# Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2503.17523 · HTML: https://mlsanity.com/paper/2503.17523/

## Key facts

- Cited by 37 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 65 of its 103 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## 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 65)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)

## Built on by (most cited first, 30 of 37)

- [Learning Personalized Agents from Human Feedback](https://mlsanity.com/paper/2602.16173/) (2026)
- [BASIL: Bayesian Assessment of Sycophancy in LLMs](https://mlsanity.com/paper/2508.16846/) (2025)
- [Agentic Forecasting using Sequential Bayesian Updating of Linguistic Beliefs](https://mlsanity.com/paper/2604.18576/) (2026)
- [Always Tell Me The Odds: Fine-grained Conditional Probability Estimation](https://mlsanity.com/paper/2505.01595/) (2025)
- [Beyond Markovian: Reflective Exploration via Bayes-Adaptive RL for LLM Reasoning](https://mlsanity.com/paper/2505.20561/) (2025)
- [Shoot First, Ask Questions Later? Building Rational Agents that Explore and Act Like People](https://mlsanity.com/paper/2510.20886/) (2025)
- [Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2509.10739/) (2025)
- [Language-Informed Synthesis of Rational Agent Models for Grounded Theory-of-Mind Reasoning On-The-Fly](https://mlsanity.com/paper/2506.16755/) (2025)
- [Martingale Score: An Unsupervised Metric for Bayesian Rationality in LLM Reasoning](https://mlsanity.com/paper/2512.02914/) (2025)
- [LLMs are not (consistently) Bayesian: Quantifying internal (in)consistencies of LLMs' probabilistic beliefs](https://mlsanity.com/paper/2605.06915/) (2026)
- [Timely Clinical Diagnosis through Active Test Selection](https://mlsanity.com/paper/2510.18988/) (2025)
- [Scaling Law in LLM Simulated Personality: More Detailed and Realistic Persona Profile Is All You Need](https://mlsanity.com/paper/2510.11734/) (2025)
- [Position: agentic AI orchestration should be Bayes-consistent](https://mlsanity.com/paper/2605.00742/) (2026)
- [Revealed Rationality: Label-Free Evaluation and Regularization from Representation Theorems](https://mlsanity.com/paper/2608.05015/) (2026)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)
- [Emergent Bayesian Behaviour and Optimal Cue Combination in LLMs](https://mlsanity.com/paper/2512.02719/) (2025)
- [Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI](https://mlsanity.com/paper/2603.18104/) (2026)
- [Empirical Characterization of Inference-Time Elicited Probability Transformations in Large Language Models](https://mlsanity.com/paper/2603.19262/) (2026)
- [Analytica: Soft Propositional Reasoning for Robust and Scalable LLM-Driven Analysis](https://mlsanity.com/paper/2604.23072/) (2026)
- [Hypothesis generation and updating in large language models](https://mlsanity.com/paper/2605.05851/) (2026)
- [ANCHOR: Abductive Network Construction with Hierarchical Orchestration for Reliable Probability Inference in Large Language Models](https://mlsanity.com/paper/2605.10328/) (2026)
- [When Does In-Context Search Help? A Sampling-Complexity Theory of Reflection-Driven Reasoning](https://mlsanity.com/paper/2607.06720/) (2026)
- [Hypotheses-Guided Self Distillation for Continual Personalization](https://mlsanity.com/paper/2609.00251/) (2026)
- [Tutorial on Reasoning for IR & IR for Reasoning](https://mlsanity.com/paper/2602.03640/) (2026)
- [Subjective-Graph LLM Agents for Simulating Uncertainty in Classroom Social Perception](https://mlsanity.com/paper/2603.20750/) (2026)
- [Decision-Centric Design for LLM Systems](https://mlsanity.com/paper/2604.00414/) (2026)
- [Medical Model Synthesis Architectures: A Case Study](https://mlsanity.com/paper/2605.09716/) (2026)
- [Turning Intent into Specifications: A Benchmark and an Interactive User-Assistant Agent](https://mlsanity.com/paper/2606.20585/) (2026)
- [Teachy Mini: Development and Preliminary Evaluation of a Knowledge-Based Generative Social Robot for Higher Education](https://mlsanity.com/paper/2607.22345/) (2026)
- [Shape Your Feed: An LLM-based Agentic System for Conversational Recommendation](https://mlsanity.com/paper/2608.06632/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used as agents that interact with users and with the world. To do so successfully, LLMs must construct representations of the world and form probabilistic beliefs about them. To provide personalized recommendations, for example, the LLM needs to infer a user's preferences from their behavior over multiple interactions. The Bayesian inference framework lays out the optimal way for an agent to update its beliefs as it receives new information. We first show that LLMs fall far short of the standard defined by the Bayesian framework. We then show that by teaching LLMs to mimic the predictions of the normative Bayesian model, we can dramatically improve their ability to update their beliefs; this ability generalizes to new tasks. We conclude that LLMs can effectively learn reasoning skills from examples and generalize those skills to new domains.