Paper Citation Record · LEDGER

Dimension-Free Saddle-Point Escape in Muon

As of 5 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2605.09331.

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

pith.paper-citation-record.v1
2605.09331 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T04:38:25.480020Z

measured 47 of 47 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

verified exact26
verified fuzzy8
unresolved3
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External citation measurements

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Outbound references

Observation f59a6df3-1a9a-430d-8349-2f6ee65504ca · outbound

This paper cites Scalable Second Order Optimization for Deep Learning.

Dimension-Free Saddle-Point Escape in Muon Scalable Second Order Optimization for Deep Learning

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.497710Z

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Observation 860b0d2d-f36e-46ff-acb5-32e01043af0c · outbound

This paper cites On the convergence of muon and beyond.

Dimension-Free Saddle-Point Escape in Muon On the convergence of muon and beyond

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.247245Z

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Observation 5f970727-f34b-4895-a93e-edd55e3de221 · outbound

This paper cites On the Convergence of Muon and Beyond.

Dimension-Free Saddle-Point Escape in Muon On the Convergence of Muon and Beyond

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-05-12T06:01:26.501307Z

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Observation 2227f415-4769-44a8-82c3-7fdefa3a0edf · outbound

This paper cites The Loss Surfaces of Multilayer Networks.

Dimension-Free Saddle-Point Escape in Muon The Loss Surfaces of Multilayer Networks

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.493478Z

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Observation 2c78eefc-018e-4761-befa-679d4fec984c · outbound

This paper cites Escaping Saddles with Stochastic Gradients.

Dimension-Free Saddle-Point Escape in Muon Escaping Saddles with Stochastic Gradients

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.489593Z

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Observation 28e869b9-887e-4231-ba0a-d6ad2d30c6e2 · outbound

This paper cites Identifying and attacking the saddle point problem in high-dimensional non-convex optimization.

Dimension-Free Saddle-Point Escape in Muon Identifying and attacking the saddle point problem in high-dimensional non-convex optimization

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.507724Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 455cf994-a3e2-4173-9470-ac528c70ac49 · outbound

This paper cites Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth.

Dimension-Free Saddle-Point Escape in Muon Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.403986Z

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Observation 3228e01b-1420-4276-be24-0f89292dad8e · outbound

This paper cites Optimal Eigenvalue Shrinkage in the Semicircle Limit.

Dimension-Free Saddle-Point Escape in Muon Optimal Eigenvalue Shrinkage in the Semicircle Limit

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.407392Z

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Observation 2d015a04-8a3a-41e8-96ac-af5a723f731f · outbound

This paper cites Du and W.

Dimension-Free Saddle-Point Escape in Muon Du and W

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.379256Z

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Observation 850892ed-ef5a-46ee-9292-91325d1636f2 · outbound

This paper cites Escaping from saddle points—online stochastic gradient for tensor decomposition.COLT.

Dimension-Free Saddle-Point Escape in Muon Escaping from saddle points—online stochastic gradient for tensor decomposition.COLT

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.265424Z

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Observation 2d55c43e-2454-490b-9db9-0bd7d7a06e08 · outbound

This paper cites Grishina, M.

Dimension-Free Saddle-Point Escape in Muon Grishina, M

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.428453Z

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Observation ca8b3c90-6e90-44b3-b0ee-e77d537ca140 · outbound

This paper cites Shampoo: Preconditioned Stochastic Tensor Optimization.

Dimension-Free Saddle-Point Escape in Muon Shampoo: Preconditioned Stochastic Tensor Optimization

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.324437Z

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Observation aab4b2e2-d315-4b82-935b-1ec91e011771 · outbound

This paper cites arXiv preprint arXiv:2511.20626 , year=.

Dimension-Free Saddle-Point Escape in Muon arXiv preprint arXiv:2511.20626 , year=

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.396409Z

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Observation 16620d68-01b8-46f6-8c52-e69ab571c383 · outbound

This paper cites How to Escape Saddle Points Efficiently.

Dimension-Free Saddle-Point Escape in Muon How to Escape Saddle Points Efficiently

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.483521Z

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Observation a6d9215a-7f7c-495a-b5ac-c199a1fa8e20 · outbound

This paper cites Muon: An optimizer for hidden layers in neural networks.

Dimension-Free Saddle-Point Escape in Muon Muon: An optimizer for hidden layers in neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.254340Z

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Observation 3f3b7c94-a42a-4c64-85cb-9505c0e3b736 · outbound

This paper cites Scaling Laws for Neural Language Models.

