Symbol P
P is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
Batch size interacts with the value of parallel experiments in a way worth costing out explicitly. If a single proposed experiment succeeds with probability p , and a batch of k proposals were independent, the probability that at least one succeeds is . which is why both systems ran in batches — parallel throughput converts a low per-attempt success probability into a high per-batch one. Two caveats matter in practice: proposals drawn from the same model on the same pool are correlated, so realised batch success rates fall short of this bound, and a larger batch is only worth its cost if throughput, not sample count, is the bottleneck actually being relieved.
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Symbol k
k is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
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Published contexts (1)
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Equation 8 · AI for Science
AI for Science and Medicine in Practice: An Advanced Technical Guide
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Batch size interacts with the value of parallel experiments in a way worth costing out explicitly. If a single proposed experiment succeeds with probability p , and a batch of k proposals were independent, the probability that at least one succeeds is . which is why both systems ran in batches — parallel throughput converts a low per-attempt success probability into a high per-batch one. Two caveats matter in practice: proposals drawn from the same model on the same pool are correlated, so realised batch success rates fall short of this bound, and a larger batch is only worth its cost if throughput, not sample count, is the bottleneck actually being relieved.