One Initialization to Rule them All: Fine-tuning via Explained Variance Adaptation

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned on a downstream task for a specific application. The most successful and most commonly used fine-tuning method is to update the pre-trained weights via a low-rank adaptation (LoRA). LoRA introduces new weight matrices that are usually initialized at random with a uniform rank distribution across the model weights. Recent works focus on different initialization schemes or the learning of adaptive ranks during fine-tuning. Both approaches have only been investigated in isolation, resulting in slow convergence or a uniform rank distribution, in turn leading to suboptimal performance. We propose to improve LoRA by initializing the new weights in a data-driven manner by computing singular value decomposition (SVD) on minibatches of activation vectors. Then, we initialize the LoRA matrices with the obtained right-singular vectors and redistribute ranks among all weight matrices to provably store the maximum amount of information of the downstream data in the newly introduced weights. In this way, only what information to maintain or neglect during the fine-tuning process needs to be learned. We call our new method Explained Variance Adaptation (EVA). We apply EVA to a variety of fine-tuning tasks ranging from language generation and understanding to image classification and reinforcement learning. EVA exhibits faster convergence than competitors and achieves the highest average score across a multitude of tasks per domain while reducing the number of trainable parameters through rank redistribution.