Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Practical Efficiency of Muon for Pretraining
As of 5 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 30 inbound Pith citation observations for arXiv:2505.02222.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T11:25:45.045809Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-09T17:36:25.409899Z
Reference resolution
0 of 0 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation 86af1c9f-556c-48ca-943c-896c458b9206 · inbound
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates cites this paper.
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Practical Efficiency of Muon for Pretraining
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T11:25:45.045809Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3ef161de-d686-4f44-acaf-fee6a21ce99a · 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 Practical Efficiency of Muon for Pretraining
Reference 3
- Resolution
- verified exact
- arxiv_id, observed 2026-05-18T15:51:34.006458Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation aafa7f7b-ac99-401a-bd7f-0abe23f8a46b · inbound
On the Convergence of Muon and Beyond cites this paper.
On the Convergence of Muon and Beyond Practical Efficiency of Muon for Pretraining
Reference 42
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-05-18T15:56:34.043222Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 55a7b33f-d76b-44ca-9ad5-5b8da9da975d · inbound
Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates cites this paper.
Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates Practical Efficiency of Muon for Pretraining
Reference 31
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6d9c33b0-99ee-4795-8c89-42204078306f · inbound
HTMuon: Improving Muon via Heavy-Tailed Spectral Correction cites this paper.
HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Practical Efficiency of Muon for Pretraining
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T06:55:26.326911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation cac04a5f-9adf-47aa-9d8b-26599e1f7b3e · inbound
MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration cites this paper.
MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration Practical Efficiency of Muon for Pretraining
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-05-14T21:12:58.520493Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b248fa8f-4d4a-41aa-a97f-0d83363b8073 · 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 Practical Efficiency of Muon for Pretraining
Reference 31
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T19:21:07.621850Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 48ed429a-230b-44cc-89b7-b686921bc1e4 · inbound
Phases of Muon: When Muon Eclipses SignSGD cites this paper.
Phases of Muon: When Muon Eclipses SignSGD Practical Efficiency of Muon for Pretraining
Reference 64
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T06:41:28.527213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation bd2fbc96-4e95-4d56-8ad2-9384536099b7 · inbound
Can Muon Fine-tune Adam-Pretrained Models? cites this paper.
Can Muon Fine-tune Adam-Pretrained Models? Practical Efficiency of Muon for Pretraining
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T06:51:28.805735Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 420bef66-0725-4256-8409-9f33221fc793 · inbound
Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters cites this paper.
Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters Practical Efficiency of Muon for Pretraining
Reference 55
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T07:02:27.357102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c018810f-77f1-493e-b2f7-79b864874de0 · inbound
When is Warmstarting Effective for Scaling Language Models? cites this paper.
When is Warmstarting Effective for Scaling Language Models? Practical Efficiency of Muon for Pretraining
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-05-14T20:02:53.040706Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 7247fd3d-6627-4a75-82b8-51ba5fc2a570 · inbound
Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered cites this paper.
Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered Practical Efficiency of Muon for Pretraining
Reference 28
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- verified exact
- arxiv_id, observed 2026-05-20T21:23:44.493653Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 9031b060-fdf4-48ba-8c8e-4971ac5fbb20 · 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 Practical Efficiency of Muon for Pretraining
Reference 47
- Resolution
- verified exact
- arxiv_id, observed 2026-05-20T09:38:10.928442Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 493da623-a6a5-4612-aa59-7e9f5008a1e2 · 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 Practical Efficiency of Muon for Pretraining
Reference 48
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:45:00.387167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1f15c100-c103-4bf7-9083-45f1c8292186 · inbound
Convergence of Spectral Descent for Non-smooth Optimization cites this paper.
Convergence of Spectral Descent for Non-smooth Optimization Practical Efficiency of Muon for Pretraining
Reference 21
- Resolution
- verified exact
- arxiv_id, observed 2026-06-29T19:33:53.990160Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 1ac60fa5-4485-416f-9551-ad5095cc62aa · inbound
Why Muon Outperforms Adam: A Curvature Perspective cites this paper.
Why Muon Outperforms Adam: A Curvature Perspective Practical Efficiency of Muon for Pretraining
Reference 182
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T07:16:44.450405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 9f62a87d-8f49-4b2f-a4b7-8f49c3f400fe · 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 Practical Efficiency of Muon for Pretraining
Reference 57
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T23:47:28.517476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 63d0d553-5048-43ec-ac3c-81872faf0db6 · 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 Practical Efficiency of Muon for Pretraining
Reference 63
- Resolution
- verified exact
- arxiv_id, observed 2026-06-29T05:43:08.844851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 077a3478-dcd3-437f-a958-bb5b14d30788 · inbound
Muon Learns More Robust and Transferable Features than Adam cites this paper.
Muon Learns More Robust and Transferable Features than Adam Practical Efficiency of Muon for Pretraining
Reference 132
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T00:27:30.130549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation f59b7dc6-7b80-43ff-8e49-ece95ba2844f · inbound
Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective cites this paper.
Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective Practical Efficiency of Muon for Pretraining
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T06:29:38.189992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation cd343fc2-81e3-4ddd-b42d-60e320a176f8 · inbound
Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? cites this paper.
Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? Practical Efficiency of Muon for Pretraining
Reference 8
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-07-04T10:09:44.613631Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 2954d78b-de09-40f5-a97c-39033652430e · inbound
How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size cites this paper.
How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size Practical Efficiency of Muon for Pretraining
Reference 30
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-07-03T21:08:57.605111Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 82943d8c-eea0-4b23-9d70-919c72525ebb · inbound
MatrixFSDP: communication-free matrix optimizers under ZeRO-3 parameter sharding cites this paper.
MatrixFSDP: communication-free matrix optimizers under ZeRO-3 parameter sharding Practical Efficiency of Muon for Pretraining
Reference 3
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-07-08T21:35:37.636034Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation e056ac96-d5d7-43fe-bb66-cb01ce86a97a · inbound
Optimization Geometrodynamics: Variational Reduction and Interaction Curvature cites this paper.
Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Practical Efficiency of Muon for Pretraining
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-07-14T15:58:18.828589Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a28e6426-abd1-451c-8c1d-9a247fbde7ab · inbound
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions cites this paper.
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions Practical Efficiency of Muon for Pretraining
Reference 72
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-07-09T17:36:25.411591Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 776cfd60-13c9-4da7-9080-7130a0e77bf7 · inbound
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions cites this paper.
Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions Practical Efficiency of Muon for Pretraining
Reference 150
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- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8ae89e6d-1844-456a-9a82-9db356e79d87 · inbound
Reassessing Muon for Matrix Factorization cites this paper.
Reassessing Muon for Matrix Factorization Practical Efficiency of Muon for Pretraining
Reference 23
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- unresolved
- no resolver link, observed 2026-08-02T05:49:19.457536Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 366f1d69-2de7-4786-ac7d-149cc0e6f122 · inbound
Reassessing Muon for Matrix Factorization cites this paper.
Reassessing Muon for Matrix Factorization Practical Efficiency of Muon for Pretraining
Reference 26
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9ac3607e-eab5-45bc-861b-281d26212261 · inbound
Muse: Representation Geometry of Muon Beyond Normalized Momentum cites this paper.
Muse: Representation Geometry of Muon Beyond Normalized Momentum Practical Efficiency of Muon for Pretraining
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T01:58:57.151505Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7910fb49-bf75-4774-be98-e01007f6edad · inbound
SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales cites this paper.
SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales Practical Efficiency of Muon for Pretraining
Reference 14
- Resolution
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.