Paper Citation Record · LEDGER

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case

As of 5 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2606.21581.

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pith.paper-citation-record.v1
2606.21581 v1

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Reference resolution

50 of 50 outbound references displayed

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Outbound references

Observation 50a51d4d-70d7-4e33-a971-d88e799733df · outbound

This paper cites International Conference on Artificial Intelligence and Statistics , pages=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case International Conference on Artificial Intelligence and Statistics , pages=

Reference 3

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This paper cites URL https://kellerjordan.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case URL https://kellerjordan

Reference 6

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This paper cites 2008 , publisher=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case 2008 , publisher=

Reference 7

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This paper cites SIAM Journal on Matrix Analysis and Applications , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case SIAM Journal on Matrix Analysis and Applications , volume=

Reference 8

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Observation f8ff43ac-d47b-46a2-b66e-a60f70e2e4ac · outbound

This paper cites International conference on learning representations (ICLR) , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case International conference on learning representations (ICLR) , volume=

Reference 10

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Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case International Conference on Learning Representations , year=

Reference 12

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Observation 82310e54-35e3-41e7-a037-c2e4448aa1a1 · outbound

This paper cites IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=

Reference 13

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Observation 5360bccb-1c3b-4591-a0d3-27d150ec82b6 · outbound

This paper cites Artificial intelligence and statistics , pages=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Artificial intelligence and statistics , pages=

Reference 15

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Observation 62fcf1f8-f4fa-45e1-9a91-08143fcf5667 · outbound

This paper cites IEEE Journal of Selected Topics in Signal Processing , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case IEEE Journal of Selected Topics in Signal Processing , volume=

Reference 16

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Observation 0282e79b-20af-4e33-b30d-d1ebd02500d9 · outbound

This paper cites Advances in neural information processing systems , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Advances in neural information processing systems , volume=

Reference 17

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Observation 8c62421f-fc35-4a1f-9ec4-26545d54b928 · outbound

This paper cites arXiv e-prints , pages=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case arXiv e-prints , pages=

Reference 18

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Observation 73eed7cb-f779-4b81-83b0-83536592cf19 · outbound

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Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case 2025 , eprint=

Reference 25

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Observation 3ed0412d-58ac-478d-a792-5bfba9975213 · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case SIAM Journal on Matrix Analysis and Applications , volume=

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation e3310697-99dd-4911-8382-59452fda4011 · outbound

This paper cites SIAM Journal on Scientific Computing , volume=.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case SIAM Journal on Scientific Computing , volume=

Reference 33

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Observation 1a7c7709-4057-4360-bec4-ee95194af63f · outbound

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Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case siam REVIEW , volume=

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 60315f6b-4ef8-4005-8a41-b848701a14d0 · outbound

This paper cites The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.597219Z

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Observation 46c2e7c7-13e1-49f0-aa3a-56c95a1db758 · outbound

This paper cites Old Optimizer, New Norm: An Anthology.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Old Optimizer, New Norm: An Anthology

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.584588Z

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Observation 670bc49a-0d92-421b-b321-428fef3a4a51 · outbound

This paper cites Small singular values can increase in lower precision.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Small singular values can increase in lower precision

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation c005eb2b-e8e5-4dcf-b46f-9921d708c7db · outbound

This paper cites Stochastic spectral descent for restricted boltzmann machines.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Stochastic spectral descent for restricted boltzmann machines

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 7478ea17-3a8e-405a-afad-b59b4081cf1a · outbound

This paper cites Stochastic spectral descent for discrete graphical models.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Stochastic spectral descent for discrete graphical models

Reference 41

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Observation 17e38e34-9f1c-4575-9f88-480e7c1a565a · outbound

This paper cites Preconditioned spectral descent for deep learning.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Preconditioned spectral descent for deep learning

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 7461f270-e413-4caf-8ff8-3e2bd807b29b · outbound

This paper cites On the Convergence of Muon and Beyond.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case On the Convergence of Muon and Beyond

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.597685Z

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Observation 0ea0ace3-4c7e-41c4-85fd-27fcf5581e8b · outbound

This paper cites Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.602384Z

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Observation 1be119c7-3543-4ffa-8544-c0aabf3a1e66 · outbound

This paper cites Error feedback for muon and friends.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Error feedback for muon and friends

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.595237Z

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Observation fad9742d-aa24-484e-8d5e-be62aa2fab66 · outbound

This paper cites Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training

Reference 46

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.559534Z

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Observation cbccdc8e-ef71-422d-a2cd-5d4f00515201 · outbound

This paper cites Functions of matrices: theory and computation.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Functions of matrices: theory and computation

Reference 47

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Observation b3e57af5-a812-4059-929f-c05c85774230 · outbound

This paper cites LiMuon: Light and Fast Muon Optimizer for Large Models.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case LiMuon: Light and Fast Muon Optimizer for Large Models

