# Bayesian Mixture of Experts For Large Language Models

arXiv: https://arxiv.org/abs/2511.08968 · HTML: https://mlsanity.com/paper/2511.08968/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 25 of 25)

- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (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)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [Not All Experts are Equal: Efficient Expert Pruning and Skipping for Mixture-of-Experts Large Language Models](https://mlsanity.com/paper/2402.14800/) (2024)
- [Mixout: Effective Regularization to Finetune Large-scale Pretrained Language Models](https://mlsanity.com/paper/1909.11299/) (2019)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [Navigating the Grey Area: How Expressions of Uncertainty and Overconfidence Affect Language Models](https://mlsanity.com/paper/2302.13439/) (2023)
- [LoRA ensembles for large language model fine-tuning](https://mlsanity.com/paper/2310.00035/) (2023)
- [Uncertainty-Penalized Reinforcement Learning from Human Feedback with Diverse Reward LoRA Ensembles](https://mlsanity.com/paper/2401.00243/) (2023)
- [On the Calibration of Pre-trained Language Models using Mixup Guided by Area Under the Margin and Saliency](https://mlsanity.com/paper/2203.07559/) (2022)
- [Preserving Pre-trained Features Helps Calibrate Fine-tuned Language Models](https://mlsanity.com/paper/2305.19249/) (2023)
- [Checkpoint Ensembles: Ensemble Methods from a Single Training Process](https://mlsanity.com/paper/1710.03282/) (2017)
- [Calibrating Transformers via Sparse Gaussian Processes](https://mlsanity.com/paper/2303.02444/) (2023)
- [Gaussian Stochastic Weight Averaging for Bayesian Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2405.03425/) (2024)
- [Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation](https://mlsanity.com/paper/2006.07584/) (2020)
- [Pathologies in priors and inference for Bayesian transformers](https://mlsanity.com/paper/2110.04020/) (2021)

## Built on by (most cited first, 4 of 4)

- [Variational Inference, Entropy, and Orthogonality: A Unified Theory of Mixture-of-Experts](https://mlsanity.com/paper/2601.03577/) (2026)
- [Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers](https://mlsanity.com/paper/2603.09453/) (2026)
- [Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation](https://mlsanity.com/paper/2602.01956/) (2026)
- [Infinite-Parameter LLMs: Generating and Adapting Weights from Live Data](https://mlsanity.com/paper/2609.18842/) (2026)

## Abstract (arXiv)

We present Bayesian Mixture of Experts (Bayesian-MoE), a post-hoc uncertainty estimation framework for fine-tuned large language models (LLMs) based on Mixture-of-Experts architectures. Our method applies a structured Laplace approximation to the second linear layer of each expert, enabling calibrated uncertainty estimation without modifying the original training procedure or introducing new parameters. Unlike prior approaches, which apply Bayesian inference to added adapter modules, Bayesian-MoE directly targets the expert pathways already present in MoE models, leveraging their modular design for tractable block-wise posterior estimation. We use Kronecker-factored low-rank approximations to model curvature and derive scalable estimates of predictive uncertainty and marginal likelihood. Experiments on common-sense reasoning benchmarks with Qwen1.5-MoE and DeepSeek-MoE demonstrate that Bayesian-MoE improves both expected calibration error (ECE) and negative log-likelihood (NLL) over baselines, confirming its effectiveness for reliable downstream decision-making.