Abstract: Low-Rank Adaptation (LoRA) is an effective fine-tuning algorithm for large models, enabling efficient adaptation with fewer trainable parameters. Despite its success, there remains significant potential for improving LoRA's performance. In this paper, we introduce iLoRA (Imbalance-Regularized LoRA), which enhances LoRA by incorporating a regularization term to capture the imbalance in forward propagation. This regularization maintains an imbalance between matrices $\mathbf{A}$ and $\mathbf{B}$, ensuring stable activation variance independent of dimension. Specifically, we first analyze forward dynamics, observe this imbalance in stable training, and introduce imbalanced regularization. Further, by combining this with preconditioning techniques [Zhang and Pilanci, 2024], we propose $\pi$-LoRA (Preconditioned iLoRA), which improves the backpropagation process. Our method is a plug-and-play algorithm that requires only minor modifications to the existing code and incurs negligible additional computational overhead. Finally, experiments on large language models and text-to-image models demonstrate that iLoRA and $\pi$-LoRA significantly outperform existing LoRA and preconditioned LoRA methods.