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Paper Citation Record · LEDGER

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations

As of 23 August 2026, this Paper Citation Record lists 100 of 194 outbound references and 0 inbound Pith citation observations for arXiv:2608.04607.

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

pith.paper-citation-record.v1
2608.04607 v1

Coverage vector

measured 100 of 194 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:05:46.090449Z

measured 100 of 100 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

100 of 194 outbound references displayed

  • verified exact10
  • verified fuzzy0
  • unresolved83
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ef6edf53-fda0-45ea-9978-63c767d65255 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 1

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Observation b624f69a-1bb4-409b-97cf-b3f04937c1a4 · outbound

This paper cites 2004 , PAGES =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2004 , PAGES =

Reference 2

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Observation 134d5db5-0b63-4047-8621-722da46f0be7 · outbound

This paper cites Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning , url =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning , url =

Reference 3

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Observation f8d873f7-d16f-4a4c-a2aa-f9cc50d36565 · outbound

This paper cites Proceedings of The 33rd International Conference on Machine Learning , pages =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Proceedings of The 33rd International Conference on Machine Learning , pages =

Reference 4

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 5

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations , TITLE =

Reference 7

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 8

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Observation 4f23f5a6-4181-4e61-b114-43e7d881a5a5 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 9

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Observation 30d6ef36-4bd3-416e-8fef-9b5864376c66 · outbound

This paper cites Gentile and G.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Gentile and G

Reference 10

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 11

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Observation 16214046-2fe2-4cbc-b650-3f503ab17333 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 12

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 13

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Observation ed335e24-56d7-4d00-9861-f5ee21770522 · outbound

This paper cites 2017 , journal=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2017 , journal=

Reference 14

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Observation 327c2b1a-dbf3-4884-b3cb-c3f6bba4997d · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 15

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations CSIAM Trans

Reference 16

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 17

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Observation 593ea46f-cbb8-4e5f-af11-d7e9b6f8bee6 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Exponential moments for numerical approximations of stochastic partial differential equations , JOURNAL =

Reference 18

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2018 , eprint =

Reference 19

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Neural networks for option pricing and hedging: a literature review

Reference 20

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Adam: A Method for Stochastic Optimization

Reference 21

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 22

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks

Reference 23

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 24

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

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This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 26

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations A Sufficient Condition for Convergences of Adam and RMSProp

Reference 27

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Observation 916294df-843c-4430-9434-fcfc2c38a0e0 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Adam Can Converge Without Any Modification On Update Rules

Reference 28

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients

Reference 29

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Learning the random variables in

Reference 30

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations IEEE Trans

Reference 31

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations SAdam: A Variant of Adam for Strongly Convex Functions

Reference 32

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Observation dd2838a0-3954-48f6-92aa-b270b4153fda · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Adaptive Gradient Methods with Dynamic Bound of Learning Rate

Reference 33

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Observation 4a427748-22ed-4098-910b-d3ec38d1d512 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations AdaLoss: A computationally-efficient and provably convergent adaptive gradient method

Reference 34

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Observation c5a7f235-05fb-4d93-9277-1f554ca8c7d2 · outbound

This paper cites AdamL: A fast adaptive gradient method incorporating loss function.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations AdamL: A fast adaptive gradient method incorporating loss function

Reference 35

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Observation 9074afea-ee3e-4338-b345-864366eec263 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations EAdam Optimizer: How $\epsilon$ Impact Adam

Reference 36

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Observation dbf6e088-0407-431f-aedd-bc40d64fc183 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2017 , eprint=

Reference 37

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Observation 52b803b2-b10c-4d3f-b041-941f7cae6726 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations IMA J. Numer. Anal. , fjournal =. 2020 , abstract =

Reference 38

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Observation 4ac3128d-025b-41dc-96e4-2ef07b6eed7d · outbound

This paper cites GPT-4 Technical Report.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations GPT-4 Technical Report

Reference 39

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Observation 655bfaf9-48d4-4e3c-b307-b68f09496e54 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 40

