Paper Citation Record · LEDGER

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

As of 16 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 35 inbound Pith citation observations for arXiv:2505.13416.

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

pith.paper-citation-record.v1
2505.13416 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:20:54.014925Z

measured 81 of 81 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 35 of 35 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T01:10:04.453731Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

46 of 46 outbound references displayed

verified exact2
verified fuzzy14
unresolved29
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 4707b3f0-32f8-4aed-897b-ae4aad481f83 · outbound

This paper cites The geometry of Sign Gradient Descent,.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The geometry of Sign Gradient Descent,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:55.127804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5a4bcb9c-345c-4bb6-9d4e-f3ba9451baab · outbound

This paper cites Modular Duality in Deep Learning.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Modular Duality in Deep Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.725031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bee42f3-5f2c-42be-8ceb-bfbc8aa8ba01 · outbound

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

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Old Optimizer, New Norm: An Anthology

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.732468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14743439-632c-4e22-a7ed-6f21242cde90 · outbound

This paper cites On biased compression for distributed learning.Journal of Machine Learning Research, 24(276):1–50, 2023.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) On biased compression for distributed learning.Journal of Machine Learning Research, 24(276):1–50, 2023

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:55.100039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6d3ef052-5b6a-48fa-9530-6fd34870c313 · outbound

This paper cites Robustness to Unbounded Smoothness of Generalized SignSGD.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Robustness to Unbounded Smoothness of Generalized SignSGD

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:20:54.451854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9665c334-6091-4e73-a0b3-ac3964307b14 · outbound

This paper cites A guide through the zoo of biased sgd.Advances in Neural Information Processing Systems, 36:23158–23171, 2023.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) A guide through the zoo of biased sgd.Advances in Neural Information Processing Systems, 36:23158–23171, 2023

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:55.074073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation edfac4c6-5781-45f8-9167-e1917eca5106 · outbound

This paper cites An algorithm for quadratic programming.Naval Research Logistics Quarterly, 3(1-2):95–110, 1956.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) An algorithm for quadratic programming.Naval Research Logistics Quarterly, 3(1-2):95–110, 1956

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.760393Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 476b967b-6f54-47eb-8660-40dbec168ee3 · outbound

This paper cites The Ball-Proximal (="Broximal") Point Method: a New Algorithm, Convergence Theory, and Applications.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The Ball-Proximal (="Broximal") Point Method: a New Algorithm, Convergence Theory, and Applications

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.768260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a04c43da-4036-4b89-9930-a617cc82c332 · outbound

This paper cites Parameter-Agnostic Optimization under Relaxed Smoothness.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Parameter-Agnostic Optimization under Relaxed Smoothness

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:20:54.380657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e611ea2f-29fe-47ad-b9d0-adefc193e91b · outbound

This paper cites Cifar-10 airbench.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Cifar-10 airbench

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:55.054230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4f7b456e-c47b-4545-ae66-960b44e28a40 · outbound

This paper cites Vlado, Y.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Vlado, Y

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.996572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d2f46db5-b347-477f-9ed4-5ec23ae23b1a · outbound

This paper cites Muon: An optimizer for hidden layers in neural networks, 2024.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Muon: An optimizer for hidden layers in neural networks, 2024

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.972770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0de49b35-0e29-4558-8ca8-5eb9baf3a853 · outbound

This paper cites Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-\L{}ojasiewicz Condition.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-\L{}ojasiewicz Condition

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.802967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60295b72-ddc6-442c-aca9-7dd91f6d4516 · outbound

This paper cites Better Theory for SGD in the Nonconvex World.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Better Theory for SGD in the Nonconvex World

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.808304Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7271be97-0fd7-4add-a491-8bd6076e367c · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Adam: A Method for Stochastic Optimization

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.816064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71fcfa0c-e72a-4410-af0d-4f238ce0ef33 · outbound

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

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.821206Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a4aaccc-5807-4c80-94f3-49dd9d9bb290 · outbound

This paper cites Scalable Optimization in the Modular Norm.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Scalable Optimization in the Modular Norm

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.828201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

This paper cites A Note on the Convergence of Muon.

