cs.AIJun 11, 2026

The Hidden Power of Scaling Factor in LoRA Optimization

Authors: Zicheng ZhangHaoran LiJiaxing WangGuoqiang GongAnqi LiYudong HuTing XiongYurong Gao+5 more

Abstract

In Low-Rank Adaptation (LoRA), the scaling factor αα is often treated as a mere complement to the learning rate, yet its role in optimization remains poorly understood. In this paper, we reveal that the scaling factor αα and the learning rate function differently, with αα emerging as the dominant driver of effective optimization, delivering gains that cannot be replicated by learning rate scaling alone. Through the synergy of extensive empirical analysis and a theoretical Signal-Drift framework, we uncover three findings into LoRA's scaling mechanism: First, LoRA's spectral suppression smooths the optimization landscape, rendering standard hyperparameters overly conservative and creating an optimization gap. Second, when leveraging this smoothness to accelerate convergence, αα outperforms the learning rate by amplifying the task signal without increasing the drift ratio. Third, the optimal scaling factor follows a sublinear relationship with the rank, well characterized by a square-root law with an unexpectedly large coefficient, revealing the insufficient scaling of existing rank-tied heuristics. Based on these insights, we propose LoRA-αα, a minimalist framework that restores αα to its principled regime, making LoRA compatible with standard small learning rates. Extensive evaluations across diverse tasks demonstrate that LoRA-αα consistently improves performance while streamlining hyperparameter search, unleashing the learning potential of LoRA.

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