Paper Citation Record · LEDGER

A New Perspective on Shampoo's Preconditioner

As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 15 inbound Pith citation observations for arXiv:2406.17748.

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

pith.paper-citation-record.v1
2406.17748 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 15 of 15 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T14:47:40.673899Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T07:06:44.892454Z

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External citation measurements

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Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 8fac65cc-bf23-49a2-80f0-151f67184ebe · inbound

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

Old Optimizer, New Norm: An Anthology A New Perspective on Shampoo's Preconditioner

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-16T07:27:52.936932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c3a67bcd-ac56-446b-b883-d372f0cb6099 · 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 New Perspective on Shampoo's Preconditioner

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-09T14:47:40.673899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34d89f11-b35a-49a3-a208-31cb801b1f64 · inbound

Towards Efficient Optimizer Design for LLM via Structured Fisher Approximation with a Low-Rank Extension cites this paper.

Towards Efficient Optimizer Design for LLM via Structured Fisher Approximation with a Low-Rank Extension A New Perspective on Shampoo's Preconditioner

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-08T11:46:47.755604Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2f0088c-3312-4925-b80e-9035197a49c6 · inbound

On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon A New Perspective on Shampoo's Preconditioner

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:22:19.171917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9549c3f5-6eb9-403e-a034-71b75a37e1b4 · inbound

On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon A New Perspective on Shampoo's Preconditioner

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-07T12:45:19.632931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca9444f0-335d-4769-a9ef-14f383d7bd66 · inbound

Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise cites this paper.

Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise A New Perspective on Shampoo's Preconditioner

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-07T10:58:35.149962Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f9068b4-d42c-48fe-8539-1770cd4965d8 · inbound

Low-rank Momentum Factorization for Memory Efficient Training cites this paper.

Low-rank Momentum Factorization for Memory Efficient Training A New Perspective on Shampoo's Preconditioner

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:40.206232Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d170c07c-29db-4282-81ce-d14bd9be40e3 · inbound

Harnessing Optimization Dynamics for Curvature-Informed Model Merging cites this paper.

Harnessing Optimization Dynamics for Curvature-Informed Model Merging A New Perspective on Shampoo's Preconditioner

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T17:03:17.036405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a47d27ec-5912-4c15-ae7a-56b36320e736 · inbound

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 A New Perspective on Shampoo's Preconditioner

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-03T03:56:41.924586Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43fe6e5c-ad76-4d92-8d2e-9b2a0442e487 · 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 New Perspective on Shampoo's Preconditioner

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:01:12.407142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3a39cd09-3025-453a-99ff-7ffadab4ce81 · inbound

Why Muon Outperforms Adam: A Curvature Perspective cites this paper.

Why Muon Outperforms Adam: A Curvature Perspective A New Perspective on Shampoo's Preconditioner

Reference 85

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:44.894077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 392f0c05-71ba-4566-bc20-9ae9625dbf8c · inbound

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature cites this paper.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature A New Perspective on Shampoo's Preconditioner

Reference 22

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 e3010bbb-d4c1-463e-9575-edb4f90f50b7 · inbound

Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions cites this paper.

Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions A New Perspective on Shampoo's Preconditioner

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T15:50:41.329016Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e96956c5-1e58-4b1b-9a58-788abb95e819 · inbound

SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales cites this paper.

SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales A New Perspective on Shampoo's Preconditioner

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-02T06:45:18.187657Z

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Unavailable: canonical work link unavailable.

Observation c82a2e30-8f78-4c9b-b370-3cbca65f8051 · inbound

BaKron: Efficient Quantization with Kronecker-Factored Hessians cites this paper.

BaKron: Efficient Quantization with Kronecker-Factored Hessians A New Perspective on Shampoo's Preconditioner

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:22.919245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.