# Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs

arXiv: https://arxiv.org/abs/2407.01082 · HTML: https://mlsanity.com/paper/2407.01082/

## Key facts

- Cited by 150 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Beam Search Strategies for Neural Machine Translation](https://mlsanity.com/paper/1702.01806/) (2017)
- [Chain-of-Thought Reasoning Without Prompting](https://mlsanity.com/paper/2402.10200/) (2024)
- [Truncation Sampling as Language Model Desmoothing](https://mlsanity.com/paper/2210.15191/) (2022)
- [On Decoding Strategies for Neural Text Generators](https://mlsanity.com/paper/2203.15721/) (2022)
- [EQ-Bench: An Emotional Intelligence Benchmark for Large Language Models](https://mlsanity.com/paper/2312.06281/) (2023)
- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
- [Confidence Regulation Neurons in Language Models](https://mlsanity.com/paper/2406.16254/) (2024)
- [EDT: Improving Large Language Models' Generation by Entropy-based Dynamic Temperature Sampling](https://mlsanity.com/paper/2403.14541/) (2024)
- [MAUVE Scores for Generative Models: Theory and Practice](https://mlsanity.com/paper/2212.14578/) (2022)
- [An Information-Theoretic Perspective on Variance-Invariance-Covariance Regularization](https://mlsanity.com/paper/2303.00633/) (2023)
- [Improving Open-Ended Text Generation via Adaptive Decoding](https://mlsanity.com/paper/2402.18223/) (2024)
- [How Optimal is Greedy Decoding for Extractive Question Answering?](https://mlsanity.com/paper/2108.05857/) (2021)

## Built on by (most cited first, 30 of 150)

- [RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2504.20073/) (2025)
- [T1: Advancing Language Model Reasoning through Reinforcement Learning and Inference Scaling](https://mlsanity.com/paper/2501.11651/) (2025)
- [Generalized Interpolating Discrete Diffusion](https://mlsanity.com/paper/2503.04482/) (2025)
- [Diverse Preference Optimization](https://mlsanity.com/paper/2501.18101/) (2025)
- [Modifying Large Language Model Post-Training for Diverse Creative Writing](https://mlsanity.com/paper/2503.17126/) (2025)
- [Weight Ensembling Improves Reasoning in Language Models](https://mlsanity.com/paper/2504.10478/) (2025)
- [ResearchCodeBench: Benchmarking LLMs on Implementing Novel Machine Learning Research Code](https://mlsanity.com/paper/2506.02314/) (2025)
- [Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGI](https://mlsanity.com/paper/2507.14172/) (2025)
- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Optimizing Temperature for Language Models with Multi-Sample Inference](https://mlsanity.com/paper/2502.05234/) (2025)
- [Training a Generally Curious Agent](https://mlsanity.com/paper/2502.17543/) (2025)
- [Creative Preference Optimization](https://mlsanity.com/paper/2505.14442/) (2025)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)
- [Diverse Preference Learning for Capabilities and Alignment](https://mlsanity.com/paper/2511.08594/) (2025)
- [Post-training Large Language Models for Diverse High-Quality Responses](https://mlsanity.com/paper/2509.04784/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [L-MTP: Leap Multi-Token Prediction Beyond Adjacent Context for Large Language Models](https://mlsanity.com/paper/2505.17505/) (2025)
- [Control the Temperature: Selective Sampling for Diverse and High-Quality LLM Outputs](https://mlsanity.com/paper/2510.01218/) (2025)
- [Knowledge Graph-extended Retrieval Augmented Generation for Question Answering](https://mlsanity.com/paper/2504.08893/) (2025)
- [G2: Guided Generation for Enhanced Output Diversity in LLMs](https://mlsanity.com/paper/2511.00432/) (2025)
- [TALON: Confidence-Aware Speculative Decoding with Adaptive Token Trees](https://mlsanity.com/paper/2601.07353/) (2026)
- [Reversal of Thought: Enhancing Large Language Models with Preference-Guided Reverse Reasoning Warm-up](https://mlsanity.com/paper/2410.12323/) (2024)
- [Foundations of Top-k Decoding For Language Models](https://mlsanity.com/paper/2505.19371/) (2025)
- [Min-p, Max Exaggeration: A Critical Analysis of Min-p Sampling in Language Models](https://mlsanity.com/paper/2506.13681/) (2025)
- [InvisibleInk: High-Utility and Low-Cost Text Generation with Differential Privacy](https://mlsanity.com/paper/2507.02974/) (2025)
- [GUARD: Glocal Uncertainty-Aware Robust Decoding for Effective and Efficient Open-Ended Text Generation](https://mlsanity.com/paper/2508.20757/) (2025)
- [Group-Aware Reinforcement Learning for Output Diversity in Large Language Models](https://mlsanity.com/paper/2511.12596/) (2025)
- [Growing a Tail: Increasing Output Diversity in Large Language Models](https://mlsanity.com/paper/2411.02989/) (2024)
- [When Life Gives You Samples: The Benefits of Scaling up Inference Compute for Multilingual LLMs](https://mlsanity.com/paper/2506.20544/) (2025)
- [Top-H Decoding: Adapting the Creativity and Coherence with Bounded Entropy in Text Generation](https://mlsanity.com/paper/2509.02510/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) generate text by sampling the next token from a probability distribution over the vocabulary at each decoding step. Popular sampling methods like top-p (nucleus sampling) often struggle to balance quality and diversity, especially at higher temperatures which lead to incoherent or repetitive outputs. We propose min-p sampling, a dynamic truncation method that adjusts the sampling threshold based on the model's confidence by using the top token's probability as a scaling factor. Our experiments on benchmarks including GPQA, GSM8K, and AlpacaEval Creative Writing show that min-p sampling improves both the quality and diversity of generated text across different model families (Mistral and Llama 3) and model sizes (1B to 123B parameters), especially at higher temperatures. Human evaluations further show a clear preference for min-p sampling, in both text quality and creativity. Min-p sampling has been adopted by popular open-source LLM frameworks, including Hugging Face Transformers, VLLM, and many others, highlighting its considerable impact on improving text generation quality.