arXiv:2603. 09923v4 Announce Type: replace Abstract: Exponential moving averages (EMAs) are a central component of widely used adaptive optimizers such as Adam.
By Ganzhao Yuan
arXiv:2609.13677v1 Announce Type: cross
Abstract: Modern real application problems involve matrix-valued parameters, yet conventional optimizers treat them as vectors, thereby motivating matrix-aware...
By Lexiao Lai, Tianyi Lin, Jiayu Zhang
arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.
By Francisco Patitucci, Aryan Mokhtari
arXiv:2609.39595v1 Announce Type: new
Abstract: Practical Muon maintains momentum and performs a small, fixed number of Newton--Schulz iterations separately for each parameter matrix, often with a Ne...
By Hanyng Peng, Hui Wang, Yue Yu
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.
By Haoyuan Cai, Sulaiman A. Alghunaim, Ali H. Sayed
The paper introduces a unified framework for first‑order optimization algorithms applied to nonconvex unconstrained problems. It incorporates adaptively preconditioned gradients and covers popular methods such as full and diagonal AdaGrad, AdaNorm, and an adaptive variant of Muon. The framework supports heterogeneous geometries across variable groups and provides a fully stochastic global convergence analysis for all methods, with or without two types of momentum, under reasonable variance assumptions without requiring bounded stochastic gradients or small step sizes.
By S. Gratton, Ph. L. Toint