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News/Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
arxiv
PublishedMay 13, 2026 at 4:00 AM

Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation

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arXiv:2605.12492v1 Announce Type: new Abstract: We introduce Pion, a spectrum-preserving optimizer for large language model (LLM) training based on orthogonal equivalence transformation. Unlike additive optimizers such as Adam and Muon, Pion updates each weight matrix through left and right orthogon

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