Equation 2 · What We Still Cannot Do: Open Problems in Frontier Model Systems
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol hatc
hatc appears in the conditional probability being evaluated. The vertical bar identifies the information or condition supplied to that probability.
Symbol c
c appears in the conditional probability being evaluated. The vertical bar identifies the information or condition supplied to that probability.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →Probability operator
The probability operator gives the chance of the event named inside its brackets or parentheses.
How to interpret it
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What the article says around this equation
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 . 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.
Sources cited in the article section
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