Equation 21 · Part 1 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
Symbol pi_θ
What this part means
pi_θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
pi_θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol pi_θ→Article meaning
The passage around this formula
Consider a task instance with a policy and a compute budget b spent at inference, whether as sequential deliberation, parallel sampling, or search against a verifier. Expected quality is some q(b) that rises and saturates. Snell and colleagues studied this directly and reported that allocating test-time compute adaptively to the difficulty of the prompt substantially outperforms uniform allocation, and that in some regimes additional inference compute is a more effective use of a marginal FLOP than additional parameters [ 9 ] . The practically important half of that finding is the first: the optimal b is a function of the instance, not of the model.
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Sources cited in the surrounding passage
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