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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Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491
13 Pith papers cite this work. Polarity classification is still indexing.
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2026 13representative citing papers
The same Transformer architecture follows different spectral scaling laws under different optimizers, with Muon achieving linear hard-rank scaling on tail representations while AdamW shows weak scaling, even when perplexity is matched.
VECA learns effective visual representations using core-periphery attention where patches interact exclusively via a resolution-invariant set of learned core embeddings, achieving linear O(N) complexity while maintaining competitive performance.
PolarAdamW disentangles spectral control from gauge-equivariance in matrix optimizers, with experiments demonstrating their distinct roles on standard versus symmetry-aware neural networks.
MuonEq introduces pre-orthogonalization equilibration schemes that improve Muon optimizer performance during large language model pretraining.
SF-NorMuon is a new schedule-free spectral optimizer that closes the gap with tuned AdamW on 125M-772M parameter models across 1-8x Chinchilla horizons while providing stationarity guarantees.
Pion is an optimizer that preserves the singular values of weight matrices in LLM training by applying orthogonal equivalence transformations.
MuonQ achieves stable 4-bit quantization of Muon optimizer states via pre-quantization normalization, singular component decomposition with power iteration, and μ-law companding, matching full-precision loss and accuracy on GPT and LLaMA models with up to 7.3x memory savings.
RMNP preconditions matrix updates via row-wise L2 normalization instead of Newton-Schulz iteration, reducing complexity to O(mn) while matching Muon's non-convex convergence rate and empirical performance.
HTMuon modifies Muon to produce heavier-tailed updates and weight spectra via HT-SR theory, yielding up to 0.98 lower perplexity on LLaMA pretraining and serving as a plug-in for other Muon variants.
Muon+ adds one normalization step after polar orthogonalization in the Muon optimizer, yielding lower training and validation perplexity and faster pre-training across 60M-7B 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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Same Architecture, Different Capacity: Optimizer-Induced Spectral Scaling Laws
The same Transformer architecture follows different spectral scaling laws under different optimizers, with Muon achieving linear hard-rank scaling on tail representations while AdamW shows weak scaling, even when perplexity is matched.
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Elastic Attention Cores for Scalable Vision Transformers
VECA learns effective visual representations using core-periphery attention where patches interact exclusively via a resolution-invariant set of learned core embeddings, achieving linear O(N) complexity while maintaining competitive performance.
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PolarAdamW: Disentangling Spectral Control and Schur Gauge-Equivariance in Matrix Optimisation
PolarAdamW disentangles spectral control from gauge-equivariance in matrix optimizers, with experiments demonstrating their distinct roles on standard versus symmetry-aware neural networks.
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MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration
MuonEq introduces pre-orthogonalization equilibration schemes that improve Muon optimizer performance during large language model pretraining.
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Anytime Training with Schedule-Free Spectral Optimization
SF-NorMuon is a new schedule-free spectral optimizer that closes the gap with tuned AdamW on 125M-772M parameter models across 1-8x Chinchilla horizons while providing stationarity guarantees.
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Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
Pion is an optimizer that preserves the singular values of weight matrices in LLM training by applying orthogonal equivalence transformations.
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MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization
MuonQ achieves stable 4-bit quantization of Muon optimizer states via pre-quantization normalization, singular component decomposition with power iteration, and μ-law companding, matching full-precision loss and accuracy on GPT and LLaMA models with up to 7.3x memory savings.
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RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization
RMNP preconditions matrix updates via row-wise L2 normalization instead of Newton-Schulz iteration, reducing complexity to O(mn) while matching Muon's non-convex convergence rate and empirical performance.
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HTMuon: Improving Muon via Heavy-Tailed Spectral Correction
HTMuon modifies Muon to produce heavier-tailed updates and weight spectra via HT-SR theory, yielding up to 0.98 lower perplexity on LLaMA pretraining and serving as a plug-in for other Muon variants.
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MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training
Muon+ adds one normalization step after polar orthogonalization in the Muon optimizer, yielding lower training and validation perplexity and faster pre-training across 60M-7B models.
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