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Equation 4 · Part 1 · AI for Science and Medicine in Practice: An Advanced Technical Guide

Symbol f^+

f+f^{+}
f+f^{+}

What this part means

the current best observed value.

Its job in the formula

f+f^+ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

The standard fix is an acquisition function such as expected improvement, which for a candidate x with predictive mean μ(x)\mu(x) , predictive standard deviation σ(x)\sigma(x) , and current best observed value f+f^{+} is

The passage around this formula

The acquisition function must trade off predicted value against uncertainty, not just rank by predicted value. A pure exploitation policy — always synthesise the top-ranked candidate — collapses quickly onto whatever region of chemical or materials space the initial training data already covered well, and stops finding anything the model did not already believe. The standard fix is an acquisition function such as expected improvement, which for a candidate x with predictive mean μ(x)\mu(x) , predictive standard deviation σ(x)\sigma(x) , and current best observed value f+f^{+} is

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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