Equation 27 · Part 5 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
subtraction
subtraction
What this part means
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
Its job in the formula
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
Full expression→subtraction→Article meaning
The passage around this formula
The parallel-sampling case makes the shape of the returns explicit. If a single attempt succeeds with probability p and attempts were independent, the probability that at least one of k succeeds is . which is concave in k and saturates quickly. Two caveats destroy any naive extrapolation from it. Attempts from one model on one prompt are strongly correlated, so realised gains fall well below this bound; and is only achievable if something can identify the successful attempt. Without a verifier, extra samples buy candidates, not answers. This is precisely why the reasoning-effort control and the availability of parallel test-time compute are architectural facts about a…
Learn the underlying idea
Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.
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Sources cited in the surrounding passage
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