mlsanityData to 7 Oct 2026

Enough Coin Flips Can Make LLMs Act Bayesian

arXiv 2503.04722 ↗First posted 6 Mar 2025cs.CL cs.AI cs.LGcited by 19

Not on the map. Why?

Abstract (arXiv)

Large language models (LLMs) exhibit the ability to generalize given few-shot examples in their input prompt, an emergent capability known as in-context learning (ICL). We investigate whether LLMs use ICL to perform structured reasoning in ways that are consistent with a Bayesian framework or rely on pattern matching. Using a controlled setting of biased coin flips, we find that: (1) LLMs often possess biased priors, causing initial divergence in zero-shot settings, (2) in-context evidence outweighs explicit bias instructions, (3) LLMs broadly follow Bayesian posterior updates, with deviations primarily due to miscalibrated priors rather than flawed updates, and (4) attention magnitude has negligible effect on Bayesian inference. With sufficient demonstrations of biased coin flips via ICL, LLMs update their priors in a Bayesian manner.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 28 of its 38 references that are in the map. First posted on arXiv 6 Mar 2025.

Builds on

28 of 38 references.

References · 28

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2024The Llama 3 Herd of Modelscited by 14,192
  3. 2023Generative Agents: Interactive Simulacra of Human Behaviorcited by 3,500
  4. 2023Lost in the Middle: How Language Models Use Long Contextscited by 3,383
  5. 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,928
  6. 2024Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phonecited by 1,883
  7. 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,734
  8. 2021Calibrate Before Use: Improving Few-Shot Performance of Language Modelscited by 1,371
  9. 2021Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivitycited by 1,122
  10. 2021An Explanation of In-context Learning as Implicit Bayesian Inferencecited by 915
  11. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 788
  12. 2022Out of One, Many: Using Language Models to Simulate Human Samplescited by 737
16 more
  1. 2022What learning algorithm is in-context learning? Investigations with linear modelscited by 671
  2. 2022Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studiescited by 506
  3. 2024OLMoE: Open Mixture-of-Experts Language Modelscited by 291
  4. 2021AI Chains: Transparent and Controllable Human-AI Interaction by Chaining Large Language Model Promptscited by 265
  5. 2024Trial and Error: Exploration-Based Trajectory Optimization for LLM Agentscited by 194
  6. 2024DriveDreamer-2: LLM-Enhanced World Models for Diverse Driving Video Generationcited by 186
  7. 2023Large Language Models Are Latent Variable Models: Explaining and Finding Good Demonstrations for In-Context Learningcited by 149
  8. 2023What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalizationcited by 112
  9. 2023A Theory of Emergent In-Context Learning as Implicit Structure Inductioncited by 86
  10. 2023In-Context Learning through the Bayesian Prismcited by 78
  11. 2024Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspectivecited by 51
  12. 2024Virtual Personas for Language Models via an Anthology of Backstoriescited by 49
  13. 2024ALOHa: A New Measure for Hallucination in Captioning Modelscited by 44
  14. 2024LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling lawcited by 32
  15. 2024Heads, Tails, and AI Fails: LLMs, Randomness, and Human Judgmentscited by 23
  16. 2024Do LLMs Play Dice? Exploring Probability Distribution Sampling in Large Language Models for Behavioral Simulationcited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 8; 2026: 11.

19 papers.

Sort:

By area:

  1. 2025String Seed of Thought: Prompting LLMs for Distribution-Faithful and Diverse Generationcited by 11
  2. 2025Flipping Against All Odds: Reducing LLM Coin Flip Bias via Verbalized Rejection Samplingcited by 7
  3. 2026The Illusion of Stochasticity in LLMscited by 7
  4. 2025Martingale Score: An Unsupervised Metric for Bayesian Rationality in LLM Reasoningcited by 5
  5. 2025Pre-trained Large Language Models Learn Hidden Markov Models In-contextcited by 4
  6. 2026Position: agentic AI orchestration should be Bayes-consistentcited by 3
  7. 2025Beyond Scaling Curves: Internal Dynamics of Neural Networks Through the NTK Lenscited by 2
  8. 2026AdaptFuse: Training-Free Sequential Preference Learning via Externalized Bayesian Inferencecited by 2
  9. 2025Express Your Doubts -- Probabilistic World Modeling Should not be Based on Token logprobscited by 1
  10. 2025SPIKE-RL: Video-LLMs meet Bayesian Surprisecited by 1
  11. 2025TextBandit: Evaluating Probabilistic Reasoning in LLMs Through Language-Only Decision Taskscited by 1
  12. 2026D-Models and E-Models: Diversity-Stability Trade-offs in the Sampling Behavior of Large Language Modelscited by 1
7 more
  1. 2026Large Language Model for Discrete Optimization Problems: Evaluation and Step-by-step Reasoningcited by 0
  2. 2026Beyond Facts: Benchmarking Distributional Reading Comprehension in Large Language Modelscited by 0
  3. 2026EviCare: Enhancing Diagnosis Prediction with Deep Model-Guided Evidence for In-Context Reasoningcited by 0
  4. 2026From Static Personal Values to Contextualized Personalization: Bayesian Personalized Value Alignment for LLMscited by 0
  5. 2026Small transformers track Bayesian evidence for latent common causes via a context-invariant mechanismcited by 0
  6. 2026Diagnosing and Improving Probabilistic Reasoning in Large Language Modelscited by 0
  7. 2026Bayesian Fine-tuning Yields Language Models that are as Bayesian as their Beliefs Allowcited by 0