Andrey Veprikov

MAdam: MLMC Adam under Markovian Noise with Application to Average-Reward Policy Optimization

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

This work proposes LionMuon, which retains the effectiveness of Muon steps while considerably cutting the averaged iteration cost, similar to sign-based methods, and proves sharp complexity bounds under heavy-tailed noise which are governed by period-averaged smoothness and noise that interpolate between Muon's and Lio...

LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates

LoRA-TSD, an optimizer that treats every LoRA step as a tangent vector of the fixed-rank matrix manifold and takes the spectral-norm steepest-descent step of Muon inside that tangent space, mapping the result back to the factors through a retraction native to the LoRA parametrization, is introduced.