# BaRA: Bayesian Adaptive Rank Allocation for Parameter-Efficient Fine-Tuning

arXiv: https://arxiv.org/abs/2606.29184 · HTML: https://mlsanity.com/paper/2606.29184/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 59 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 30 of 50)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [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)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)

## Built on by (most cited first, 2 of 2)

- [Statistical Inference for Rank Allocation in Low-Rank Adaptation](https://mlsanity.com/paper/2607.20205/) (2026)
- [Automatic Rank Allocation for Low-Rank Adaptation in Large Language Models via lp Regularization](https://mlsanity.com/paper/2609.28998/) (2026)

## Abstract (arXiv)

While Low-rank adaptation (LoRA) enables highly efficient fine-tuning by constraining task-specific updates to fixed low-rank subspaces, this rigid design limits representational flexibility and often results in overconfident predictions and miscalibrated uncertainty, especially in low-data regimes. Recent Bayesian LoRA variants improve uncertainty estimation by modeling posterior distributions over adaptation parameters. However, these approaches typically rely on fixed or heuristically determined ranks, overlooking the inherently context-dependent nature of adaptation capacity. In this paper, we propose BaRA, a Bayesian Adaptive Rank Allocation framework for parameter-efficient fine-tuning. Drawing inspiration from probabilistic topic models, BaRA dynamically allocates adaptation capacity by activating a sparse, context-dependent subset of disentangled latent factors, enabling instance-wise variation in effective rank. This Bayesian formulation provides principled, data-driven capacity control, mitigating over-parameterization while preserving expressiveness. Beyond the modeling contribution, we provide a complexity-theoretic generalization analysis showing that the generalization gap of BaRA depends on the learned joint effective rank barsPhi,θ induced by the global-local gate, rather than the maximum rank r. This result explains why sparse adaptive rank allocation can reduce the effective hypothesis complexity while preserving input-dependent expressiveness. Extensive experiments on diverse natural language benchmarks demonstrate that BaRA consistently improves predictive performance, robustness, and uncertainty calibration compared to standard LoRA and existing Bayesian LoRA variants.