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 417ac115-75f1-449b-a8bc-a512b427781e · outbound

This paper cites Loss landscapes and optimization in over- parameterized non-linear systems and neural networks.Applied and Computational Harmonic Analysis, 59, 01 2022.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Loss landscapes and optimization in over- parameterized non-linear systems and neural networks.Applied and Computational Harmonic Analysis, 59, 01 2022

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.844542Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 028cb0e8-4c3a-454e-949c-4db792c06f44 · outbound

This paper cites Muon is Scalable for LLM Training.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Muon is Scalable for LLM Training

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.850011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a704b8d-4120-4225-b90e-d4ab74f0ce2c · outbound

This paper cites AdaGrad under Anisotropic Smoothness.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) AdaGrad under Anisotropic Smoothness

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.857065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1986e2e7-1855-4a1e-a9ac-933fd39e6b6e · outbound

This paper cites Decoupled Weight Decay Regularization.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Decoupled Weight Decay Regularization

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.864042Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79e580b7-1342-4ea4-88ae-b72c088cc8ba · outbound

This paper cites Scion.https://github.com/LIONS-EPFL/scion.git, 2025.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Scion.https://github.com/LIONS-EPFL/scion.git, 2025

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.944929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8eaa1c86-4cd9-4684-a2c5-8570efffc9d5 · outbound

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

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Training Deep Learning Models with Norm-Constrained LMOs

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.875073Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b1c9f91-c0db-4666-a422-a460af5537f0 · outbound

This paper cites The Frank-Wolfe algorithm: a short introduction.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The Frank-Wolfe algorithm: a short introduction

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.925048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f4e03318-57b4-4045-8c1d-13f916774b47 · outbound

This paper cites Practical Efficiency of Muon for Pretraining.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Practical Efficiency of Muon for Pretraining

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.886920Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eadd520a-8796-426f-a0f6-4d72d9e82931 · outbound

This paper cites Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.893055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 462ef365-e9fa-4221-b5f4-b897387eb338 · outbound

This paper cites The Marginal Value of Adaptive Gradient Methods in Machine Learning.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The Marginal Value of Adaptive Gradient Methods in Machine Learning

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.899388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1aca7122-1d31-47d5-a1bb-5ed1595389c6 · outbound

This paper cites Block- normalized gradient method: An empirical study for training deep neural network, 2018.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Block- normalized gradient method: An empirical study for training deep neural network, 2018

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.895603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d04c7c55-161c-4324-baa4-ebbc8a39c3a6 · outbound

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

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Why gradient clipping accelerates training: A theoretical justification for adaptivity

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.916516Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9aaed78a-351b-4854-820b-9f53c70b7b0f · outbound

This paper cites • Training CNNs.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) • Training CNNs

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.869285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c1198eb7-63c9-494b-be68-979e8e6de5f3 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.832681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a686cd0a-8a4e-40e1-882e-63a292fc7913 · outbound

This paper cites Remark 4.Let us compare bounds(17) and (19).

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Remark 4.Let us compare bounds(17) and (19)

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.811954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1198f803-0260-4ae9-abf8-a6715695df40 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.790968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ce2fc8f7-30e2-4818-b02b-4f4432400c93 · outbound

This paper cites Since the functionψ is increasing fort >0, ψ−1 exists.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Since the functionψ is increasing fort >0, ψ−1 exists

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.758175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1b4454d1-f607-4091-93a8-bebc22ddf7d1 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.735709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bc1f7b65-7bd9-46c5-a1a0-f44db7164ead · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.696272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 345fac87-003c-40b3-bd05-b02819d64dad · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.663731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8380974b-77be-4f06-8f6c-09e5e3046eaf · outbound

