Training-Free Bayesianization for Low-Rank Adapters of Large Language Models

Hao Wang (City University of Hong Kong) · Haizhou Shi (Rutgers University) · Yibin Wang (Huazhong University of Science and Technology) · Ligong Han (Rutgers University) · Huan Zhang (UIUC)

bayesian methodsbayesian transformationfine-tuning generalizationisotropic gaussian distributionskl-regularized variational optimizationlow-rank adapterslow-rank weight updatespost-training proceduressearch processtheoretical analysistraining-free bayesianizationuncertainty estimation variational inferenceweight posterior

Estimating the uncertainty of responses from Large Language Models (LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose **T**raining-**F**ree **B**ayesianization (**TFB**), a simple yet theoretically grounded framework that efficiently transforms trained low-rank adapters into Bayesian ones without additional training. TFB systematically searches for the maximally acceptable level of variance in the weight posterior, constrained within a family of low-rank isotropic Gaussian distributions. Our theoretical analysis shows that under mild conditions, this search process is equivalent to KL-regularized variational optimization, a generalized form of variational inference. Through comprehensive experiments, we show that TFB achieves superior uncertainty estimation and generalization compared to existing methods while eliminating the need for complex Bayesianization training procedures.