Spectral clipping of leading singular values in gradient matrices stabilizes SGD for non-convex problems with heavy-tailed noise and achieves the optimal convergence rate O(K^{(2-2α)/(3α-2)}).
Hübler, I
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Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.
GT-NSGDm achieves the optimal non-asymptotic convergence rate O(1/T^{(p-1)/(3p-2)}) for decentralized nonconvex stochastic optimization under zero-mean heavy-tailed noise with p-th moment.
LionMuon alternates Lion sign steps and Muon spectral steps with shared dual-EMA momentum to match Lion memory while outperforming both at P=2 on 124M-720M models, backed by heavy-tailed complexity bounds that predict the optimal period.
RSC-ZO achieves high-probability ε-stationary points for stochastic ZO optimization under weak-L_p heavy-tailed noise with Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) function queries.
citing papers explorer
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Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters
Spectral clipping of leading singular values in gradient matrices stabilizes SGD for non-convex problems with heavy-tailed noise and achieves the optimal convergence rate O(K^{(2-2α)/(3α-2)}).
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Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition
Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.
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Decentralized Nonconvex Optimization under Heavy-Tailed Noise: Normalization and Optimal Convergence
GT-NSGDm achieves the optimal non-asymptotic convergence rate O(1/T^{(p-1)/(3p-2)}) for decentralized nonconvex stochastic optimization under zero-mean heavy-tailed noise with p-th moment.
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LionMuon: Alternating Spectral and Sign Descent for Efficient Training
LionMuon alternates Lion sign steps and Muon spectral steps with shared dual-EMA momentum to match Lion memory while outperforming both at P=2 on 124M-720M models, backed by heavy-tailed complexity bounds that predict the optimal period.
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Stochastic Zeroth-Order Optimization Under Heavy-Tailed Noise
RSC-ZO achieves high-probability ε-stationary points for stochastic ZO optimization under weak-L_p heavy-tailed noise with Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) function queries.