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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DP-Muon adapts matrix-orthogonalized momentum optimization to differential privacy via per-matrix clipping and noise addition, with proofs of inherited privacy and optimization guarantees plus a bias-corrected version that improves private fine-tuning utility.
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.
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 achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
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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DP-Muon: Differentially Private Optimization via Matrix-Orthogonalized Momentum
DP-Muon adapts matrix-orthogonalized momentum optimization to differential privacy via per-matrix clipping and noise addition, with proofs of inherited privacy and optimization guarantees plus a bias-corrected version that improves private fine-tuning utility.
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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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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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Dimension-Free Saddle-Point Escape in Muon
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.