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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 7 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 2026-08-07T06:34:17.273281+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
  • metadata mismatch7

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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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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

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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 , journal=

Reference 14

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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 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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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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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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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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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

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 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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source=arxiv_source observed=2026-08-06T21:05:45.952121Z digest=sha256:5818b09a016015813c2f104d5033d256aa9540e95d5bc740e24fa81767cd72ce

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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source=arxiv_source observed=2026-08-06T21:05:45.954944Z digest=sha256:6bd57b95410e3d4a223b0250d55001ca3b2d0b8d31408c81721d5041a0782882

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=sha256:03560f6ae9e2cbc73f1de6a31ea7428f61ced5f73db80b6a0665c69cd35894be

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=sha256:5c713b62f4e635cdfbc48fd923f7cfcc00303123b1c4f9b987b1c0bb437cc27d

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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source=arxiv_source observed=2026-08-06T21:05:45.963044Z digest=sha256:d66cdc6756933506a0c30b8d696e9c65208a1de76d5c30da0692abe835d9cb91

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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source=arxiv_source observed=2026-08-06T21:05:45.966006Z digest=sha256:6af12ae8a8d330ccf61ae078b14f261b9994ca77477ff4b95e188d6e3fdbe32c

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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source=arxiv_source observed=2026-08-06T21:05:45.968834Z digest=sha256:db2553c0701b1afbbab7100d99817450de7be8bebf425ca0e3a0eeaaa128381f

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

This paper cites (2021), xii+946 , PAGES =.

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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source=arxiv_source observed=2026-08-06T21:05:45.977230Z digest=sha256:266ff91780442dbec61acde4c4fdbc0af1aa51a09456eef237cc51f8f2f87fcd

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:a0132d45e3a4f3f7c764a6d062f7b18b4e1eb20fb291419502dab7ba927caa91

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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source=arxiv_source observed=2026-08-06T21:05:45.982716Z digest=sha256:d412200da2c06bb905eb64e576ae2bead3263eee18ea211f1ec6a9da6748f3a5

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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source=arxiv_source observed=2026-08-06T21:05:45.986570Z digest=sha256:a132726f6aa640c58648fa6db42e5cd7d7f6fc8aabed328edd39d5cb31b3a9e5

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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source=arxiv_source observed=2026-08-06T21:05:45.994848Z digest=sha256:d11412f0cfcd45445bfda34c3dd343b7fd758d4e0f6e573898ccb4f91f5d85f5

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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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:c8b22664d5973d85ab03df5b82628b9bea42b9b16eb515177d5dc46eedfb3cc2

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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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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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source=arxiv_source observed=2026-08-06T21:05:46.013974Z digest=sha256:920f2f0ba0473f76e699ff20e8a8002cdef07b22b6846278cebdd4190ffc2cb0

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.017023Z digest=sha256:ba83336f24c69a4f0ce2785e11c1fd884629c9d6421226c13d91e917f30502d3

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=sha256:6603d1d8cb75ea06bb32406eba010ee85f9442b1ef121554424d65ebf12ac3c5

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.024462Z digest=sha256:ceb4e9355f116d76a43185405d7ffef0bfab6e9b7bc8b1dedd7891780c6cd4fb

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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source=arxiv_source observed=2026-08-06T21:05:46.026932Z digest=sha256:6442c00d6e828e855deb4b2a7087911e4814cc4e022b15b40abc42e7c229d00f

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-reported events for the cited work

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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=sha256:56cd5f9f83f90af2a022b104f391ddbfbca62bb5bba3e963718b452f32cb394c

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=sha256:8a04a6961850583adfa8c32af36293b2d12d582431c614a39377360eff49c5aa

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=sha256:2f850c85b40691f9564c9f3f37caaca38f30e977c879d58e0fe8db7068796a81

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=sha256:924126601e97a4dde140a810f6fff1b582aa4afe650cd9b65bde348232ffbfd5

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=sha256:67bac6ff06f010aaca08696792a535408f4204c492f63796a094d39a20f392e3

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=arxiv_source observed=2026-08-06T21:05:46.045501Z digest=sha256:01a5d0e328fef046c46aa02025adc8bae22e2151684e2151550bbe046861e27a

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:f29422acaa7e988b3919d4b01f52699046d3e6dc70e5db04ba5ed331a80d1d7a

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:ac41a91149e857a7f73861faef29dbc746d026c795d0fee68a0795774db81324

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=sha256:70deed8827c56e46960fdf4eceefbf67c8d795da187c27681a48e44b72a6ab8d

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=sha256:350f08093a271b641bd3edea6eaf2347496b58cc0a0c6a21cf7508e445a680cd

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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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.057675Z digest=sha256:e59dfff1d4e7debeb4e505489e70c1a33866709b5726a56aa0c9ed6674cdaaa1

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:bf66faadde84f3edc2a8c1195ed83438d82d7c235c3db6e85e664f20939dde9e

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=sha256:40aab7a672b6bfbe095938146b73f042ed62af7b15100768823e45b13d0899dc

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=arxiv_source observed=2026-08-06T21:05:46.065197Z digest=sha256:d49f4306fba9e4225a12cb02bc6ea80a030a8d999398c888d5e3d964c6d6fc79

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=arxiv_source observed=2026-08-06T21:05:46.067718Z digest=sha256:7304c3e028f5f9cbbb03a56f7d0a9fe5da8b938f40583ed29b7a1eb728f54100

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:bd691fdc0b6bb38af220c9c02b29150c3049482761ab743f62ab8271d2d48b9b

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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.072617Z digest=sha256:3a538c66cd50f564c903f4e98209e3cb95bd59de93a9d835dee75ede8aad2575

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=sha256:12f985a84e1e479d8b192de201dfec3085970c68893ef0b708ac0a27c46a2765

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:b50406f6a37505401910547e52267163e3241b261b41ea18f469a40e362eb040

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=sha256:8364b0b23b6565bbcbedab18d2ba072888d37829bf582f47437b2b68e265a14b

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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Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:05:46.083006Z digest=sha256:4e67abd3d151ae33e8843bf2f4e6f9feb2b64cc7954f16b8c39114e64a8a7c4e

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=sha256:9451989204203a3377ded375b42f562c7483998988ca2312429210375e330433

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

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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 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-06T21:05:46.088014Z digest=sha256:cf08de205d4b2e213d28996bfd22115a6ec2a0890bf02e56569d097c180eb26a

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:e896fe7dc2c90784c9d3af1a4ddc1bd24dec0be310a0d4f0d63d33f4f5af2d66

Pith citing papers

No inbound Pith citation observations are available.