Paper Citation Record · LEDGER

A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 30 inbound Pith citation observations for arXiv:2309.06497.

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

pith.paper-citation-record.v1
2309.06497 v1

Coverage vector

measured 0 of 0 reference resolution

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Source: paper_references, paper_reference_links

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 30 of 30 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T04:35:57.949886Z

measured 1 of 1 external citation measurements

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

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

Reference resolution

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External citation measurements

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

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 9215efe9-e270-4cbb-b857-68acc22d380f · inbound

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

Old Optimizer, New Norm: An Anthology A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 32

Resolution: metadata mismatch; arxiv_id, observed 2026-05-16T07:27:52.941479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 840b886c-4ca4-4976-9d25-026b41b288c8 · inbound

MARS: Unleashing the Power of Variance Reduction for Training Large Models cites this paper.

MARS: Unleashing the Power of Variance Reduction for Training Large Models A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 75

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Observation 1458026b-f75b-4f94-84e3-c5f9a354b5c9 · inbound

Materials Learning Algorithms (MALA): Scalable Machine Learning for Electronic Structure Calculations in Large-Scale Atomistic Simulations cites this paper.

Materials Learning Algorithms (MALA): Scalable Machine Learning for Electronic Structure Calculations in Large-Scale Atomistic Simulations A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 73

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Observation 4da20aa6-8ab7-4c1e-8e21-8c47e36fb61a · inbound

Memory-Efficient 4-bit Preconditioned Stochastic Optimization cites this paper.

Memory-Efficient 4-bit Preconditioned Stochastic Optimization A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 43

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Observation 50362495-f249-4a7d-bd41-0e1ed9c1767d · inbound

SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training cites this paper.

SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 55

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Observation 5ce83e7f-3c9c-4240-9c0a-ed5c29df1bf1 · inbound

On The Concurrence of Layer-wise Preconditioning Methods and Provable Feature Learning cites this paper.

On The Concurrence of Layer-wise Preconditioning Methods and Provable Feature Learning A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 99

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Observation a5ee00b1-8cf5-4761-bc55-477f7dd8b99e · inbound

Spectral-factorized Positive-definite Curvature Learning for NN Training cites this paper.

Spectral-factorized Positive-definite Curvature Learning for NN Training A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 55

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Observation 9b2fc8e5-cbe0-4a3f-9627-e9adc83f1ef1 · inbound

DHO$_2$: Accelerating Distributed Hybrid Order Optimization via Model Parallelism and ADMM cites this paper.

DHO$_2$: Accelerating Distributed Hybrid Order Optimization via Model Parallelism and ADMM A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 12

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Observation 774ec820-ea2a-42c4-9cb4-74490d2ff5f8 · inbound

Learning by solving differential equations cites this paper.

Learning by solving differential equations A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 55

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Observation a2ee34b3-b56c-4a37-a986-75b2883a309f · inbound

Understanding and Improving Shampoo and SOAP via Kullback-Leibler Minimization cites this paper.

Understanding and Improving Shampoo and SOAP via Kullback-Leibler Minimization A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-05T11:03:40.394757Z

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Observation 9ec66fb5-b447-420e-8fef-c969e22a2760 · inbound

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization cites this paper.

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-15T07:49:50.787770Z

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Observation f7799bca-5bf9-4092-bb26-3a19778cd3b2 · inbound

Demystifying Manifold Constraints in LLM Pre-training cites this paper.

Demystifying Manifold Constraints in LLM Pre-training A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 38

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T17:16:08.604600Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation de53d088-01a2-481a-be0b-cd623329dde2 · inbound

Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization cites this paper.

Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 15

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T19:01:12.783437Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 29a8efb0-f48f-454f-8e0d-08b8ac786a8f · inbound

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

Phases of Muon: When Muon Eclipses SignSGD A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 66

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:41:29.878617Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5e8147c0-a478-4d4c-a0a2-7757f8f6de36 · inbound

Second-Order Multi-Level Variance Correction for Modality Competition in Multimodal Models cites this paper.

Second-Order Multi-Level Variance Correction for Modality Competition in Multimodal Models A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-20T19:03:39.552743Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 27b85356-b987-4a75-ae0a-e606698c19aa · inbound

Runtime-Orchestrated Second-Order Optimization for Scalable LLM Training cites this paper.

Runtime-Orchestrated Second-Order Optimization for Scalable LLM Training A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T18:32:42.896458Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2e523952-ef52-4d32-9045-51b22cf1a7e0 · 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 Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 139

Resolution: verified exact; arxiv_id, observed 2026-05-20T09:38:11.084495Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8899af77-1701-440b-9ed2-a0f582976f4a · inbound

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

Reference 141

Resolution: verified exact; arxiv_id, observed 2026-06-30T18:45:00.341379Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 23a46ad9-1f96-4330-8661-9f5a74ec8462 · inbound

FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo cites this paper.

FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-07-01T22:06:16.001137Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b05e4df-5e09-4577-b05a-e3ff329b9e69 · inbound

Spectral Scaling Laws of Muon cites this paper.

Spectral Scaling Laws of Muon A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T02:06:26.379608Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 14c2112f-286a-498c-ab05-649dc17b70d9 · inbound

Double Preconditioning (DoPr): Optimization for Test-Time Performance, not Validation Loss cites this paper.

Double Preconditioning (DoPr): Optimization for Test-Time Performance, not Validation Loss A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 84

Resolution: verified exact; arxiv_id, observed 2026-07-02T12:06:55.400219Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0f602b61-e958-4214-81c3-0332ca7b31a6 · inbound

SOAP-Bubbles: Structured Weight Uncertainty for Neural Networks cites this paper.

SOAP-Bubbles: Structured Weight Uncertainty for Neural Networks A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 4

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Observation d4ed3575-bfbf-49d8-86df-f929d40420ba · inbound

DMuon: Efficient Distributed Muon Training with Near-Adam Overhead cites this paper.

DMuon: Efficient Distributed Muon Training with Near-Adam Overhead A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T14:39:58.558807Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8afea9ee-df30-476b-8d85-8941f75027c9 · inbound

MatrixFSDP: communication-free matrix optimizers under ZeRO-3 parameter sharding cites this paper.

MatrixFSDP: communication-free matrix optimizers under ZeRO-3 parameter sharding A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 8

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Observation 6d826c50-3951-4413-bbf3-3c7d8feafd5f · inbound

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

Muse: Representation Geometry of Muon Beyond Normalized Momentum A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 35

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Observation 891d468f-8722-410b-92a1-9391048fd58d · inbound

PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer cites this paper.

PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-01T17:32:35.758665Z

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Observation fc89e38e-cb7b-4ec1-99c0-eda052520eaf · inbound

OneShot: Index-in-Ranking with Neural Scoring for Large-Scale Retrieval cites this paper.

OneShot: Index-in-Ranking with Neural Scoring for Large-Scale Retrieval A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T07:21:46.180322Z

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Observation 18859707-d211-499f-8c3e-d8fcb74962e9 · inbound

OneShot: Index-in-Ranking with Neural Scoring for Large-Scale Retrieval cites this paper.

OneShot: Index-in-Ranking with Neural Scoring for Large-Scale Retrieval A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-03T01:45:23.261226Z

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Observation 6ec7bf56-7c37-4897-b8e9-256fc8d7d013 · inbound

Muon Meets Mamba: Spectral Optimization for State Space Models cites this paper.

Muon Meets Mamba: Spectral Optimization for State Space Models A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T05:27:17.313102Z

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Observation 4a0b3809-ca41-41cc-aa65-bcf638e00f14 · 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 A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.781870Z

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Unavailable: canonical work link unavailable.