This paper cites −tk i∥∇ifξk(Xk)∥(i)⋆ +tk i∥∇if(Xk)−∇ifξk(Xk)∥(i)⋆ + L0 i +L1 i∥∇if(Xk)∥(i)⋆ 2 tk i 2 # ≤f(Xk) + pX i=1.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) −tk i∥∇ifξk(Xk)∥(i)⋆ +tk i∥∇if(Xk)−∇ifξk(Xk)∥(i)⋆ + L0 i +L1 i∥∇if(Xk)∥(i)⋆ 2 tk i 2 # ≤f(Xk) + pX i=1

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.636074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 97771d4e-ccc5-4b4c-8d60-7a72d79da163 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.609922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation df135228-fbe3-4f5f-9915-0c9fc5254255 · outbound

This paper cites Since the functionψ is increasing fort> 0, ψ−1 exists.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Since the functionψ is increasing fort> 0, ψ−1 exists

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:20:54.583048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f91c723c-5858-413e-890c-8e7067bbda78 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:54.563061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0229bb54-78c7-4804-93f3-90fcfbae1fbd · outbound

This paper cites D ∇if(Xk),Xk+1 i −Xk i E (i) + L0 i +L1 i∥∇if(Xk)∥(i)⋆ 2 ∥Xk i −Xk+1 i ∥2 (i) # = f(Xk) + pX i=1.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) D ∇if(Xk),Xk+1 i −Xk i E (i) + L0 i +L1 i∥∇if(Xk)∥(i)⋆ 2 ∥Xk i −Xk+1 i ∥2 (i) # = f(Xk) + pX i=1

Reference 47

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:20:54.542313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 707beac3-ca49-4756-8f35-369b2ef9cdaa · outbound

This paper cites The Geometry of Sign Gradient Descent.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The Geometry of Sign Gradient Descent

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.717677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80a48df0-9afb-422b-ab48-2fdbb8d4e114 · outbound

This paper cites Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.929552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e0cce71-b68c-47fb-a477-2d0f91fb8b07 · outbound

This paper cites an unresolved cited work.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Unresolved cited work

Reference 2024

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:20:55.022259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation a44a1b75-d60b-4fa6-ac84-2ea22d3d0d44 · inbound

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration cites this paper.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:10.527295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 343e4d9b-96f6-47c0-919a-4ff4d0c073e2 · inbound

Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees cites this paper.

Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 1697

Resolution: unresolved; no resolver link, observed 2026-08-05T15:43:57.042277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e56f3e9c-f65b-43f4-ba78-0851382efaac · inbound

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

Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-18T15:51:34.049441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 89b0056e-4ca2-4751-b148-1cc2c7646d97 · inbound

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

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T13:25:32.825270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95a62f5f-478d-46fb-89b6-07d1f2248832 · inbound

Why Do We Need Warm-up? A Theoretical Perspective cites this paper.

Why Do We Need Warm-up? A Theoretical Perspective Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-04T12:38:59.776219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 627a7a76-0783-4fda-b7b0-e2a4541b683d · inbound

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods cites this paper.

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:10:38.760232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 38357879-9624-470a-8f55-eb555ee657e4 · inbound

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

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T22:20:05.602621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 107d7054-db86-4268-8265-90a09bc9ff55 · inbound

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates cites this paper.

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T18:37:49.615408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01af50d3-6af2-442a-80c6-d57f0bc2f4ea · inbound

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning cites this paper.

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-13T10:41:51.251736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29bae2f1-1cda-4efd-be6c-701af07ac116 · inbound

Communication-Efficient Gluon in Federated Learning cites this paper.

Communication-Efficient Gluon in Federated Learning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-11T10:56:03.206285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a8ef95f0-3b7c-4691-a2e9-3fc79a68d2ba · inbound

SUDA-Muon: Structural Design Principles and Boundaries for Fully Decentralized Muon cites this paper.

