Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization | Paper Citation Record

Observation 71fcfa0c-e72a-4410-af0d-4f238ce0ef33 · inbound

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) cites this paper.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 16

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On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 11

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On the Convergence Analysis of Muon cites this paper.

On the Convergence Analysis of Muon Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 11

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration cites this paper.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 25

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Convergence Bound and Critical Batch Size of Muon Optimizer cites this paper.

Convergence Bound and Critical Batch Size of Muon Optimizer Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 2015

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Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees cites this paper.

Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 1993

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AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates cites this paper.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 19

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Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training cites this paper.

Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 30

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LiMuon: Light and Fast Muon Optimizer for Large Models cites this paper.

LiMuon: Light and Fast Muon Optimizer for Large Models Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 2014

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Observation 57eb9d9d-2d5d-4dea-8cf8-b3e09d8adc77 · inbound

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs cites this paper.

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 5

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Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates cites this paper.

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 35

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Observation 32aafd05-c463-4274-82c8-177a95cc14d9 · inbound

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

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 31

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MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training cites this paper.

MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 15

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Optimal Projection-Free Adaptive SGD for Matrix Optimization cites this paper.

Optimal Projection-Free Adaptive SGD for Matrix Optimization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 16

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Observation 5644bc27-0c90-4460-8b7f-13fdffb925a8 · inbound

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning cites this paper.

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 12

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Communication-Efficient Gluon in Federated Learning cites this paper.

Communication-Efficient Gluon in Federated Learning Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 19

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Observation 68c33c2a-8056-46bc-818c-01ca6e0e7086 · inbound

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition cites this paper.

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:00:56.679583Z

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

Dimension-Free Saddle-Point Escape in Muon cites this paper.

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

Reference 19

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Observation f84eac50-3db7-4eda-937f-962f38444cd5 · inbound

Can Muon Fine-tune Adam-Pretrained Models? cites this paper.

Can Muon Fine-tune Adam-Pretrained Models? Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:51:28.816677Z

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Observation 2da3c9a3-fd34-4e5b-8432-e89c744aaf97 · inbound

Muon is Not That Special: Random or Inverted Spectra Work Just as Well cites this paper.

Muon is Not That Special: Random or Inverted Spectra Work Just as Well Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-05-13T04:17:13.744761Z

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Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives cites this paper.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 30

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Observation cc020d3c-5332-471f-b36b-22789052180e · 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 Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:53.124895Z

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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 Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 83

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Observation dd6c9bb4-3fd9-4e3d-a8c6-c59268ee4379 · 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 Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 85

Resolution: verified exact; arxiv_id, observed 2026-06-30T18:45:00.379916Z

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Observation 3ae51170-44fa-4757-bf12-cac193dd8c65 · inbound

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method cites this paper.

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 291

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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise cites this paper.

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 65

Resolution: verified exact; arxiv_id, observed 2026-07-01T14:55:48.633794Z

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Observation e5bdcb5e-c7a0-4ad1-9652-0246994ced76 · inbound

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models cites this paper.

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-20T08:13:08.332905Z

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LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging cites this paper.

LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 292

Resolution: verified exact; arxiv_id, observed 2026-05-21T05:49:40.639082Z

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Observation a9e57df4-e912-4f7a-a6c6-13c2da87d407 · inbound

Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer cites this paper.

Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 5

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Observation d1b21808-3b1a-460c-a8c0-61c11dbe8459 · inbound

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering cites this paper.

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-02T01:56:27.803949Z

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Observation d15c3da6-790d-4fde-9e38-517bc61fda1d · inbound

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

Why Muon Outperforms Adam: A Curvature Perspective Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 158

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:16:44.401048Z

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Observation a6d4c29e-6ceb-4b6d-b6e2-277b35a6c2aa · 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 Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 174

Resolution: verified exact; arxiv_id, observed 2026-07-02T11:56:55.972612Z

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Observation 9a7b1be7-92a7-45b0-8396-c61ef473872c · inbound

Muon Learns More Robust and Transferable Features than Adam cites this paper.

Muon Learns More Robust and Transferable Features than Adam Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 80

Resolution: verified exact; arxiv_id, observed 2026-07-03T00:27:30.190097Z

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Observation a83a9502-bad2-4dd0-ac1c-c4ee563acc12 · inbound

Restart and Adaptive Acceleration in Stochastic Gradient Methods cites this paper.

Restart and Adaptive Acceleration in Stochastic Gradient Methods Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-04T06:59:37.581655Z

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Observation 27877e57-6a11-4f20-8e68-4525bcd92350 · inbound

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case cites this paper.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 52

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Observation d81577a1-d2f5-4d0a-a6e7-1d7e99935950 · inbound

One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining cites this paper.

One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T06:44:18.874749Z

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Observation 90e3855b-ec5b-4461-bb0d-7df4849b25c5 · inbound

Muon as a Residual Connection cites this paper.

Muon as a Residual Connection Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 2

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Observation 0fdde877-86a3-400f-b3c7-77b547e89579 · inbound

How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size cites this paper.

How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:08:57.594636Z

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Observation 286bd7cf-619e-4dde-b067-ce118df92e4b · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 29

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Observation 83163206-68a5-4987-a452-0f8b275f4bbc · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 97

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Observation f121ad90-f4bb-4347-be89-68b31afbfc2e · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 32

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Observation ce417a14-eb4d-400d-8945-4f731974707c · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 100

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Observation 9fd80c70-3004-4e13-a6ce-3a669fbf97e4 · inbound

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback cites this paper.

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-03T02:09:01.948787Z

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Observation cac7645d-81c6-4c70-a7d9-f8b90b295011 · inbound

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization cites this paper.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 32

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Observation 6192ee82-19e9-4df3-ac41-20cae44fb588 · inbound

Federated Compositional Muon Optimizer for Matrix-Wise Models cites this paper.

Federated Compositional Muon Optimizer for Matrix-Wise Models Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 7

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