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Observation 113350d9-4411-4d25-94cd-99b1f360fde8 · outbound

This paper cites Language Models are Few-Shot Learners.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Language Models are Few-Shot Learners

Reference 41

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Observation 3fef7b56-7cdb-44ce-be2e-17d1251ead28 · outbound

This paper cites 2024 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2024 , eprint=

Reference 42

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Observation 3e9058e8-f214-4ccc-bf0c-ff11b2e398c1 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 43

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Observation c21ec59b-74b9-4224-a17b-d2ef119b0399 · outbound

This paper cites Physics-informed neural networks (PINNs) for fluid mechanics: A review.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Physics-informed neural networks (PINNs) for fluid mechanics: A review

Reference 44

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Observation 271e7004-38ac-45c0-9d85-6f390262e10a · outbound

This paper cites 2021 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2021 , eprint=

Reference 45

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Observation 28a00e1d-c232-43f6-ab35-fdf2c7069dac · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 46

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Observation 936873fd-e673-4463-b6ea-c41dc8bc6f04 · outbound

This paper cites Discrete Contin.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Discrete Contin

Reference 47

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Observation 71ea76ee-ce58-4751-b697-a7c1c371dc23 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 48

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Observation da743a29-7a52-40f8-8239-a373cb478296 · outbound

This paper cites 2016 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2016 , eprint=

Reference 49

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Observation b6ca29d9-bc46-4b86-82ec-7c7382548e95 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 50

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Observation db754b54-44f2-4b8a-9067-40dc487d7e42 · outbound

This paper cites and Perdikaris, P.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations and Perdikaris, P

Reference 51

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source=arxiv_source observed=2026-08-06T21:05:45.957683Z digest=sha256:fd39c301fad3451911c5618abf1abcba4dd24d094dc84a7ae977b4e83b1f4126

Observation dba54739-f6b2-4912-bd2c-1ad97020a6c8 · outbound

This paper cites 2024 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2024 , eprint=

Reference 52

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source=arxiv_source observed=2026-08-06T21:05:45.960403Z digest=sha256:dcad282310ad8e36b29d8bbfefd1a2e52c311c0c3debbdf06fceb9df99ff17c3

Observation 63e6af98-2245-4982-b6a8-789ff45f2788 · outbound

This paper cites Zero-Shot Text-to-Image Generation.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Zero-Shot Text-to-Image Generation

Reference 53

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Observation a1a299e3-ad0f-45b5-b8ca-e7042b925e8c · outbound

This paper cites Nonlinearity , FJOURNAL =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Nonlinearity , FJOURNAL =

Reference 54

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Observation 3c4a2616-d829-4701-96e7-7f79aaba2d17 · outbound

This paper cites (2004) , publisher=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (2004) , publisher=

Reference 55

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Observation 666d008b-54a2-4eea-8dbb-a83ba4ac4423 · outbound

This paper cites (2014), xii+638 , publisher=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (2014), xii+638 , publisher=

Reference 56

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Observation 3495882c-9527-4380-a56a-ec75828ea298 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (2021), xii+946 , PAGES =

Reference 57

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Observation 0c5e4bbb-4ab9-4a9c-863f-14ddacf91521 · outbound

This paper cites 2012 , numpages =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2012 , numpages =

Reference 58

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Observation 05b3c1b1-c39b-4e39-999a-4887e28b5442 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 59

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source=arxiv_source observed=2026-08-06T21:05:45.980040Z digest=sha256:3676373e16eaf0583a7d58323357d5c3ae1f4e9b4f304e619f1cad96ac691989

Observation fde2b7ae-d8aa-4dca-af0c-4e7a4fd6aaa7 · outbound

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On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (2014), xviii+493 , PAGES =

Reference 60

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Observation b05289f5-6412-4866-9761-f801d686ca29 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 61

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Observation 4ce9fdcb-a434-450d-8e3f-46a0d6a9dfa0 · outbound

