Minimal Ranks, Maximum Confidence: Parameter-efficient Uncertainty Quantification for LoRA

TL;DR

This paper introduces a parameter-efficient Bayesian LoRA method that models uncertainty effectively in low-dimensional spaces, maintaining efficiency and improving calibration for large language models.

Contribution

It proposes a novel subspace inference approach for Bayesian LoRA, enabling effective uncertainty quantification with minimal additional parameters.

Findings

Uncertainty can be modeled in low-dimensional spaces effectively.

Weight covariances exhibit low ranks.

The method improves calibration and generalization.

Abstract

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language 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 parameter-efficient Bayesian LoRA via subspace inference, 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: (1) uncertainty can be effectively modeled in a low-dimensional space, and (2) weight covariances exhibit low ranks.