Rethinking confidence in reasoning models

You roll two fair six-sided dice. What is the probability that their sum is at least 10?

A model might hesitate at first. Then it counts the possibilities: three ways to roll 10, two ways to roll 11, and one way to roll 12. Six outcomes out of 36. The answer is 1/6 .

In our illustrative example (figure below, on the left), the model starts at 25% confidence and finishes at 88%. Those percentages describe its confidence in getting the answer right, not the probability of the dice outcome. Working through the problem has changed its assessment.

CALIBER trains the model to report both estimates in one response: initial confidence, reasoning, an answer, and final confidence. The two numbers can disagree because reasoning gives the model new information to assess. The goal is to make these estimates meaningful enough to support decisions about when to accept an answer, verify it, or seek help.

Confidence can move the other way, too (figure below, on the right). Reasoning through a solution that initially looks straightforward may reveal a mistaken assumption or a contradiction. A useful confidence estimate should be able to reflect that change, even when the model still gives the wrong answer. However, standard reasoning models do not necessarily come with this ability: producing a detailed reasoning process does not guarantee that a model can reliably assess and communicate its uncertainty.

This is the idea behind our method CALIBER : train a reasoning model to estimate its chance of success before it begins, then assess its particular answer afterwards. On our math benchmark, the calibrated 7B model reduces calibration error by more than half compared with the best single-confidence baseline on this metriic. The key is that the two confidence estimates answer different questions.

Before reasoning, the model has only seen the question. It can recognise the topic and judge whether the problem looks manageable. Its confidence answers: “How likely am I to solve this?”