Act 09 · The limits 2:30 Measuring confidence — up to a guarantee

Reading confidence from the logits.

You can read a model's uncertainty straight from the logits: how much probability sits on the chosen token, summarized by entropy (peaked = confident, flat = unsure). It turns the internal signal into a number — but it's per-token and shallow.

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Key ideas

  • The one idea — You can read a model's uncertainty straight from the logits: how much probability sits on the chosen token, summarized by entropy (peaked = confident, flat = unsure). It turns the internal signal into a number — but it's per-token and shallow.
  • How it is shown — Two next-token distributions side by side — one a sharp spike (low entropy, confident), one spread flat (high entropy, unsure) — turned into a confidence score.
  • The trap to avoid — Trusting token-probability confidence as whole-answer truth — it flags local uncertainty, not a confidently-stated made-up fact; low entropy can sit on a wrong token.
  • What it sets up — Per-token entropy misses confident confabulation — we need to measure at the level of MEANING.

Your chatbot won't tell you when it's guessing — but the numbers underneath already do. Every word comes with a hidden confidence score you can actually read.

The one idea

You can read a model's uncertainty straight from the logits: how much probability sits on the chosen token, summarized by entropy (peaked = confident, flat = unsure). It turns the internal signal into a number — but it's per-token and shallow.

Last group, we found a real uncertainty signal hiding in the logits. Now let's read it out — turn "the model is unsure" into an actual number you can use. It's the first, cheapest uncertainty meter there is, and it comes straight off the model's own outputs. Recall that at each step the model gives probabilities over the next token. That's the raw signal. If almost all the probability lands on one token, the model is confident about that word. If it's spread thin across many, it's unsure. You can just look at where the probability piles up. To summarize how spread out the distribution is in a single number, you use entropy.

How it works — the demo

Two next-token distributions side by side — one a sharp spike (low entropy, confident), one spread flat (high entropy, unsure) — turned into a confidence score.

Low entropy means the distribution is peaked — confident. High entropy means it's flat — uncertain, because many words looked about equally good. Entropy is just uncertainty, quantified, one number per token. That's the whole tool. With that number you can flag shaky moments: highlight low-confidence tokens, average confidence across an answer, or refuse to answer when uncertainty runs high. It's a cheap uncertainty meter, read straight off the model's own outputs — no second model, no extra training. But it's shallow. Token entropy tells you the model was unsure about the next word — not whether the whole claim is true. A model can be perfectly confident, low entropy, on every single token of a completely made-up citation.

The trap to avoid

Trusting token-probability confidence as whole-answer truth — it flags local uncertainty, not a confidently-stated made-up fact; low entropy can sit on a wrong token.

Why it matters — and what’s next

Per-token entropy misses confident confabulation — we need to measure at the level of MEANING.

Fluent and wrong looks exactly like fluent and right, one token at a time. The meter never sees the lie. The trap: trusting per-token confidence as a truth detector. It catches local wobble, not confident confabulation. The dangerous failures — a made-up fact stated smoothly — sail right past it, because each token was high-probability. Local certainty can sit on complete global fiction. So entropy turns the logits into an uncertainty number — useful, cheap, but per-token and shallow. To catch a confidently made-up fact, you have to measure uncertainty at the level of meaning, across whole answers, not single words. Next: semantic entropy.

This is one short episode in AI: Zero → Frontier, a step-by-step climb through how AI actually works. Each episode builds only on the ones before it.

Full transcript 2:30 of narration

Last group, we found a real uncertainty signal hiding in the logits. Now let's read it out — turn "the model is unsure" into an actual number you can use. It's the first, cheapest uncertainty meter there is, and it comes straight off the model's own outputs.

Recall that at each step the model gives probabilities over the next token. That's the raw signal. If almost all the probability lands on one token, the model is confident about that word. If it's spread thin across many, it's unsure. You can just look at where the probability piles up.

To summarize how spread out the distribution is in a single number, you use entropy. Low entropy means the distribution is peaked — confident. High entropy means it's flat — uncertain, because many words looked about equally good. Entropy is just uncertainty, quantified, one number per token. That's the whole tool.

With that number you can flag shaky moments: highlight low-confidence tokens, average confidence across an answer, or refuse to answer when uncertainty runs high. It's a cheap uncertainty meter, read straight off the model's own outputs — no second model, no extra training.

But it's shallow. Token entropy tells you the model was unsure about the next word — not whether the whole claim is true. A model can be perfectly confident, low entropy, on every single token of a completely made-up citation. Fluent and wrong looks exactly like fluent and right, one token at a time. The meter never sees the lie.

The trap: trusting per-token confidence as a truth detector. It catches local wobble, not confident confabulation. The dangerous failures — a made-up fact stated smoothly — sail right past it, because each token was high-probability. Local certainty can sit on complete global fiction.

So entropy turns the logits into an uncertainty number — useful, cheap, but per-token and shallow. To catch a confidently made-up fact, you have to measure uncertainty at the level of meaning, across whole answers, not single words. Next: semantic entropy.

LimitsUncertaintyEntropy