This paper cites and Lahiri, Soumendra N.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations and Lahiri, Soumendra N

Reference 62

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Observation 17b57d93-96c3-4f1f-89fd-609523e1efc1 · outbound

This paper cites Nature Reviews Physics , volume=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Nature Reviews Physics , volume=

Reference 63

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Observation 5bbf577b-e4d6-4ea8-9ade-eb26d146b2a3 · outbound

This paper cites European J.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations European J

Reference 64

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Observation 5de6506a-a9bf-451c-8710-0f8a3eba76c3 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 65

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source=arxiv_source observed=2026-08-06T21:05:45.997845Z digest=sha256:c62dbb093999ea5deb0e875fb58907147341c247d1981b79f4bdde6edfd271ec

Observation 3c19cc74-fb5f-496f-b65b-51ecc69aa5f1 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 66

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source=arxiv_source observed=2026-08-06T21:05:46.000473Z digest=sha256:cba47d0e769f2174e26a335bcaf27cb065fc5135fd43cd189034f2f4b4e371ef

Observation a1d75aa5-d140-4b16-b7ff-85ae34942ced · outbound

This paper cites , TITLE =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations , TITLE =

Reference 67

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Observation 680e00b8-0dea-4470-8857-a1d801fb1a4e · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 68

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Observation ace1c0c9-e6ee-46fe-8608-0918f902d4ad · outbound

This paper cites (2023), 426–452 , X=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations (2023), 426–452 , X=

Reference 69

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source=arxiv_source observed=2026-08-06T21:05:46.008274Z digest=sha256:441b7e2aee5e4a9e4a1474c5c920e0276884941437be970a45914478970cffee

Observation 9b2be8f5-7ff3-4821-89f5-fa5b8b4b3d55 · outbound

This paper cites Optimization for deep learning: theory and algorithms , year =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Optimization for deep learning: theory and algorithms , year =

Reference 70

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Observation 44f502ab-686b-476a-8bef-d113b5caa7b1 · outbound

This paper cites Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications

Reference 71

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Observation cd0fb3d7-0d90-43ba-afdb-8a3510797c7e · outbound

This paper cites SIAM Journal on Mathematics of Data Science , volume =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations SIAM Journal on Mathematics of Data Science , volume =

Reference 72

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation f6a43a63-ace8-4132-a38f-57d82434ac39 · outbound

This paper cites 2021 , number =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2021 , number =

Reference 73

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Observation bcf0c3dd-7bbf-4d9c-a3b4-b140347e1af3 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 74

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source=arxiv_source observed=2026-08-06T21:05:46.021984Z digest=sha256:f57d969d7d59a1f32ed8bc8809009e54a5e0f36bae390945a3e590e0329a04ba

Observation 9be26feb-79ba-4624-a794-d45fe06393f6 · outbound

This paper cites Revisiting Convergence of AdaGrad with Relaxed Assumptions.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Revisiting Convergence of AdaGrad with Relaxed Assumptions

Reference 75

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local_arxiv, observed 2026-08-06T21:05:46.763234Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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Observation b0895d6e-ca3c-494a-9ef8-c40093079df1 · outbound

This paper cites 2024 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2024 , eprint=

Reference 76

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Observation f38bf10b-fc28-4631-b1c3-f59f796adda8 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 77

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source=arxiv_source observed=2026-08-06T21:05:46.029335Z digest=sha256:fbce8c3acd6c4e944a28f9a2febdc6397aa1274f5125a4a6d8acca5755b5ea40

Observation fe6e7149-ed87-40e7-9380-9b4398ea84eb · outbound

This paper cites 2016 , journal=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2016 , journal=

Reference 78

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source=arxiv_source observed=2026-08-06T21:05:46.031913Z digest=sha256:ed8e2151963cb5719ed308eb28e34ffd3dbe121d977a1eaddf7e86ac48b72fc6

Observation 5cb91c23-7554-41a4-861b-7deacdb74107 · outbound

This paper cites Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Reference 79

