Paper Citation Record · LEDGER

Muon Optimizer Accelerates Grokking

As of 17 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 7 inbound Pith citation observations for arXiv:2504.16041.

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

pith.paper-citation-record.v1
2504.16041 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:17:14.259102Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T04:45:20.907841Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T19:33:54.016778Z

Reference resolution

14 of 14 outbound references displayed

verified exact5
verified fuzzy2
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e06a35be-b46a-4f1b-a3cc-35f10d862b8d · outbound

This paper cites Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets.

Muon Optimizer Accelerates Grokking Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.184149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation efe5b9b7-8233-4797-b294-318234cfbb08 · outbound

This paper cites Jordan,Muon Optimizer (Original GitHub Repo), GitHub repository, November 2024.

Muon Optimizer Accelerates Grokking Jordan,Muon Optimizer (Original GitHub Repo), GitHub repository, November 2024

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:17:14.637312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 91451b7a-ee39-4e38-876f-d412250d37a7 · outbound

This paper cites Muon is Scalable for LLM Training.

Muon Optimizer Accelerates Grokking Muon is Scalable for LLM Training

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.195980Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a19ba0f-56d4-47b5-8415-991824a12864 · outbound

This paper cites Grokking at the Edge of Numerical Stability.

Muon Optimizer Accelerates Grokking Grokking at the Edge of Numerical Stability

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.201298Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80e9bf6e-e5f3-4ddd-914d-c7fa89d0fd0b · outbound

This paper cites From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification.

Muon Optimizer Accelerates Grokking From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.208747Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20ddc806-d5fd-4781-b935-95abbc1902cc · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

Muon Optimizer Accelerates Grokking Progress measures for grokking via mechanistic interpretability

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.214743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab448b9f-f875-44a4-9511-66a8256e3d30 · outbound

This paper cites Towards Understanding Grokking: An Effective Theory of Representation Learning.

Muon Optimizer Accelerates Grokking Towards Understanding Grokking: An Effective Theory of Representation Learning

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:14.220899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de1a4e71-e097-4278-a0b9-f6a5e110d065 · outbound

This paper cites On the recent-$k$-record of discrete random variables.

Muon Optimizer Accelerates Grokking On the recent-$k$-record of discrete random variables

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:17:14.470047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c44a9bef-0feb-4425-b99b-42c51f0995f0 · outbound

This paper cites Spatial Acoustic Projection for 3D Imaging Sonar Reconstruction.

Muon Optimizer Accelerates Grokking Spatial Acoustic Projection for 3D Imaging Sonar Reconstruction

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:17:14.436480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 56d48838-341a-497d-a23a-fdceab825b16 · outbound

This paper cites Generating Minimal Training Sets for Machine Learned Potentials.

Muon Optimizer Accelerates Grokking Generating Minimal Training Sets for Machine Learned Potentials

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:17:14.409246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 15ba3247-fdff-446d-a0fc-5df7fc8f5749 · outbound

This paper cites Davies, L.

Muon Optimizer Accelerates Grokking Davies, L

Reference 11

Resolution: verified exact; raw_fallback, observed 2026-08-16T11:17:14.385428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fc42423c-6086-4c70-afbb-8d3f67072e90 · outbound

This paper cites DMDD: A Large-Scale Dataset for Dataset Mentions Detection.

Muon Optimizer Accelerates Grokking DMDD: A Large-Scale Dataset for Dataset Mentions Detection

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:17:14.304063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e7edb522-0c36-43a4-8cb7-e579c40c4863 · outbound

This paper cites Tveit,PyTorch Grokking Experiments Codebase, GitHub repository, 2024.

Muon Optimizer Accelerates Grokking Tveit,PyTorch Grokking Experiments Codebase, GitHub repository, 2024

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:17:14.619459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9d144b13-10cc-49ff-8941-f829369120ca · outbound

This paper cites an unresolved cited work.

Muon Optimizer Accelerates Grokking Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:17:14.602966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation e8b0b3f7-4124-4b7d-af20-62d8e62811d5 · 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 Muon Optimizer Accelerates Grokking

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:21:07.625327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 88155c43-a13c-4031-82b2-de76b4abb055 · 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 Muon Optimizer Accelerates Grokking

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:53.104043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2078771d-a702-41be-906f-4a447711f5cd · inbound

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

Convergence of Spectral Descent for Non-smooth Optimization Muon Optimizer Accelerates Grokking

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-29T19:33:54.018396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 05481e2a-5303-4e6c-8ffc-c75d21f7ad41 · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Muon Optimizer Accelerates Grokking

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-02T05:49:25.829773Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7aeb7f8-b799-4088-b80f-36f79f4ad905 · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Muon Optimizer Accelerates Grokking

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-04T04:23:01.281987Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1af1a4dd-1c2d-494d-902a-a07bf5fe19f4 · inbound

The Active Ingredient in Muon's Grokking cites this paper.

The Active Ingredient in Muon's Grokking Muon Optimizer Accelerates Grokking

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T08:28:32.969860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9bf2c24f-978d-4e23-9314-e62cbbd8c86d · inbound

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers cites this paper.

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers Muon Optimizer Accelerates Grokking

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T04:45:20.907841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.