Paper Citation Record · LEDGER

Modular Duality in Deep Learning

As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 26 inbound Pith citation observations for arXiv:2410.21265.

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

pith.paper-citation-record.v1
2410.21265 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 26 of 26 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:35:40.098289Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T19:30:07.293501Z

Reference resolution

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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 a2a3852c-5027-443b-9386-3ce4e941ed6d · inbound

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

Training Deep Learning Models with Norm-Constrained LMOs Modular Duality in Deep Learning

Reference 159

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:22:37.015602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3fe12a6e-83c1-43dd-9681-700cffe0ce6e · inbound

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

Low-rank Momentum Factorization for Memory Efficient Training Modular Duality in Deep Learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:40.098289Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e00d30f1-c896-45e8-ba9c-a7ccd1f43fe1 · inbound

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods cites this paper.

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods Modular Duality in Deep Learning

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:10:38.704244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 930d441e-fe2f-4a3c-987e-6ee6a1291d18 · 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 Modular Duality in Deep Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T03:56:38.947343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9c45aab-3c14-4310-8aea-872a5b89da6f · inbound

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction cites this paper.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Modular Duality in Deep Learning

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.275684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c0116fc5-4d2e-4979-9593-d089c92fb0c3 · inbound

GaussianGPT: Towards Autoregressive 3D Gaussian Scene Generation cites this paper.

GaussianGPT: Towards Autoregressive 3D Gaussian Scene Generation Modular Duality in Deep Learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-13T17:23:44.758186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db426e5b-2fb2-4d34-bd53-a983ca87e1ae · inbound

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 Modular Duality in Deep Learning

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-10T07:26:59.843993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2d37797a-e03f-4428-9578-ca93e927fb41 · inbound

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

Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization Modular Duality in Deep Learning

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:01:13.028343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 05939d19-8bed-4420-aa10-1108901a159c · inbound

OrScale: Orthogonalised Optimization with Layer-Wise Trust-Ratio Scaling cites this paper.

OrScale: Orthogonalised Optimization with Layer-Wise Trust-Ratio Scaling Modular Duality in Deep Learning

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:05:55.574343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5032579b-e852-48fe-b4d2-32b3f299236a · inbound

Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning cites this paper.

Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning Modular Duality in Deep Learning

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-12T02:16:16.351281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cea3ec6e-975a-4a7d-9a9f-0cd67e452abc · inbound

Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning cites this paper.

Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning Modular Duality in Deep Learning

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-19T15:12:37.509271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0c75b1d6-b680-493e-a7c3-8db89b406a4d · inbound

Muon Does Not Converge on Convex Lipschitz Functions cites this paper.

Muon Does Not Converge on Convex Lipschitz Functions Modular Duality in Deep Learning

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:41:39.538565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f0a92b1b-bc02-4461-a8d5-d8205ee71d44 · inbound

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds cites this paper.

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds Modular Duality in Deep Learning

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:36:26.332930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 22b56f48-9114-4ecb-82bc-b4684cbbd276 · inbound

Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation cites this paper.

Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation Modular Duality in Deep Learning

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-13T04:57:17.587986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6af8c644-af95-4eac-be6f-c0dd6148f0e0 · inbound

How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization cites this paper.

How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization Modular Duality in Deep Learning

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-05-15T04:49:44.879652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1f35a431-1ba4-40b5-bb84-723b7c000f67 · inbound

Orth-Dion: Eliminating Geometric Mismatch in Distributed Low-Rank Spectral Optimization cites this paper.

Orth-Dion: Eliminating Geometric Mismatch in Distributed Low-Rank Spectral Optimization Modular Duality in Deep Learning

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-20T22:23:47.614326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d94318c5-ba2a-41b8-84c9-77de146f909a · inbound

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

Stochastic convergence of parallel asynchronous adaptive first-order methods Modular Duality in Deep Learning

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-01T23:16:24.970235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 74080cf3-bf21-4c9d-98ac-f0a235cdc9ee · inbound

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

Why Muon Outperforms Adam: A Curvature Perspective Modular Duality in Deep Learning

Reference 125

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:44.919762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e51a6a11-9b07-4631-9ac8-f32a7f4c1236 · inbound

Lifelong In-Context Learning with Transformers Requires Parametric Forms of Attention cites this paper.

Lifelong In-Context Learning with Transformers Requires Parametric Forms of Attention Modular Duality in Deep Learning

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-04T19:30:07.295201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c0f5a01f-11f3-4852-b61f-a9c78ecb7727 · inbound

Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks cites this paper.

Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks Modular Duality in Deep Learning

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-06-30T08:04:28.174134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8566f835-0bb8-4445-bcd8-5b67c161c980 · inbound

Token Geometry cites this paper.

Token Geometry Modular Duality in Deep Learning

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:08:57.423707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9730bbcb-219e-4d03-bd52-e9e427275bec · inbound

Token Geometry cites this paper.

Token Geometry Modular Duality in Deep Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-12T08:48:22.161005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 130d9530-7a86-475b-8cf2-b4a381aa0fd3 · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Modular Duality in Deep Learning

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-02T05:49:24.942195Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3773977a-28d1-4cee-b341-83bd46971ade · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Modular Duality in Deep Learning

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-04T04:23:00.756777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9344d4b5-482f-4669-bde0-23ea357f164f · inbound

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

SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales Modular Duality in Deep Learning

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T06:45:13.333343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e03d072-2279-4b47-86ce-f4814c5d1017 · inbound

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

Muon Meets Mamba: Spectral Optimization for State Space Models Modular Duality in Deep Learning

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T05:27:17.610179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.