math.OC · 2026-06-15 · No. 24
Optimization and Control, 2026-06-15.
2 new papers in math.OC. Titles, authors,
abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →
01 — The papers
2 entries-
01
Free Heavy-Tailed Lunch for Muon: A Theoretical Justification of Empirical Success
Florian Hübler, Thomas Pethick, Suvrit Sra
math.OC · cs.LG · stat.ML
Non-Euclidean optimisation methods with matrix-valued updates, such as Muon and Scion, have recently shown strong empirical performance for training Transformer models, yet their theoretical advantages over Euclidean methods remain poorly understood. We address this gap in the heavy-tailed non-convex regime, where stochastic gradients have bounded $p$-th central moments, $p \in (1,2]$. We show that certain non-Euclidean methods achieve...
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02
Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory
Pekka Malo, Lauri Viitasaari, Patrik Nummi, Antti Suominen, Ankur Sinha, Olli Tahvonen
math.OC · cs.LG · cs.NE · math.NA · stat.ML
Population-based and distributional optimization methods, from evolution strategies and consensus-based optimization to covariance-matrix adaptation and stochastic gradient methods viewed as distributional dynamics, are widely used for nonconvex or black-box problems, yet their convergence analyses remain fragmented across algorithm-specific techniques. We introduce an operator calculus in which a broad class of such methods, after choosing...
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