Mitigating Forgetting in Low Rank Adaptation

Parameter-efficient fine-tuning methods, such as Low-Rank Adaptation (LoRA), enable fast specialization of large pre-trained models to different downstream applications. However, this process often leads to catastrophic forgetting of the model's prior domain knowledge. We address this issue with LaLoRA, a weight-space regularization technique that applies a Laplace approximation to Low-Rank Adaptation. Our approach estimates the model's confidence in each parameter and constrains updates in high-curvature directions, preserving prior knowledge while enabling efficient target-domain learning. By applying the Laplace approximation only to the LoRA weights, the method remains lightweight. We evaluate LaLoRA by fine-tuning a Llama model for mathematical reasoning and demonstrate an improved learning-forgetting trade-off, which can be directly controlled via the method's regularization strength. We further explore different loss landscape curvature approximations for estimating parameter confidence, analyze the effect of the data used for the Laplace approximation, and study robustness across hyperparameters.