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source=arxiv_source observed=2026-08-06T21:05:46.034470Z digest=sha256:017b57bf8cb8ccd227aa4ac42b8bb04ad7dc7ed3a3dc453e2320bc3618f30d9c

Observation fbc48e27-0ed3-4a34-9c3a-49b64e3093de · outbound

This paper cites 2024 , ISBN =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2024 , ISBN =

Reference 80

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source=arxiv_source observed=2026-08-06T21:05:46.037447Z digest=sha256:6f4dcacf1626246c554377ad2f38a896b3b25f0847adc4681f402f5d534a78b1

Observation 31724c79-80b6-499e-a949-e531f8fcac33 · outbound

This paper cites , TITLE =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations , TITLE =

Reference 81

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source=arxiv_source observed=2026-08-06T21:05:46.039807Z digest=sha256:cc3a4e76c9437b50c72b6913eea29d24cb8ce77ffa712fa48aea7e1d7ce9feac

Observation fa6dc24e-0a64-4d15-a9f1-7d332399b3b6 · outbound

This paper cites 2019 , eprint=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations 2019 , eprint=

Reference 82

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source=arxiv_source observed=2026-08-06T21:05:46.042710Z digest=sha256:74f35c2a867e7f18d4071e9c5b2ad07adf10f2f1af4147fadaf4554fe7167733

Observation 271322d3-a056-4038-8ca7-841bfc3f6dc2 · outbound

This paper cites Kingma and Jimmy Ba , title =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Kingma and Jimmy Ba , title =

Reference 83

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Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:05:46.045501Z digest=sha256:33f61c091f7390f54181d46756478dfa9ab81249717aa380650a63ee67aefe29

Observation 01166245-1965-43f6-9f76-6726337de619 · outbound

This paper cites Incorporating.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Incorporating

Reference 84

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source=arxiv_source observed=2026-08-06T21:05:46.047935Z digest=sha256:f8cb01f49ef489dca9a87cccb2bfaef20120eeea0454ec06b9b2ff1a82dcb3ee

Observation 7c5c1c11-65bc-4b8a-adc7-521f9c8c8cef · outbound

This paper cites Zeiler , title=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Zeiler , title=

Reference 85

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source=arxiv_source observed=2026-08-06T21:05:46.050368Z digest=sha256:56ef0427b81660fa838fd5d77d73986dbafefd0edb553f49ef0e091dd93631cd

Observation 563c6af3-713c-486d-96df-e4d886cffaff · outbound

This paper cites Journal of Machine Learning Research , year =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Journal of Machine Learning Research , year =

Reference 86

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source=arxiv_source observed=2026-08-06T21:05:46.052669Z digest=sha256:743c51251e77f83513ab374291867193cb7d84bbabbf7dfbaeb0b3ff0de82e57

Observation d0b6e99e-e1a4-4186-8bc3-283cb4983ddb · outbound

This paper cites Proceedings of the USSR Academy of Sciences , year=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Proceedings of the USSR Academy of Sciences , year=

Reference 87

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source=arxiv_source observed=2026-08-06T21:05:46.055088Z digest=sha256:5322f1a422242cc8c357dbf0fc1b8832b48498c49c19ce71cc7fac912e583d2f

Observation 800bd81c-f5d3-4628-bf4c-09e34a768288 · outbound

This paper cites SIAM/ASA J.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations SIAM/ASA J

Reference 88

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doi, observed 2026-08-06T21:05:46.452822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.057675Z digest=sha256:a3b157a0ac1801b5f3c6e246440ed790ea11c70bd76422956684243e3b72a0c8

Observation c748cfbb-63c8-4edb-80f8-efd619b156cf · outbound

This paper cites Muller and Philippe von Wurstemberger , title=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Muller and Philippe von Wurstemberger , title=

Reference 89

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source=arxiv_source observed=2026-08-06T21:05:46.060366Z digest=sha256:ac2724ad94eafabe161bcd6b45577b166f1be2940f3208dc7a885451b4d301b5