SUDA-Muon: Structural Design Principles and Boundaries for Fully Decentralized Muon Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-11T22:26:13.675800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 09849b3b-a548-40b8-964d-9c064b044a18 · 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 Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:00:56.688807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7de08db2-5eec-4436-906c-583c332fcba2 · inbound

Local LMO: Constrained Gradient Optimization via a Local Linear Minimization Oracle cites this paper.

Local LMO: Constrained Gradient Optimization via a Local Linear Minimization Oracle Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-12T08:06:29.281354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 735db6c0-d70e-4e20-84e1-27ad06c33f70 · inbound

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

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:36:26.141427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 31fe0f84-231d-4823-bbf3-461b53326504 · inbound

Phases of Muon: When Muon Eclipses SignSGD cites this paper.

Phases of Muon: When Muon Eclipses SignSGD Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 63

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:41:28.870190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a2a3fb1b-d128-45ec-9d7d-2ece8cb301c5 · inbound

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives cites this paper.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-05-13T05:37:19.241420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f9874835-7e65-4b90-ad62-dd2862a588f9 · inbound

Rescaled Asynchronous SGD: Optimal Distributed Optimization under Data and System Heterogeneity cites this paper.

Rescaled Asynchronous SGD: Optimal Distributed Optimization under Data and System Heterogeneity Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:32:50.953656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation dc100e25-4d67-42e6-a078-35ace105e5ae · 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 Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 132

Resolution: verified exact; arxiv_id, observed 2026-05-20T09:38:11.220931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation efbc976d-7e8e-47e0-b8e1-62996c62c824 · inbound

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

Reference 134

Resolution: verified exact; arxiv_id, observed 2026-06-30T18:45:00.306143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4de886da-5418-4f81-b0af-1259e899adb4 · inbound

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method cites this paper.

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 299

Resolution: verified exact; arxiv_id, observed 2026-05-20T13:13:18.456147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 66c05d6b-7ffb-47a8-9121-8ac607731255 · inbound

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

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-20T08:13:08.300435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8bbd071c-aec9-48dc-b830-ca6fbd5bd813 · inbound

LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging cites this paper.

LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 300

Resolution: verified exact; arxiv_id, observed 2026-05-21T05:49:40.580934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 193a8c53-2099-4705-85ea-e67c2468cd29 · inbound

Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra cites this paper.

Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-06-30T13:54:43.950467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4cc498d6-8686-4782-bce3-6e003d64a20c · inbound

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling cites this paper.

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-06-28T22:52:44.824841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 65da08d7-24ba-41a4-9e99-d29d78f95584 · inbound

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality cites this paper.

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-07-02T23:47:28.520199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b7f867de-3da4-4d2a-9862-098defe77260 · inbound

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality cites this paper.

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-06-29T05:43:08.823150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 340cbad2-4ed3-42cf-bb9e-75342b618a0c · inbound

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning cites this paper.

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-03T17:08:43.708424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a709a072-8953-4030-8981-52c91daf5d42 · inbound

Restart and Adaptive Acceleration in Stochastic Gradient Methods cites this paper.

Restart and Adaptive Acceleration in Stochastic Gradient Methods Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-07-04T06:59:37.619277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case cites this paper.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4327bb8e-b43a-430d-ae29-0adfc816039a · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T05:49:18.355300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2942369d-0b12-4d62-b9fb-938b1af576fd · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T04:22:55.756619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfeb62f0-1d00-4501-bfbd-f5e4fcbd400b · inbound

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback cites this paper.

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T02:09:02.175951Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05988b0b-7922-4fda-9be0-d7af88850989 · inbound

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization cites this paper.

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T06:04:04.278683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83ca53af-758f-44ee-92e4-c7ce32a792e1 · inbound

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature cites this paper.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.719180Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 566bf412-d620-4961-9df4-47fd531ec102 · inbound

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

Federated Compositional Muon Optimizer for Matrix-Wise Models Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-16T01:10:04.453731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.