Rotated Manifold Optimization for Low-Rank Adaptation

Yuhui Ding; Javier Zazo; James Hensman

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arXiv · 2609.34264

Rotated Manifold Optimization for Low-Rank Adaptation

Yuhui Ding·Javier Zazo·James Hensman

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Abstract

We propose a novel optimizer for low-rank adaptation (LoRA) that explicitly incorporates the gauge symmetry of low-rank factorization. Our optimizer extends recent matrix optimizers for full-parameter training to the manifold of fixed-rank matrices by interpreting them as normalization under a rotated basis. We show how rotation and normalization can be integrated with the fixed-rank manifold efficiently. Our optimizer converges faster to lower held-out loss and achieves better or comparable downstream performance on both supervised finetuning and reinforcement learning tasks.

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Yuhui Ding, Javier Zazo, James Hensman. 2026-09-28. Rotated Manifold Optimization for Low-Rank Adaptation. https://arxiv.org/abs/2609.34264

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