min_p Sampling in Ollama & llama.cpp Explained

Definition

Top-k keeps a fixed number of candidates and top-p looks at cumulative probability. min_p moves the cutoff with the model's confidence at that step:

threshold = min_p × p_max

p_max is the probability of the most likely token. Every candidate below the threshold is removed; sampling happens among the rest.

Confident model (p_max = 0.9, min_p = 0.1) → threshold 0.09 → only a few candidates survive, the junk tail is gone.
Uncertain model (p_max = 0.2) → threshold drops to 0.02 → many plausible candidates survive, diversity is preserved.

The method was introduced in 2024 in "Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs" (Nguyen et al., arXiv 2407.01082). The paper reports gains in both quality and diversity, especially at high temperature where top-p struggles (GPQA, GSM8K, AlpacaEval Creative Writing; Mistral and Llama 3, 1B-123B).

Defaults (as of October 2026):

Engine	Parameter	Default
Ollama	`min_p`	0.0 (off)
llama.cpp	`--min-p` / `min_p`	0.05
vLLM	`min_p`	0.0 (off)
OpenAI API	none	—

llama.cpp's default sampler order is penalties → DRY → top-n-sigma → top-k → typical-p → top-p → min-p → XTC → temperature. So the min_p threshold is computed on the distribution before temperature is applied.

Analogy

A competition with a "relative to the winner" cutoff. If the winner scores 90 and the cutoff is 10%, anyone under 9 is out. If the winner only scores 20 (everyone is close), the cutoff drops to 2 and many people make the final. A fixed "top 40" rule (top-k) can't tell the difference.

Real-world example

The model is completing "For breakfast I ate ___", with min_p = 0.1:

Candidate	Probability	Threshold (0.1 × 0.55)	Result
eggs	0.55	0.055	kept
cheese	0.25	0.055	kept
toast	0.12	0.055	kept
pancakes	0.06	0.055	kept
screws	0.01	0.055	dropped

Tail junk like "screws" can't be picked even if you raise the temperature, because it was removed before temperature runs.

To turn it on in Ollama: send "min_p": 0.05 in the request or add PARAMETER min_p 0.05 to the Modelfile. In llama.cpp it is already on at 0.05.

Code examples

                                            Ollama API · creative but coherent output with min_p
                                            bash
                                        
curl http://localhost:11434/api/generate -d '{
  "model": "llama3.2",
  "prompt": "Write a short poem about a lighthouse.",
  "options": {
    "min_p": 0.1,
    "top_p": 1.0,
    "temperature": 1.2
  }
}'

                                            llama.cpp · sampling with min-p only
                                            bash
                                        
# New install (llama.app): llama serve
# Older binary name: llama-server
llama serve -hf ggml-org/Qwen3.5-0.8B-GGUF \
  --min-p 0.1 \
  --top-p 1.0 \
  --top-k 0 \
  --temp 1.2
# top-p 1.0 and top-k 0 = off; only min-p trims the tail

When to use

Creative writing, brainstorming — use high temperature without the gibberish
When top-p feels too narrow on some steps and too wide on others
On Ollama with tail problems — the default is 0.0, i.e. off
When you want one simple knob (top-p 1.0, top-k 0, min_p 0.05-0.1)

When not to use

Deterministic output (temperature 0) — the top token is chosen anyway, min_p does nothing
OpenAI API — the parameter doesn't exist
Code, JSON, classification and other single-answer tasks — low temperature is the cleaner fix

Common pitfalls

Different defaults across engines

The same model runs with min_p 0.05 in llama.cpp and 0.0 in Ollama. Part of the 'fine in llama.cpp, rambling in Ollama' gap can come from this. When comparing, set the sampling options explicitly on both.

Setting min_p too high

Values like 0.3-0.5 leave a single candidate on most steps; output drifts toward greedy decoding and can fall into repetition loops. Start low if you want variety.

Stacking it on top-p and top-k

In llama.cpp, top-k (40) and top-p (0.95) are on by default and run before min-p. To actually see min-p's effect, turn the others off: --top-k 0 --top-p 1.0.