Parameter Efficient Fine-tuning via Explained Variance Adaptation

Fabian Paischer, Lukas Hauzenberger, Thomas Schmied, Benedikt Alkin, Marc Peter Deisenroth, Sepp Hochreiter

Keywords: Foundation Models, PEFT, LoRA

TL;DR: We propose EVA, a parameter-efficient fine-tuning method that initalizes LoRA weights in a variance-optimal manner and performs adaptive rank allocation to provably maximize the expected gradient signal at the beginning of fine-tuning.

Abstract:

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned for a specific downstream task. The most common fine-tuning method is to update pretrained weights via low-rank adaptation (LoRA). Existing initialization strategies for LoRA often rely on singular value decompositions (SVD) of gradients or weight matrices. However, they do not provably maximize the expected gradient signal, which is critical for fast adaptation. To this end, we introduce **E**xplained **V**ariance **A**daptation (EVA), an initialization scheme that uses the directions capturing the most activation variance, provably maximizing the expected gradient signal and accelerating fine-tuning. EVA performs incremental SVD on minibatches of activation vectors and selects the right-singular vectors for initialization once they converged. Further, by selecting the directions that capture the most activation-variance for a given rank budget, EVA accommodates adaptive ranks that reduce the number of trainable parameters. We apply EVA to a variety of fine-tuning tasks as language generation and understanding, 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. In summary, EVA establishes a new Pareto frontier compared to existing LoRA
initialization schemes in both accuracy and efficiency.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 16283