# BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Models

arXiv: https://arxiv.org/abs/2406.11675 · HTML: https://mlsanity.com/paper/2406.11675/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 87 of its 123 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 30 of 87)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [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)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Ethical and social risks of harm from Language Models](https://mlsanity.com/paper/2112.04359/) (2021)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)

## Built on by (most cited first, 30 of 50)

- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [On Calibration of LLM-based Guard Models for Reliable Content Moderation](https://mlsanity.com/paper/2410.10414/) (2024)
- [Training-Free Bayesianization for Low-Rank Adapters of Large Language Models](https://mlsanity.com/paper/2412.05723/) (2024)
- [Scalable Bayesian Low-Rank Adaptation of Large Language Models via Stochastic Variational Subspace Inference](https://mlsanity.com/paper/2506.21408/) (2025)
- [C-LoRA: Contextual Low-Rank Adaptation for Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2505.17773/) (2025)
- [Beyond Markovian: Reflective Exploration via Bayes-Adaptive RL for LLM Reasoning](https://mlsanity.com/paper/2505.20561/) (2025)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Random-Set Large Language Models](https://mlsanity.com/paper/2504.18085/) (2025)
- [Functional-level Uncertainty Quantification for Calibrated Fine-tuning on LLMs](https://mlsanity.com/paper/2410.06431/) (2024)
- [Improving LoRA with Variational Learning](https://mlsanity.com/paper/2506.14280/) (2025)
- [Promoting Ensemble Diversity with Interactive Bayesian Distributional Robustness for Fine-tuning Foundation Models](https://mlsanity.com/paper/2506.07247/) (2025)
- [Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers](https://mlsanity.com/paper/2603.09453/) (2026)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [SOAP-Bubbles: Structured Weight Uncertainty for Neural Networks](https://mlsanity.com/paper/2606.23357/) (2026)
- [Uncertainty-Aware Adaptation of Large Language Models for Protein-Protein Interaction Analysis](https://mlsanity.com/paper/2502.06173/) (2025)
- [PoGDiff: Product-of-Gaussians Diffusion Models for Imbalanced Text-to-Image Generation](https://mlsanity.com/paper/2502.08106/) (2025)
- [Toward Efficient Uncertainty in LLMs through Evidential Knowledge Distillation](https://mlsanity.com/paper/2507.18366/) (2025)
- [Fine-tuning LLMs with variational Bayesian last layer for high-dimensional Bayesian optimization](https://mlsanity.com/paper/2510.01471/) (2025)
- [Bayesian-LoRA: Probabilistic Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2601.21003/) (2026)
- [Scalable Variational Bayesian Fine-Tuning of LLMs via Orthogonalized Low-Rank Adapters](https://mlsanity.com/paper/2604.03388/) (2026)
- [BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2606.29184/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [Dist2ill: Distributional Distillation for One-Pass Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2505.11731/) (2025)
- [Learning Adapter Rank via Symmetry Breaking](https://mlsanity.com/paper/2506.22809/) (2025)
- [Meta-Learning at Scale for Large Language Models via Low-Rank Amortized Bayesian Meta-Learning](https://mlsanity.com/paper/2508.14285/) (2025)
- [Bayesian Low-Rank Factorization for Robust Model Adaptation](https://mlsanity.com/paper/2510.18723/) (2025)
- [Quantifying the Uncertainty of Foundation Models with Singular Value Ensembles](https://mlsanity.com/paper/2601.22068/) (2026)
- [Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation](https://mlsanity.com/paper/2602.01956/) (2026)
- [Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation](https://mlsanity.com/paper/2602.15925/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) often suffer from overconfidence during inference, particularly when adapted to downstream domain-specific tasks with limited data. Previous work addresses this issue by employing approximate Bayesian estimation after the LLMs are trained, enabling them to quantify uncertainty. However, such post-training approaches' performance is severely limited by the parameters learned during training. In this paper, we go beyond post-training Bayesianization and propose Bayesian Low-Rank Adaptation by Backpropagation (BLoB), an algorithm that continuously and jointly adjusts both the mean and covariance of LLM parameters throughout the whole fine-tuning process. Our empirical results verify the effectiveness of BLoB in terms of generalization and uncertainty estimation, when evaluated on both in-distribution and out-of-distribution data.