Reference 48

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Observation b8d6bb79-0608-4362-96f3-42321d39568a · outbound

This paper cites Muon: An optimizer for hidden layers in neural networks.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Muon: An optimizer for hidden layers in neural networks

Reference 49

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Observation 3b01870f-4bd0-433b-b896-bcde773c415d · outbound

This paper cites A Study of BFLOAT16 for Deep Learning Training.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case A Study of BFLOAT16 for Deep Learning Training

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.589486Z

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Observation ea72f1aa-2fdd-4bf1-9261-0441cbdc0bfd · outbound

This paper cites Adam: A method for stochastic optimization.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Adam: A method for stochastic optimization

Reference 51

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Observation 27877e57-6a11-4f20-8e68-4525bcd92350 · outbound

This paper cites Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 52

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Observation 8c274bd7-ed77-486b-9e25-740ef5211890 · outbound

This paper cites Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates

Reference 53

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Observation 34279f47-c4cd-4344-a8f4-05da9685dd05 · outbound

This paper cites A note on the convergence of muon and further.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case A note on the convergence of muon and further

Reference 54

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Observation cb2b21f7-e8a7-449c-992f-1c62820a0a62 · outbound

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Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Decoupled weight decay regularization

Reference 55

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Observation 2b941c19-323e-4902-a4a8-b5d0cf767b5a · outbound

This paper cites SignMuon: Communication-Efficient Distributed Muon Optimization.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case SignMuon: Communication-Efficient Distributed Muon Optimization

Reference 56

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.553803Z

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Observation 6ff3a804-d1c0-4ccf-b48e-02762dae078e · outbound

This paper cites Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: The power of zolotarev's functions.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: The power of zolotarev's functions

Reference 57

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 463bbc4f-1102-49dc-8b98-afa645c3be57 · outbound

This paper cites Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the svd.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the svd

Reference 58

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 8c74cb59-779a-419b-942f-b1ee2802a143 · outbound

This paper cites Optimizing halley's iteration for computing the matrix polar decomposition.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Optimizing halley's iteration for computing the matrix polar decomposition

Reference 59

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation cda32948-fa00-45b5-8978-c904a11298f1 · outbound

This paper cites Training Deep Learning Models with Norm-Constrained LMOs.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Training Deep Learning Models with Norm-Constrained LMOs

Reference 60

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.559259Z

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Observation 88699c99-b069-4ca7-9134-fc49e8e71103 · outbound

This paper cites Muon is provably faster with momentum variance reduction.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Muon is provably faster with momentum variance reduction

Reference 61

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.573699Z

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Observation 0508b09a-0a78-4aa0-8230-34ba39abcb6f · outbound

This paper cites Communication-Efficient Gluon in Federated Learning.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Communication-Efficient Gluon in Federated Learning

Reference 62

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.594783Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation ef38b3df-dd45-483c-9769-bc734d0e0403 · outbound

This paper cites On the Convergence of Adam and Beyond.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case On the Convergence of Adam and Beyond

Reference 63

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.584237Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5d1fd162-1d0c-46df-b5a3-1a348df4ddb9 · outbound

This paper cites Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs).

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.586902Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 6f8f85b7-2b46-4743-b02e-a7a9dda7dda4 · outbound

This paper cites Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise

Reference 65

Resolution: verified exact; arxiv_id, observed 2026-07-28T01:21:32.152085Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c0759b39-5621-48ed-aa1d-cd5aaf0f6f04 · outbound

This paper cites On the Convergence Analysis of Muon.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case On the Convergence Analysis of Muon

Reference 66

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.602692Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation ea43d056-d27d-427a-84cd-4e778208cc60 · outbound

This paper cites Beyond the ideal: Analyzing the inexact muon update.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Beyond the ideal: Analyzing the inexact muon update

Reference 67

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.589531Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1be18445-db9c-46d7-b888-64b0a5e84945 · outbound

This paper cites MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization

Reference 68

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.600242Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 30ee7390-dfed-4226-9316-ae1d3652e5a5 · outbound

This paper cites Adan: Adaptive nesterov momentum algorithm for faster optimizing deep models.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Adan: Adaptive nesterov momentum algorithm for faster optimizing deep models

Reference 69

Resolution: unresolved; no resolver link, observed 2026-06-26T13:28:36.618788Z

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Observation 73ab61f4-3356-4830-8d1d-e42820f50ce0 · outbound

This paper cites Why gradient clipping accelerates training: A theoretical justification for adaptivity.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Why gradient clipping accelerates training: A theoretical justification for adaptivity

Reference 70

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T07:29:38.574235Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 85b2d184-3f87-455b-bc28-8d499d0290cb · outbound

This paper cites On provable benefits of Muon in federated learning.arXiv preprint arXiv:2510.03866.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case On provable benefits of Muon in federated learning.arXiv preprint arXiv:2510.03866

Reference 71

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.565179Z

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