SignSGD provably beats SGD by a factor of d under sparse noise via matched ℓ1-norm upper and lower bounds, with an equivalent result for Muon on matrices, and this predicts faster GPT-2 pretraining.
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ArXiv Preprint: 2511.00674 , Year =
13 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 13representative citing papers
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
Muon in matrix factorization avoids saddle-to-saddle dynamics, learns top modes simultaneously, conserves sqrt(P^TP) - sqrt(Q^TQ), and reaches balanced solutions from small initialization with a two-step alignment schedule.
Double preconditioning (DoPr) improves downstream task performance in test-time feedback settings without consistent gains in validation loss.
Momentum in Muon functions as a spectral filter on signal-plus-perturbation gradients, enlarging the gap to stabilize singular subspaces before orthogonalization and outperforming the reverse order.
Establishes matching Ω and O(min{m,n} ε^-(3p-2)/(p-1)) bounds for scale-invariant spectral-norm methods under heavy-tailed noise, plus an improved O(min{m,n} ε^-(5p-3)/(2p-2)) rate via transported Scion under Hessian Lipschitz continuity.
Proposes equivariant optimizer updates matched to layer symmetries for embeddings, SwiGLU MLPs, and MoE routers, with reported gains in validation loss and training stability on several language model architectures.
Muon-OGD introduces a spectral-norm constrained orthogonal projection method solved via dual iterations and Newton-Schulz approximations to improve stability-plasticity trade-off in sequential LLM adaptation.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
MiMuon is a hybrid optimizer that achieves a generalization error bound of O(1/N) independent of the small singular-value gap that limits the original Muon bound, while retaining the same O(1/T^{1/4}) convergence rate.
Convergence analysis shows Muon outperforms gradient descent by exploiting low-rank structure in neural network Hessians.
Constraining fine-tuning updates with LoRA mitigates performance degradation when switching from Adam to Muon on pretrained models.
citing papers explorer
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When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds
SignSGD provably beats SGD by a factor of d under sparse noise via matched ℓ1-norm upper and lower bounds, with an equivalent result for Muon on matrices, and this predicts faster GPT-2 pretraining.
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Phases of Muon: When Muon Eclipses SignSGD
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
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Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Muon achieves higher storage capacity than SGD and matches Newton's method in one-step recovery rates for associative memory under power-law distributions, while saturating at larger critical batch sizes and showing faster initial multi-step dynamics.
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Muon learns balanced solutions in matrix factorization without slow saddle-to-saddle dynamics
Muon in matrix factorization avoids saddle-to-saddle dynamics, learns top modes simultaneously, conserves sqrt(P^TP) - sqrt(Q^TQ), and reaches balanced solutions from small initialization with a two-step alignment schedule.
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Double Preconditioning (DoPr): Optimization for Test-Time Performance, not Validation Loss
Double preconditioning (DoPr) improves downstream task performance in test-time feedback settings without consistent gains in validation loss.
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Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering
Momentum in Muon functions as a spectral filter on signal-plus-perturbation gradients, enlarging the gap to stabilize singular subspaces before orthogonalization and outperforming the reverse order.
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Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise
Establishes matching Ω and O(min{m,n} ε^-(3p-2)/(p-1)) bounds for scale-invariant spectral-norm methods under heavy-tailed noise, plus an improved O(min{m,n} ε^-(5p-3)/(2p-2)) rate via transported Scion under Hessian Lipschitz continuity.
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Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers
Proposes equivariant optimizer updates matched to layer symmetries for embeddings, SwiGLU MLPs, and MoE routers, with reported gains in validation loss and training stability on several language model architectures.
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Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning
Muon-OGD introduces a spectral-norm constrained orthogonal projection method solved via dual iterations and Newton-Schulz approximations to improve stability-plasticity trade-off in sequential LLM adaptation.
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Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
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MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models
MiMuon is a hybrid optimizer that achieves a generalization error bound of O(1/N) independent of the small singular-value gap that limits the original Muon bound, while retaining the same O(1/T^{1/4}) convergence rate.
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On the Convergence Analysis of Muon
Convergence analysis shows Muon outperforms gradient descent by exploiting low-rank structure in neural network Hessians.
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Can Muon Fine-tune Adam-Pretrained Models?
Constraining fine-tuning updates with LoRA mitigates performance degradation when switching from Adam to Muon on pretrained models.