Equation 3 · Part 4 · OpenAI and Claude on Formal Reasoning: What the Benchmarks Show, and Where They Mislead
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What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
Consider what the o1 numbers alone expose about how these gains are produced. If a single attempt at a problem succeeds with probability p , and k attempts were independent, the probability that at least one succeeds is . a curve that climbs fast and then saturates. It is tempting to read o1’s jump from 74% (one sample) to 83% (64-sample consensus) to 93% (1,000-sample rerank) as roughly this shape. It is not, for two reasons that matter for how the number should be read. First, repeated attempts by one model on one problem are correlated — the same misconception that causes one failure tends to recur — so the realised gain from added samples falls well below what…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.