Normalized Low-Rank Adaptation

arXiv:2608.31036v1 Announce Type: new Abstract: While low-rank adaptation (LoRA) is widely used for parameter-efficient model adaptation, how to regularize its training dynamics for stable and effective optimization remains underexplored. Because LoRA initializes the up-projection to zero, its early optimization dynamics are largely governed by the down-projection. Building on this observation, we introduce Normalized Low-Rank Adaptation (NoRA), a simple yet effective method that normalizes the down-projection matrices during training. We further show that the same normalization can be applied only at initialization, improving standard LoRA without requiring repeated normalization throughout training. Across pretraining, supervised finetuning, and reinforcement learning, NoRA consistently accelerates convergence, improves performance and training stability, and mitigates catastrophic forgetting. These benefits require neither additional trainable parameters nor inference-time computation, making NoRA a simple and broadly applicable enhancement to LoRA.

Related

• EulerLoRA: Rank-Driven Jump Dynamics for Calibrated Parameter-Efficient Fine-Tuning
• Understanding Catastrophic Forgetting In LoRA via Mean-Field Attention Dynamics
• On the Construction and Implications of Low-Loss Valleys in LoRA-based Bayesian Inference

Source: arXiv cs.LG | 2026-09-01