Observation 398ea0be-cd3f-4e77-ad7b-d9f61f127a72 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 90

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source=arxiv_source observed=2026-08-06T21:05:46.062751Z digest=sha256:75712d075f076dbbe8037da8b2bd4efe335c049a71839080c0b47850f05c6a85

Observation a56e1711-d39a-476f-9bb0-004303208d02 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 91

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Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:05:46.065197Z digest=sha256:61fd24c6b3c91a4430777e87b5e407190f1fdd7be1a83416a9857a1dbcfbd8ad

Observation 6d7c19a8-da87-46df-a3fb-08221a56e887 · outbound

This paper cites The analysis of linear partial differential operators.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations The analysis of linear partial differential operators

Reference 92

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Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:05:46.067718Z digest=sha256:5bca1b068018d7ca9cbaa8c7593e4c8f030a8b8836e8d1a11ae84b016d311ede

Observation 86ce3d9d-631f-45ae-846c-a538e978bf9f · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 93

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source=arxiv_source observed=2026-08-06T21:05:46.070084Z digest=sha256:0cf7c593e8bed2835f3c0978c93a3a51895143efee7ecaf13bd24d5c622b3d93

Observation e2a9b84d-e898-44e5-bced-ef3e07834e7d · outbound

This paper cites A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions

Reference 94

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local_arxiv, observed 2026-08-06T21:05:46.744214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.072617Z digest=sha256:e4418a777f749988d6bb01c339a756cc4fbb082991c68165d12f43ee81cb71bd

Observation 680be056-bcc0-42d3-b004-40129425f5e3 · outbound

This paper cites A mathematical model for automatic differentiation in machine learning , url =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations A mathematical model for automatic differentiation in machine learning , url =

Reference 95

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Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:05:46.075434Z digest=sha256:b6ab32f02dd86227499820a0a4043726b7dbdebc4e46d36d29245115bd88eabd

Observation f35830b2-dd04-4713-9d95-945a6d9c9552 · outbound

This paper cites On Correctness of Automatic Differentiation for Non-Differentiable Functions , url =.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations On Correctness of Automatic Differentiation for Non-Differentiable Functions , url =

Reference 96

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source=arxiv_source observed=2026-08-06T21:05:46.078144Z digest=sha256:1a9df07f51e880036bdf3aaa7895cdb054f1b3f1ba4565b88ff751a66423e293

Observation 596f7fcb-c1d5-4a32-a976-7d55a5353cbb · outbound

This paper cites NeurIPS , year=.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations NeurIPS , year=

Reference 97

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source=arxiv_source observed=2026-08-06T21:05:46.080521Z digest=sha256:1bfe8ae9ec3ed6075eb4b658467e65c834c170c8f87f31422073c3833b4df618

Observation 65aa3f06-98ac-4417-a44f-6099037da30d · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 98

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Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T21:05:46.083006Z digest=sha256:7bd73562afc959fdeabf30636cdabfc0ee24e31652fdd6e31945f00df3c34390

Observation da180ae2-960a-447c-81dd-5d7fbdc7145e · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 99

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no resolver link, observed 2026-08-06T21:05:46.085503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T21:05:46.085503Z digest=sha256:6285788b9d3261db0a1da070ba1229d00c5d750c55e242d5c4497956216f47b1

Observation 7b525e43-a7ed-479b-bffd-cab009ca7f66 · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 100

Resolution
verified exact
doi, observed 2026-08-06T21:05:46.443906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.088014Z digest=sha256:bcfd0afaaf361bb211c5e4d6c13293b4d8f7651fb83a727d31be5186c1a998f5

Observation 35cabb40-1329-4f68-9982-ce269dd0d7cc · outbound

This paper cites an unresolved cited work.

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations Unresolved cited work

Reference 101

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source=arxiv_source observed=2026-08-06T21:05:46.090449Z digest=sha256:bb6a6d67b1cd03d3c67856d861672abd6fc60cf03577432440817db03d3d590c

Pith citing papers

No inbound Pith citation observations are available.