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Free Heavy-Tailed Lunch for Muon: A Theoretical Justification of Empirical Success

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arXiv:2606. 14560v1 Announce Type: cross Abstract: Non-Euclidean optimisation methods with matrix-valued updates, such as Muon and Scion, have recently shown strong empirical performance for training Transformer models, yet their theoretical advantages over Euclidean methods remain poorly understood.

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Authors: Florian H\"ubler, Thomas Pethick, Suvrit Sra
Released: 2026-06-15 (2mo ago)
Topic: Related to current project
Relation to my work: Read next because Free Heavy-Tailed Lunch for Muon: A Theoretical Justification of Empirical Success overlaps with clean result "LoRA persona trained on <A> alone emits <B> at 23.5% when a co-trained partner learns <A>...<B>, vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: strong, under, without, language, model. Source: arxiv stat.ML (Machine Learning).
arXiv: 2606.14560

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