归一化低秩自适应

摘要

尽管低秩适配（LoRA）被广泛用于参数高效的模型适配，但如何规范化其训练动态以实现稳定且有效的优化仍缺乏充分研究。由于LoRA将上投影初始化为零，其早期的优化动态主要由下投影决定。基于这一观察，我们提出了归一化低秩适配（NoRA），这是一种简单而有效的方法，在训练过程中对下投影矩阵进行归一化。我们进一步表明，相同的归一化可以仅在初始化时应用，从而改进标准LoRA，而无需在整个训练过程中反复归一化。在预训练、监督微调和强化学习中，NoRA一致地加速收敛、提升性能和训练稳定性，并缓解灾难性遗忘。这些优势既不需要额外的可训练参数，也不需要推理时的计算开销，使得NoRA成为一种简单且广泛适用的LoRA增强方法。

English

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.