@misc{xie-2026-derivative-free-muon,
  author        = {Pengcheng Xie},
  title         = {Derivative-Free Structured Updates for {Muon}},
  year          = {2026},
  month         = sep,
  eprint        = {2609.17759},
  archivePrefix = {arXiv},
  doi           = {10.48550/arXiv.2609.17759},
  url           = {https://arxiv.org/abs/2609.17759},
  keywords      = {machine learning, optimization}
}

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