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SignSGD and Muon optimizers' performance gains theoretically explained

Researchers have theoretically analyzed why sign-based optimization algorithms like SignSGD and Muon can outperform standard SGD in training large models. A new study suggests that SignSGD's advantage stems from its effectiveness under specific conditions, such as sparse noise and $\ell_1$-norm stationarity, which standard SGD does not handle as efficiently. Another paper questions the necessity of Muon's complex geometric structure, proposing that simpler methods like random or inverted spectra can achieve similar performance by focusing on local alignment and descent potential. AI

Summary written by gemini-2.5-flash-lite from 4 sources. How we write summaries →

IMPACT Provides theoretical underpinnings for why certain optimizers may be better suited for training large foundation models, potentially guiding future research and development.

RANK_REASON The cluster contains two academic papers analyzing optimization algorithms for machine learning.

Read on arXiv cs.AI →

COVERAGE [4]

  1. arXiv cs.LG TIER_1 · Hongyi Tao, Dingzhi Yu, Lijun Zhang ·

    When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds

    arXiv:2605.06615v1 Announce Type: new Abstract: Sign-based optimization algorithms, such as SignSGD and Muon, have garnered significant attention for their remarkable performance in training large foundation models. Despite this empirical success, we still lack a theoretical unde…

  2. arXiv cs.AI TIER_1 · Lijun Zhang ·

    When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds

    Sign-based optimization algorithms, such as SignSGD and Muon, have garnered significant attention for their remarkable performance in training large foundation models. Despite this empirical success, we still lack a theoretical understanding of when and why these sign-based metho…

  3. arXiv stat.ML TIER_1 · Zakhar Shumaylov, Natha\"el Da Costa, Peter Zaika, B\'alint Mucs\'anyi, Alex Massucco, Yoav Gelberg, Carola-Bibiane Sch\"onlieb, Yarin Gal, Philipp Hennig ·

    Muon is Not That Special: Random or Inverted Spectra Work Just as Well

    arXiv:2605.11181v1 Announce Type: cross Abstract: The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear minimization oracle (LMO) theory. In this paper, we c…

  4. arXiv stat.ML TIER_1 · Philipp Hennig ·

    Muon is Not That Special: Random or Inverted Spectra Work Just as Well

    The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear minimization oracle (LMO) theory. In this paper, we challenge this geometric narrative through three co…