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cs.LG2026
Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko +2
Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many mode…
cs.LG2025
LoRA meets Riemannion: Muon Optimizer for Parametrization-independent Low-Rank Adapters
Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko +4
This work presents a novel, fully Riemannian framework for Low-Rank Adaptation (LoRA) that geometrically treats low-rank adapters by optimizing them directly on the fixed-rank mani…