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.
arXiv preprint arXiv:2511.00674 , year=
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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.
Full finetuning with the pretraining optimizer reduces forgetting compared to other optimizers or LoRA while achieving comparable new-task performance.
Muon-OGD integrates Muon-style spectral-norm geometry with orthogonal gradient constraints to improve the stability-plasticity trade-off during sequential LLM adaptation.
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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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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Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning
Muon-OGD integrates Muon-style spectral-norm geometry with orthogonal gradient constraints to improve the stability-plasticity trade-off during sequential LLM adaptation.
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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.