Paper Citation Record · LEDGER

A Note on the Convergence of Muon

As of 19 August 2026, this Paper Citation Record lists 4 of 4 outbound references and 29 inbound Pith citation observations for arXiv:2502.02900.

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

pith.paper-citation-record.v1
2502.02900 v2

Coverage vector

measured 4 of 4 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T10:49:58.963670Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 29 of 29 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T01:10:04.433781Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T14:55:48.649763Z

Reference resolution

4 of 4 outbound references displayed

verified exact0
verified fuzzy2
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 873af3f9-a1d5-4534-8055-085e58a1c027 · outbound

This paper cites an unresolved cited work.

A Note on the Convergence of Muon Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-09T10:49:58.950140Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e572abb3-67b1-467e-8c09-0ef5aae50b34 · outbound

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

A Note on the Convergence of Muon Old Optimizer, New Norm: An Anthology

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-09T10:49:58.955001Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f19883b-6aeb-4b95-99f6-4f538c24bb2f · outbound

This paper cites Cutkosky and H.

A Note on the Convergence of Muon Cutkosky and H

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T10:49:59.018936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2e27914a-2be0-4c20-9965-d176b722c811 · outbound

This paper cites Ghadimi, A.

A Note on the Convergence of Muon Ghadimi, A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T10:49:59.007143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 0194fa99-d066-4862-a18e-6e15e2fe9e8e · inbound

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

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) A Note on the Convergence of Muon

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.836458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33bbe1c8-04a9-4328-8ea1-88e158adae71 · inbound

On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon A Note on the Convergence of Muon

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T13:22:19.185771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ebda5b0f-822d-4c67-af3e-5fa5071ecb7c · inbound

On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon A Note on the Convergence of Muon

Reference 1998

Resolution: unresolved; no resolver link, observed 2026-08-07T12:45:19.270341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a72966a7-c59d-43e6-b22c-a7c09a28aea5 · inbound

Convergence Bound and Critical Batch Size of Muon Optimizer cites this paper.

Convergence Bound and Critical Batch Size of Muon Optimizer A Note on the Convergence of Muon

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T20:57:10.267712Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99f74c96-b6a2-4132-a03b-32b9a53398a6 · inbound

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates cites this paper.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates A Note on the Convergence of Muon

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T11:25:45.022770Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1617535-e581-4a84-ae70-d4e53864db90 · inbound

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

LiMuon: Light and Fast Muon Optimizer for Large Models A Note on the Convergence of Muon

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-15T15:57:38.252688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3207c4b9-d644-46cd-a8b9-1a6dc8dbc78e · inbound

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs cites this paper.

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs A Note on the Convergence of Muon

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T13:25:32.755528Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92c17085-248e-4243-921c-d9fabb3413b9 · inbound

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws cites this paper.

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws A Note on the Convergence of Muon

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-03T04:14:15.720274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd023f38-35e7-4309-8c3c-f2b687a5e8c8 · inbound

A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models cites this paper.

A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models A Note on the Convergence of Muon

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:15:48.160424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cc34f344-88f4-4bcb-a6ac-cdffea249e48 · inbound

A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo cites this paper.

A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo A Note on the Convergence of Muon

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-10T07:26:59.877633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d2343cb-20b8-4f9e-a668-78220d49b858 · inbound

Convergence Rate Analysis of SOAP with Arbitrary Orthogonal Projection Matrices cites this paper.

Convergence Rate Analysis of SOAP with Arbitrary Orthogonal Projection Matrices A Note on the Convergence of Muon

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T14:36:08.945038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 454d282c-57e9-4686-8284-dffc1d783698 · inbound

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds cites this paper.

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds A Note on the Convergence of Muon

Reference 19

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T19:21:07.748441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 18656574-09d5-4b8f-a887-377f86d938fa · inbound

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

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition A Note on the Convergence of Muon

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:00:56.697202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 28ec8b40-b32e-4f94-9c58-bb8194f4d64e · inbound

Muon Does Not Converge on Convex Lipschitz Functions cites this paper.

Muon Does Not Converge on Convex Lipschitz Functions A Note on the Convergence of Muon

Reference 83

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T07:41:40.749834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 89bd6027-65b1-4b51-86df-7a1d870498e3 · inbound

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds cites this paper.

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds A Note on the Convergence of Muon

Reference 36

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T05:36:26.319762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0fa260f9-c874-49a9-bb56-d8f5a59e3f11 · inbound

Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence cites this paper.

Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence A Note on the Convergence of Muon

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:53.090623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7b688b05-a3b4-4b14-8d48-b72ed4d42696 · inbound

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers cites this paper.

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers A Note on the Convergence of Muon

Reference 97

Resolution: verified exact; arxiv_id, observed 2026-05-20T09:38:11.064233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6a8e3728-f8ce-4797-b864-25239fdbbf05 · inbound

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers cites this paper.

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers A Note on the Convergence of Muon

Reference 99

Resolution: verified exact; arxiv_id, observed 2026-06-30T18:45:00.430700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 61eacf10-5fab-4f83-8737-4d8d37798a98 · inbound

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise cites this paper.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise A Note on the Convergence of Muon

Reference 76

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.651364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c707ac7f-1707-4829-b40b-80accbec84ce · inbound

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models cites this paper.

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models A Note on the Convergence of Muon

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T08:13:08.311412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 92067062-0c16-4ea9-9e26-074f8ea8f6ec · inbound

LionMuon: Alternating Spectral and Sign Descent for Efficient Training cites this paper.

LionMuon: Alternating Spectral and Sign Descent for Efficient Training A Note on the Convergence of Muon

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T07:28:06.795219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2086ae6f-f4aa-4372-a7af-db28820b9abc · inbound

LionMuon: Alternating Spectral and Sign Descent for Efficient Training cites this paper.

LionMuon: Alternating Spectral and Sign Descent for Efficient Training A Note on the Convergence of Muon

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T18:35:00.399798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation de0e3aa4-45dc-4d3e-8fa1-4584cce08d28 · inbound

Anytime Training with Schedule-Free Spectral Optimization cites this paper.

Anytime Training with Schedule-Free Spectral Optimization A Note on the Convergence of Muon

Reference 63

Resolution: verified exact; arxiv_id, observed 2026-05-25T05:40:24.354022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e79bc207-c617-4d5a-aba3-851def6c81c7 · inbound

Convergence of Spectral Descent for Non-smooth Optimization cites this paper.

Convergence of Spectral Descent for Non-smooth Optimization A Note on the Convergence of Muon

Reference 15

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T19:33:54.007090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 55deafad-0763-46fd-a87f-b86a8d9af8a7 · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization A Note on the Convergence of Muon

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T05:49:18.273502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f15dc13a-07e9-4edb-ba90-ff5c91a74823 · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization A Note on the Convergence of Muon

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T04:22:55.629450Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3adbebd-adde-4e3d-aeb9-4b56aa6c498c · inbound

Muse: Representation Geometry of Muon Beyond Normalized Momentum cites this paper.

Muse: Representation Geometry of Muon Beyond Normalized Momentum A Note on the Convergence of Muon

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T01:58:56.521365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1d3c900-c92c-43cc-bc91-b7dfc30743e0 · inbound

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization cites this paper.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A Note on the Convergence of Muon

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.624471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd031040-54ac-49a9-8e46-9273ffc48d28 · inbound

Federated Compositional Muon Optimizer for Matrix-Wise Models cites this paper.

Federated Compositional Muon Optimizer for Matrix-Wise Models A Note on the Convergence of Muon

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-16T01:10:04.433781Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.