正規化低秩適應

摘要

雖然低秩適應（LoRA）廣泛用於參數高效的模型適配，但如何對其訓練動態進行正則化以實現穩定且有效的優化，仍未被充分探索。由於 LoRA 將上投影初始化為零，其早期優化動態主要由下投影主導。基於此觀察，我們提出歸一化低秩適應（NoRA），一種簡單而有效的方法，在訓練期間對下投影矩陣進行歸一化。我們進一步證明，同樣的歸一化可以僅在初始化時應用，從而改善標準 LoRA，無需在整個訓練過程中重複歸一化。在預訓練、監督式微調和強化學習中，NoRA 持續加速收斂、提升效能與訓練穩定性，並緩解災難性遺忘。這些優勢既不需要額外的可訓練參數，也不需要推論時的計算，使 NoRA 成為一種簡單且廣泛適用的 LoRA 增強方法。

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.