Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
Sophie Weber
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We introduce Pion, a spectrum-preserving optimizer for large language model (LLM) training based on orthogonal equivalence transformation. Unlike…
Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
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 orthogonal transformations, preserving its singular values throughout training. This yields an optimization mechanism that modulates the geometry of weight matrices while keeping their spectral norm fixed. We derive the Pion update rule, systematically examine its design choices, and analyze its convergence behavior along with several key properties. Empirical results show that Pion offers a stable and competitive alternative to standard optimizers for both LLM pretraining and finetuning.
Source
Original Article: Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
Published: May 12, 2026
Author: Kexuan Shi
Disclaimer: This article is for informational purposes only and does not constitute financial advice. Consult a licensed financial advisor before making investment decisions.
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Sophie Weber tests and evaluates AI tools for finance and accounting. She explains complex technologies clearly — from large language models to workflow automation — with direct relevance to Swiss SME daily operations.
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References
- [1]NewsCredibility: 9/10ArXiv AI Papers. "Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation." May 12, 2026.
Transparency Notice: This article may contain AI-assisted content. All citations link to verified sources. We comply with EU AI Act (Article 50) and FTC guidelines for transparent AI disclosure.
Original Source
This article is based on Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation (ArXiv AI Papers)
