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Equation 2 · Part 5 · What We Still Cannot Do: Open Problems in Frontier Model Systems

Probability operator

Pr⁡(correct∣c^=c)≈c\Pr(\text{correct} \mid \hat{c} = c) \approx c
Pr⁡\Pr

What this part means

The probability operator gives the chance of the event named inside its brackets or parentheses.

Its job in the formula

Pr appears in the conditional probability being evaluated. The vertical bar identifies the information or condition supplied to that probability.

The passage around this formula

The structural difficulty is that a next-token distribution is not an epistemic state. A model trained to maximise likelihood over text produces a confident-sounding continuation because confident-sounding continuations are what the corpus contains, not because it has assessed its own evidence. Calibration can be measured — for a predicted confidence c one can ask whether Pr⁡(correct∣c^=c)≈c\Pr(\text{correct} \mid \hat{c} = c) \approx c. holds across bins — and it can be improved by post-hoc adjustment. What has not been demonstrated is a mechanism by which a model represents its own ignorance in a way that survives fine-tuning, distribution shift, and the pressure of an objective that rewards answering.

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Learn the underlying idea

Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.

Open the illustrated probability: a quantified chance guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.