Min-p & Typical Sampling Calculator

A language model outputs a raw score — a logit — for every token in its vocabulary. Sampling parameters turn those logits into a probability distribution and then decide how much of the tail to keep. This tool covers the two samplers that the temperature & top-p visualizer leaves out — min-p and locally-typical— in the common reference order used by Hugging Face's generation code: temperature → softmax → truncate → renormalize.

1. Tempered softmax. Each logit is divided by temperature T and run through softmax: p_i = exp(z_i / T) / Σ_j exp(z_j / T). We subtract the maximum scaled logit before exponentiating (the log-sum-exp trick) so large logits never overflow. At T = 0 the math collapses to greedy decoding — the top token gets probability 1.
2. Min-p truncation. Let p_max be the highest probability. Compute the cutoff θ = min_p × p_max and keep every token with p_i ≥ θ. Because the cutoff is relative to the top token, a confident (peaked) distribution truncates aggressively while an uncertain (flat) one keeps more candidates — the defining behaviour of min-p (Nguyen et al., 2024; HF MinPLogitsWarper).
3. Typical truncation. Compute the distribution's entropy H = −Σ p_i ln p_i (nats). Score each token by s_i = |−ln p_i − H| — the distance of its surprisal from the entropy — then keep the smallest set, sorted by that score, whose cumulative probability reaches typical_p. This drops both the over-confident and the wildly surprising tokens (Meister et al., 2022; HF TypicalLogitsWarper).
4. Renormalize. Divide the surviving probabilities by their sum so they total 1 — the actual probabilities the sampler draws from.

As a credibility check, the tool verifies the min-p cutoff two ways: once on the softmax probabilities (p_i ≥ min_p·p_max) and once directly in logit space (z_i/T ≥ ln(min_p) + z_max/T), which is algebraically the same test. The summary chips add an entropy readout in bits and an effective choices count. Backends differ in whether temperature is applied before or after truncation and in tie-breaking, so this tool states its reference order rather than claiming to mirror any one implementation exactly. Everything is deterministic and runs entirely in your browser.

All three use the base distribution cat=2.0, dog=1.0, bird=0.5, fish=0.0 at T = 1.0, whose tempered softmax is p = [0.5793, 0.2131, 0.1293, 0.0784] (so p_max = 0.5793), except Example B, which uses a deliberately flat distribution.

• Nguyen, Baker et al. (2024) — Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs
• Meister, Pimentel, Wiher & Cotterell (2022) — Locally Typical Sampling
• Hugging Face Transformers — MinPLogitsWarper & TypicalLogitsWarper (reference implementations)
• llama.cpp — sampling documentation (--min-p default 0.05)
• Goodfellow, Bengio & Courville (2016) — Deep Learning (tempered softmax)

The formulas above were last cross-checked against these sources on 2026-07-11. The sampling math is standard; the worked examples double as the tool's reconciliation fixtures (tolerance 1e-4).