Symbol q
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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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Symbol b
b is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Equation 23 · Foundation Models
OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
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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