Dimension-Free Saddle-Point Escape in Muon Scaling Laws for Neural Language Models

Reference 16

Resolution: metadata mismatch; local_arxiv, observed 2026-05-12T06:01:26.443101Z

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Observation 739cf1f6-369e-41e5-ae5c-36893d148efd · outbound

This paper cites The isotropic semicircle law and deformation of wigner matrices.

Dimension-Free Saddle-Point Escape in Muon The isotropic semicircle law and deformation of wigner matrices

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.257018Z

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Observation 479b4d0b-e687-4e18-b49e-6b1dc2190a98 · outbound

This paper cites The Isotropic Semicircle Law and Deformation of Wigner Matrices.

Dimension-Free Saddle-Point Escape in Muon The Isotropic Semicircle Law and Deformation of Wigner Matrices

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-04T18:06:30.586525Z

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Observation c5e23c37-b1b4-4987-a14c-ec5eacfec255 · outbound

This paper cites Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization.

Dimension-Free Saddle-Point Escape in Muon Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 19

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.384083Z

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Observation 7feb29eb-f14a-45c4-ab4a-acfd356b6c2e · outbound

This paper cites Muon in Associative Memory Learning: Training Dynamics and Scaling Laws.

Dimension-Free Saddle-Point Escape in Muon Muon in Associative Memory Learning: Training Dynamics and Scaling Laws

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-26T03:04:11.161880Z

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Observation cd84be3b-6c64-4028-b4bf-6b52a458b634 · outbound

This paper cites Muon is Scalable for LLM Training.

Dimension-Free Saddle-Point Escape in Muon Muon is Scalable for LLM Training

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-05-12T06:01:26.345270Z

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Observation 7de2fc96-f8da-428e-b62c-8c049a6c9e6d · outbound

This paper cites Specinfer: Ac- celerating generative llm serving with speculative inference and token tree verification.

Dimension-Free Saddle-Point Escape in Muon Specinfer: Ac- celerating generative llm serving with speculative inference and token tree verification

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.262835Z

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Observation a2a717b1-2f1d-4543-ac23-d247d64e2d64 · outbound

This paper cites Behavior of Accelerated Gradient Methods Near Critical Points of Nonconvex Functions.

Dimension-Free Saddle-Point Escape in Muon Behavior of Accelerated Gradient Methods Near Critical Points of Nonconvex Functions

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-04T23:06:18.256341Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 31d05a58-e970-4715-baff-0ad003873fe2 · outbound

This paper cites Large-scale distributed second-order optimization using kronecker-factored approximate cur- vature for deep convolutional neural networks.

Dimension-Free Saddle-Point Escape in Muon Large-scale distributed second-order optimization using kronecker-factored approximate cur- vature for deep convolutional neural networks

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.271341Z

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Observation aa298b80-d942-45f0-b8a6-06136e6156e7 · outbound

This paper cites Asymptotics of sample eigenstructure for a large dimensional spiked covariance model.Statistica Sinica, 17(4):1617–1642.

Dimension-Free Saddle-Point Escape in Muon Asymptotics of sample eigenstructure for a large dimensional spiked covariance model.Statistica Sinica, 17(4):1617–1642

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.317345Z

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Observation 61b32963-0f94-40a8-898c-80f337a1b65e · outbound

This paper cites The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale.

Dimension-Free Saddle-Point Escape in Muon The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-13T04:36:45.776658Z

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Observation 9d6fecd1-0225-47fd-94ff-0578a4537e20 · outbound

This paper cites Geometry of neural network loss surfaces via random matrix theory.

Dimension-Free Saddle-Point Escape in Muon Geometry of neural network loss surfaces via random matrix theory

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.279576Z

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Observation 56ac1282-7192-403b-873c-dbd8f6d51870 · outbound

This paper cites A Generic Approach for Escaping Saddle points.

Dimension-Free Saddle-Point Escape in Muon A Generic Approach for Escaping Saddle points

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.374440Z

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Observation 19947cad-324d-49cc-9d1d-06ad9cbeece0 · outbound

This paper cites Hanson-Wright inequality and sub-gaussian concentration.

Dimension-Free Saddle-Point Escape in Muon Hanson-Wright inequality and sub-gaussian concentration

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.400049Z

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Observation 0c29467b-652e-436e-9146-ef5df46b6b30 · outbound

This paper cites Escaping Saddle Points with Adaptive Gradient Methods.

