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Dmitrii Andriianov

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#machine learning Preprint Sep 2026

LoRA-TSD: Tangent-Space Spectral Descent for LoRA via Muon-Style Updates

LoRA-TSD, an optimizer that treats every LoRA step as a tangent vector of the fixed-rank matrix manifold and takes the spectral-norm steepest-descent step of Muon inside that tangent space, mapping the result back to the factors through a retraction native to the LoRA parametrization, is introduced.

Dmitrii Andriianov, Andrey Veprikov, A. Beznosikov · 0 citations