@inproceedings{pang-etal-2026-htmuon,
    title = "{HTM}uon: Improving Muon via Heavy-Tailed Spectral Correction",
    author = "Pang, Tianyu  and
      Fang, Yujie  and
      Liu, Zihang  and
      Deng, Shenyang  and
      Hsiung, Lei  and
      Yu, Shuhua  and
      Yang, Yaoqing",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.1819/",
    pages = "36504--36535",
    ISBN = "979-8-89176-395-1",
    abstract = "has recently shown promising results in LLM training. In this work, we study how to further improve . We argue that `s orthogonalized update rule suppresses the emergence of heavy-tailed weight spectra and over-emphasizes the training along noise-dominated directions. Motivated by the Heavy-Tailed Self-Regularization (HT-SR) theory, we propose . preserves `s ability to capture parameter interdependencies while producing heavier-tailed updates and inducing heavier-tailed weight spectra. Experiments on LLM pretraining and image classification show that consistently improves performance over state-of-the-art baselines and can also serve as a plug-in on top of existing variants. For example, on LLaMA pretraining on the C4 dataset, reduces perplexity by up to 0.98 compared to . We further theoretically show that corresponds to steepest descent under the Schatten-$q$ norm constraint and provide convergence analysis in smooth non-convex settings. The implementation of is available at \url{https://github.com/TDCSZ327/HTmuon}."
}