Dimension-Free Saddle-Point Escape in Muon Escaping Saddle Points with Adaptive Gradient Methods

Reference 30

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Observation 44c20eae-566d-41b6-a340-09f19488e962 · outbound

This paper cites Kimi-VL Technical Report.

Dimension-Free Saddle-Point Escape in Muon Kimi-VL Technical Report

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-05-12T06:01:26.439415Z

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Observation c6e98094-9d31-4e2d-9bd8-b66ef739dd97 · outbound

This paper cites LLaMA: Open and Efficient Foundation Language Models.

Dimension-Free Saddle-Point Escape in Muon LLaMA: Open and Efficient Foundation Language Models

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-05-12T06:01:26.361365Z

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Observation 5ef40fd0-929c-459c-beb5-8f91b85b802c · outbound

This paper cites Analysis of singular subspaces under random perturbations.The Annals of Statistics, 54(2):667 – 691.

Dimension-Free Saddle-Point Escape in Muon Analysis of singular subspaces under random perturbations.The Annals of Statistics, 54(2):667 – 691

Reference 33

Resolution: verified exact; doi, observed 2026-05-12T04:41:20.585383Z

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Observation 1f869155-3ee0-4605-b58b-c7316c105ac5 · outbound

This paper cites Muon outperforms adam in tail-end associative memory learning.

Dimension-Free Saddle-Point Escape in Muon Muon outperforms adam in tail-end associative memory learning

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.474432Z

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Observation a73c2707-3f8c-4199-a448-fc8893299004 · outbound

This paper cites A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima.

Dimension-Free Saddle-Point Escape in Muon A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.388383Z

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Observation d9f5da7a-132f-4dd7-a240-c2b0d449895f · outbound

This paper cites Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum.

Dimension-Free Saddle-Point Escape in Muon Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.462784Z

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Observation f1281a6f-6027-4366-b9d4-6ead6757ef18 · outbound

This paper cites Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization.

Dimension-Free Saddle-Point Escape in Muon Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.470681Z

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Observation 00b8f7d7-5b24-4c4a-b031-4c5b8d6ef34e · outbound

This paper cites On the Overlooked Structure of Stochastic Gradients.

Dimension-Free Saddle-Point Escape in Muon On the Overlooked Structure of Stochastic Gradients

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.392329Z

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Observation 11669c50-0a47-4b36-8474-1d3be3fd0604 · outbound

This paper cites Prism: Structured optimization via anisotropic spectral shaping.

Dimension-Free Saddle-Point Escape in Muon Prism: Structured optimization via anisotropic spectral shaping

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.432115Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 3d435b8b-b38b-4b2d-a19f-3d5128be4c08 · outbound

This paper cites arXiv preprint arXiv:2603.09697 , year=.

Dimension-Free Saddle-Point Escape in Muon arXiv preprint arXiv:2603.09697 , year=

Reference 40

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:01:26.454031Z

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Observation c2cc530e-7c23-4149-ae60-1706e36e6dfc · outbound

This paper cites Stochastic Nested Variance Reduction for Nonconvex Optimization.

Dimension-Free Saddle-Point Escape in Muon Stochastic Nested Variance Reduction for Nonconvex Optimization

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.478380Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation f3863c38-a9a1-4abd-ac77-65079a2daf25 · outbound

This paper cites The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Sharp Minima and Regularization Effects.

Dimension-Free Saddle-Point Escape in Muon The Anisotropic Noise in Stochastic Gradient Descent: Its Behavior of Escaping from Sharp Minima and Regularization Effects

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:01:26.335370Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation f03697e6-b4f6-4bb5-bbac-7de47b00768e · outbound

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Dimension-Free Saddle-Point Escape in Muon Unresolved cited work

Reference 43

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Observation 56434c55-76c6-4e75-a239-e46055769c5c · outbound

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Dimension-Free Saddle-Point Escape in Muon Unresolved cited work

Reference 44

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Observation 3d9fbb5c-2f79-4eff-a196-b15a5e5faeff · outbound

This paper cites born locked.

Dimension-Free Saddle-Point Escape in Muon born locked

Reference 45

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Observation 13d255e9-8c74-478d-98fa-b9bc50284aa4 · outbound

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Dimension-Free Saddle-Point Escape in Muon Unresolved cited work

Reference 46

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Observation f68ea294-c385-4453-a800-bc78fb1a9fe8 · outbound

This paper cites Spike Range.

Dimension-Free Saddle-Point Escape in Muon Spike Range

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T14:11:37.277025Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Pith citing papers

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