Bayesian Fine-tuning in Projected Subspaces

TL;DR

This paper introduces a Bayesian fine-tuning framework that models uncertainty efficiently in low-dimensional subspaces, improving calibration and generalization of large models.

Contribution

It presents a novel method for Bayesian fine-tuning that maintains efficiency by operating in projected low-dimensional spaces, addressing calibration and stability issues.

Findings

Effective uncertainty quantification in very low-dimensional spaces.

Weight covariances exhibit low ranks, enabling efficient modeling.

Improved calibration and generalization performance.

Abstract

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks mechanisms for uncertainty quantification, leading to overconfident and poorly calibrated models. Bayesian variants of LoRA address this limitation, but at the cost of a significantly increased number of trainable parameters, partially offsetting the original efficiency gains. Additionally, these models are harder to train and may suffer from unstable convergence. In this work, we propose a novel framework for parameter-efficient Bayesian fine-tuning, demonstrating that effective uncertainty quantification can be achieved in very low-dimensional parameter spaces. The proposed method achieves strong performance with improved calibration and generalization while maintaining computational efficiency. Our empirical findings show that, with the appropriate projection of the weight space uncertainty can be effectively modeled in a low-dimensional space, and weight covariances exhibit low ranks.