Min-p sampling sets a floor that FLOATS with confidence: keep only tokens whose probability is at least min_p times the TOP token’s probability. When the model is certain (one tall bar) the floor is high and few survive; when it’s unsure (flat bars) the floor is low and many do. It adapts where top-k and top-p are rigid. Slide the floor.
Min-p keeps tokens with pᵢ ≥ min_p · maxⱼ pⱼ — a threshold scaled to the peak probability. Unlike top-k (fixed count) or top-p/nucleus (fixed cumulative mass), the surviving set shrinks automatically when the model is confident and widens when it is uncertain, which preserves diversity in flat distributions while cutting the tail in peaked ones. min_p=0 keeps everything; min_p=1 keeps only tokens tied with the max. A fail-loud self-check throws unless raising min_p never increases the survivor count and min_p=0 keeps all. ◆ real decoding, node-verified.
The distribution is illustrative; the relative-threshold rule and its monotonicity are exact. Which of min-p / top-p / typical reads best is task-dependent — not settled here.