Paper Citation Record · LEDGER

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

As of 7 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 14 inbound Pith citation observations for arXiv:2509.02981.

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

pith.paper-citation-record.v1
2509.02981 v2

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

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measured 51 of 51 standing notices

One-hop event checks from named stored sources.

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measured 14 of 14 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T22:20:05.658343Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T23:47:28.482161Z

Reference resolution

37 of 37 outbound references displayed

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External citation measurements

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Outbound references

Observation 55228883-d60d-4b28-99af-e41cc39ba88f · outbound

This paper cites an unresolved cited work.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 1

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Observation 932413bd-43a6-4c71-a84e-1d5998d8bea8 · outbound

This paper cites Arjevani, Y.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Arjevani, Y

Reference 2

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Observation 3d4cd85a-8500-4f38-b0b2-98ab8d173e44 · outbound

This paper cites Bernstein.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Bernstein

Reference 3

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Observation 98caf305-b7df-43f8-8a63-f5e5000050ed · outbound

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

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Old Optimizer, New Norm: An Anthology

Reference 4

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 5

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Observation 9cf5a8a6-542c-4a04-9a2d-32b45a59117d · outbound

This paper cites Carmon, J.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Carmon, J

Reference 6

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 7

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This paper cites Cutkosky and H.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Cutkosky and H

Reference 8

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Observation 7f41d6dc-93ed-43c9-b1b3-f139ef5955cc · outbound

This paper cites A Simple Convergence Proof of Adam and Adagrad.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates A Simple Convergence Proof of Adam and Adagrad

Reference 9

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Duchi, E

Reference 10

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 11

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 12

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Observation ae365134-7745-4d1d-b093-bd5228c2ee4b · outbound

This paper cites Gupta, T.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Gupta, T

Reference 13

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

Reference 14

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Observation 6b42fc69-1414-4047-8ba9-73c6273a0f74 · outbound

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Jordan, Y

Reference 15

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This paper cites Jordan, Y.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Jordan, Y

Reference 16

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Observation 47772327-da82-4098-b2d0-99eb4f9539a0 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Adam: A Method for Stochastic Optimization

Reference 17

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Observation 9dc0d79f-39bd-4637-bbcc-d4781fe1d75c · outbound

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

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 18

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Observation 2a56226a-725f-4d22-b5f4-0a573f71370d · outbound

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

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 19

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

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This paper cites A Note on the Convergence of Muon.

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

Reference 21

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Li and F

Reference 22

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Muon is Scalable for LLM Training

Reference 23

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Normalized Gradients for All

Reference 25

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Observation 2c29e27d-20b5-49b8-8018-aa827ec51cea · outbound

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

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Training Deep Learning Models with Norm-Constrained LMOs

Reference 26

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Convergence Bound and Critical Batch Size of Muon Optimizer

Reference 27

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Practical Efficiency of Muon for Pretraining

Reference 28

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates On the Convergence Analysis of Muon

Reference 29

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Less Regret via Online Conditioning

Reference 31

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates SOAP: Improving and Stabilizing Shampoo using Adam

Reference 32

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Unresolved cited work

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Structured Preconditioners in Adaptive Optimization: A Unified Analysis

Reference 35

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor

Reference 36

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This paper cites On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization

Reference 37

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Pith citing papers

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 62

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Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization cites this paper.

Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 56

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 45

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

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 169

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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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 173

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

Convergence of Spectral Descent for Non-smooth Optimization AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 28

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Observation d82ffd97-af17-4e69-94f2-0dc282420f62 · inbound

Stochastic convergence of parallel asynchronous adaptive first-order methods cites this paper.

Stochastic convergence of parallel asynchronous adaptive first-order methods AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 54

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Observation dab43c79-82ed-4ba4-9a22-fe0bde0473ab · 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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

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Observation 48e55a4b-3dbd-4517-b1b2-e9c40e0f19ea · 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 AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 195

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Observation 8f607fc3-1577-41df-8aeb-72df68af1289 · inbound

OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers cites this paper.

OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 133

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

Muse: Representation Geometry of Muon Beyond Normalized Momentum AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Reference 44

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