math.NA · 2026-06-26 · No. 35

Numerical Analysis, 2026-06-26.

2 new papers in math.NA. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Hierarchical Muon: Tiled Newton-Schulz Updates for Efficient Muon Optimization

    Ziyuan Tang, Tianshi Xu, Yousef Saad, Yuanzhe Xi

    math.NA · cs.LG

    Muon-type optimizers construct update directions for dense neural-network weights by applying a finite Newton-Schulz map to momentum-gradient matrices. For an $H \times W$ matrix, with $r=\min\{H,W\}$ and $s=\max\{H,W\}$, $K$ steps of the full-matrix Newton-Schulz update require $O(r^2 s K)$ work and couple all rows and columns through repeated Gram matrix products. We introduce Hierarchical Muon (HiMuon), a tiled Newton-Schulz scheme for...

    arxiv.org/abs/2606.27216 · PDF

  2. 02

    Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics

    Benedict Leimkuhler, Peter A. Whalley

    math.NA · cs.LG · stat.CO

    We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and \emph{position-adaptive Langevin} (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact...

    arxiv.org/abs/2606.26881 · PDF

This edition is part of The Daily Abstract — math.NA archive. Subscribe to receive these in your inbox each morning, automatically translated to Spanish, with reply-to-PDF: arxivdaily.ignorelist.com.

Colophon Set in Georgia, with system sans for interface chrome and a monospaced stack for code and paper identifiers. Sole accent: amber #D99C5E. Built and served on an always-free VM. The masthead is set 14% letterspaced because newspapers do that and it works.