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Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs
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Proposes min-p sampling, a dynamic truncation rule that scales a base threshold by the top token's probability, and shows it keeps accuracy and creative-writing quality higher than top-p and other samplers at high temperatures.
Problem
Standard truncation samplers such as top-p and top-k trade off quality against diversity and become incoherent at high temperature, so LLM text generation lacks a method that stays coherent while remaining creative.
Approach
Truncate the next-token distribution with a threshold equal to a base probability p_base times the maximum token probability, so the pool widens when the model is uncertain and narrows when it is confident; the method is simple and integrates as a logits processor.
Key results
- On GPQA Main with Mistral 7B at temperature 3.0, min-p reaches 24.55% accuracy versus 0.46% for top-p 0.9.
- On AlpacaEval Creative Writing at temperature 1.5, min-p (p_base=0.1) achieves a 56.54% win rate versus 50.43% for top-p at temperature 1.0.
- Human evaluation (54 valid responses) rated min-p outputs higher on quality and diversity at temperature 3, e.g., quality 7.74 for min-p 0.2 vs 5.75 for top-p 0.1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use min-p instead of top-p at higher temperatures | Mistral 7B on GPQA Main · GPQA Main, τ=3.0 | accuracy: 0.46 -> 24.55 | Helped |
| Use min-p instead of top-p at higher temperatures | Mistral 7B on GSM8K CoT · GSM8K CoT, τ=1.0 | accuracy: 27.67 -> 30.86 | Helped |
| Use min-p instead of top-p | Mistral Large on GPQA Main · GPQA Main, τ=3.0 | accuracy: 2.01 -> 22.77 | Helped |
| Use min-p instead of temperature-only sampling | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing, τ=1.5 | win rate: 53.18 -> 56.54 | Helped |
| Replace top-p=0.1 with min-p=0.2 | Llama 3 70B creative-writing outputs · Human evaluation, T=3, lower diversity | quality: 5.75$\pm$0.3201 -> 7.74$\pm$0.2418 | Helped |
| Replace top-p=0.9 with min-p=0.05 | Llama 3 70B creative-writing outputs · Human evaluation, T=3, higher diversity | diversity: 7.49$\pm$0.2396 -> 7.66$\pm$0.1996 | Helped |
| Set min-p to 0.1 at temperature 1.5 (ablation) | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing | win rate: 50.43 -> 56.54 | Helped |
| Vary min-p from 0.1 to 0.15 at temperature 1.5 (ablation) | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing | win rate: 56.54 $\pm$ 3.68 -> 53.37 $\pm$ 3.70 | Hurt |
| Vary min-p from 0.1 to 0.2 at temperature 1.5 (ablation) | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing | win rate: 56.54 $\pm$ 3.68 -> 53.38 $\pm$ 3.71 | Hurt |
| Vary min-p from 0.1 to 0.05 at temperature 1.5 (ablation) | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing | win rate: 56.54 $\pm$ 3.68 -> 48.57 $\pm$ 3.71 | Hurt |
| Vary min-p from 0.1 to 0.02 at temperature 1.5 (ablation) | openchat-3.5-0106 on AlpacaEval Creative Writing · AlpacaEval Creative Writing | win rate: 56.54 $\pm$ 3.68 -> 44.83 $\pm$ 3.70 | Hurt |
| Increase p_base from 0.1 to 0.2 (ablation) | Llama 3.1 70B on GSM8K CoT · GSM8K CoT, τ=3.0 | accuracy: 0.08 -> 61.03 | Helped |
Surprising findings
- Greedy decoding was outperformed by min-p across a range of temperatures on task benchmarks, challenging the assumption that greedy is optimal for them.
- eta and epsilon sampling runtime grew exponentially with temperature and they failed completely above roughly tau 1.5 in the reported experiments.
Limitations
- Human evaluation used a small sample (54 valid responses, one triplet per condition), so results are directional.
- Min-p and top-p perform comparably at low temperatures, and the method's gains are concentrated at high temperature.
- Top-k and other baselines required hyperparameter choices made by the authors via Risk Levels and MAUVE references, making fair comparison dependent on those selections.
Experimental setup
Datasets: GPQA Main GSM8K CoT
Benchmarks: GPQA Main GSM8K CoT AlpacaEval Creative Writing EQ-Bench Creative Writing
Metrics: accuracy win rate length-controlled win rate entropy of correct predictions quality score diversity score
Baselines: top-p sampling top-k sampling temperature only sampling eta sampling epsilon sampling mirostat sampling greedy decoding
Builds on: top-p sampling top-k sampling eta sampling epsilon sampling mirostat sampling
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