GPan-LoRA: Gaussian Process Amortized Networks for Bayesian Low-Rank Adaptation in Large Language Models

Principled uncertainty quantification (UQ) is increasingly recognized as essential for trustworthy artificial general intelligence (AGI). Bayesian Low-Rank Adaptation (LoRA) provides a principled mechanism for uncertainty-aware fine-tuning of large language models (LLMs). However, existing techniques either face scalability constraints, e.g. Laplace-LoRA, or rely on approximate inference schemes that lead to poorly calibrated posterior uncertainty, often manifesting as overconfident predictions under distribution shift. To address this challenge, we propose GPan-LoRA, the first scalable Gaussian Process (GP)-based framework for Bayesian LoRA, which integrates neural network-based sparse GP approximations with amortized variational inference. By preserving the Bayesian function prior and posterior semantics intrinsic to GPs, GPan-LoRA achieves a faithful balance between computational scalability and principled UQ. Empirically, GPan-LoRA produces well-calibrated uncertainty that remains reliable under distribution shift, mitigating overconfident failures while preserving competitive task performance.