# Bayesian Sparse Low-Rank Adaptation for Large Language Model Uncertainty Estimation

arXiv: https://arxiv.org/abs/2607.02182 · HTML: https://mlsanity.com/paper/2607.02182/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 38)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [LoRA ensembles for large language model fine-tuning](https://mlsanity.com/paper/2310.00035/) (2023)
- [BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Models](https://mlsanity.com/paper/2406.11675/) (2024)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Uncertainty quantification in fine-tuned LLMs using LoRA ensembles](https://mlsanity.com/paper/2402.12264/) (2024)
- [ALoRA: Allocating Low-Rank Adaptation for Fine-tuning Large Language Models](https://mlsanity.com/paper/2403.16187/) (2024)
- [Calibrating LLMs with Information-Theoretic Evidential Deep Learning](https://mlsanity.com/paper/2502.06351/) (2025)
- [Training-Free Bayesianization for Low-Rank Adapters of Large Language Models](https://mlsanity.com/paper/2412.05723/) (2024)
- [Dynamic Low-Rank Sparse Adaptation for Large Language Models](https://mlsanity.com/paper/2502.14816/) (2025)
- [C-LoRA: Contextual Low-Rank Adaptation for Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2505.17773/) (2025)
- [UQLM: A Python Package for Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2507.06196/) (2025)
- [A Guardrail for Safety Preservation: When Safety-Sensitive Subspace Meets Harmful-Resistant Null-Space](https://mlsanity.com/paper/2510.14301/) (2025)
- [Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answering](https://mlsanity.com/paper/2510.02671/) (2025)
- [Functional-level Uncertainty Quantification for Calibrated Fine-tuning on LLMs](https://mlsanity.com/paper/2410.06431/) (2024)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.