mlsanityData to 14 Oct 2026

Flipping Against All Odds: Reducing LLM Coin Flip Bias via Verbalized Rejection Sampling

arXiv 2506.09998 ↗First posted 11 Jun 2025cs.LG cs.CLcited by 7

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Abstract (arXiv)

Large language models (LLMs) can often accurately describe probability distributions using natural language, yet they still struggle to generate faithful samples from them. This mismatch limits their use in tasks requiring reliable stochasticity, such as Monte Carlo methods, agent-based simulations, and randomized decision-making. We investigate this gap between knowledge and sampling in the context of Bernoulli distributions. We introduce Verbalized Rejection Sampling (VRS), a natural-language adaptation of classical rejection sampling that prompts the LLM to reason about and accept or reject proposed samples. Despite relying on the same Bernoulli mechanism internally, VRS substantially reduces sampling bias across models. We provide theoretical analysis showing that, under mild assumptions, VRS improves over direct sampling, with gains attributable to both the algorithm and prompt design. More broadly, our results show how classical probabilistic tools can be verbalized and embedded into LLM workflows to improve reliability, without requiring access to model internals or heavy prompt engineering.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 13 of its 21 references that are in the map. First posted on arXiv 11 Jun 2025.

Builds on

13 of 21 references.

References · 13

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  4. 2024Qwen2.5 Technical Reportcited by 4,942
  5. 2024Benchmarking Distributional Alignment of Large Language Modelscited by 61
  6. 2024LLM Processes: Numerical Predictive Distributions Conditioned on Natural Languagecited by 55
  7. 2025Specializing Large Language Models to Simulate Survey Response Distributions for Global Populationscited by 53
  8. 2024Heads, Tails, and AI Fails: LLMs, Randomness, and Human Judgmentscited by 26
  9. 2025Enough Coin Flips Can Make LLMs Act Bayesiancited by 22
  10. 2024Verbalized Machine Learning: Revisiting Machine Learning with Language Modelscited by 17
  11. 2024Do LLMs Play Dice? Exploring Probability Distribution Sampling in Large Language Models for Behavioral Simulationcited by 14
  12. 2023Vocabulary for Universal Approximation: A Linguistic Perspective of Mapping Compositionscited by 6
1 more
  1. 2025Evaluating Binary Decision Biases in Large Language Models: Implications for Fair Agent-Based Financial Simulationscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 7.

7 papers.

  1. 2026The Illusion of Stochasticity in LLMscited by 9
  2. 2026Large Language Models Are Bad Dice Players: LLMs Struggle to Generate Random Numbers from Statistical Distributionscited by 6
  3. 2026Probabilistic Calibration Is a Trainable Capability in Language Modelscited by 2
  4. 2026Instruction-Tuned Language Models Cannot Sample from Distributions They Can Describecited by 1
  5. 2026Structured Inference with Large Language Gibbscited by 0
  6. 2026Sample What You Say: Aligning Language Models to Sample the Distributions They Statecited by 0
  7. 2026Beyond Answer Confidence: A Controlled Audit of Self-Knowledge in a Black-Box Decision Modelcited by 0