-9d88-df00a533ecd0 · outbound

This paper cites On the optimization landscape of neural collapse under MSE loss: Global optimality with unconstrained features.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers On the optimization landscape of neural collapse under MSE loss: Global optimality with unconstrained features

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.227964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.795762Z digest=sha256:b51bb6dbd77adcab0e37e9b82750d968caa1afcda884a2c2e565e61a28a6e7a4

Observation 79accd6d-8faa-4f16-b31e-6d35dd780fef · outbound

This paper cites Are all losses created equal: A neural collapse perspective.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Are all losses created equal: A neural collapse perspective

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:38.032659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:35.889103Z digest=sha256:dd8cc5152755383b73e5c57d456699c6b7b930b011370db7b7ccdc28012261d5

Observation 8c71310e-3e41-489b-b6bd-0bf272ab0da8 · outbound

This paper cites Balanced contrastive learning for long-tailed visual recognition.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Balanced contrastive learning for long-tailed visual recognition

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:37.888997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.003232Z digest=sha256:675459033e52263bffb50253bb9485cc637b2085078c9ea656723896ae72144a

Observation 2e013ca7-6580-4f40-bba9-14319a1a5f86 · outbound

This paper cites A geometric analysis of neural collapse with unconstrained features.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers A geometric analysis of neural collapse with unconstrained features

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:37.714048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.085256Z digest=sha256:71486babf359559c4a5186b1345fbf1485d85b2318b36d20b8007de85b1aeba4

Observation a5894bf0-263a-452b-8fe5-f9ae6ed08186 · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 72

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:37.507633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.170930Z digest=sha256:cfa40fd5f95c94f24b054c8ac75b5c6cd41fa1844d92421e1fb77d9cf5d8403f

Observation 5b281216-730f-4172-afb7-a4fa83dd585a · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 73

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:37.357653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.251304Z digest=sha256:b9e61b986d60ad8758c3b64ce4cfab350fe692577fabf673478a2a3d6804f9ff

Observation b93ca3a1-4317-4bfa-95d0-92fb2ae6fb6a · outbound

This paper cites Denote ¯Gki as the set of points on Gki between xki and ¯xki.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Denote ¯Gki as the set of points on Gki between xki and ¯xki

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:37.217865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.355317Z digest=sha256:a9098ca6deff62fb6f4fb392c80976e18a4749b9ec321d4f9e13e1ed8e4631f6

Observation 504d3e5c-e801-4baf-8d1a-10c881083362 · outbound

This paper cites an unresolved cited work.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers Unresolved cited work

Reference 75

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:29:37.032452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.470034Z digest=sha256:708b22d7fbe8142a20ac474511b99d98d4bcd1e7b8eae9f86e0c86202803f8e2

Observation aa7dd894-af75-4b6e-a532-d941f3a1f824 · outbound

This paper cites 10cm ≤ (d − max j(ki)̸=j(lp) ¯hT j(ki) ¯hj(lp))/d.

Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers 10cm ≤ (d − max j(ki)̸=j(lp) ¯hT j(ki) ¯hj(lp))/d

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:29:36.864014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-07T15:29:36.563390Z digest=sha256:39a430b6f1e0eed04a4d588c3f1438d4909997b2382a3f24cf8c17d2dd0f515b

Pith citing papers

Observation 78cb20d8-3a16-480d-ae28-4153551ad9f7 · inbound

Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension cites this paper.

Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers

Reference 19

Resolution
verified exact
arxiv_id, observed 2026-05-18T10:22:33.217125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-05-18T10:22:28.096542Z digest=sha256:f8b0f0fa0db41c8e07465918daea1887ae4d08d87092035ec0888484cd376a2a

Observation 1ec783da-1013-460e-92c7-5ee46817e75b · inbound

Structure Before Collapse: Transient semantic geometry in next-token prediction cites this paper.

Structure Before Collapse: Transient semantic geometry in next-token prediction Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers

Reference 4

Resolution
verified exact
arxiv_id, observed 2026-07-04T13:29:50.957179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=arxiv_source observed=2026-06-26T05:14:07.208255Z digest=sha256:cecbc39d34aff6d958ac54a1ba6cd97041725b4b5d2db4efbeb292538db80c72