Equation 16 · The Token Tax of Giving a Model More Tools
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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol m
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What the article says around this equation
Widening the shortlist drives the first term toward zero and the second term upward; narrowing it does the reverse. There is no value of m that eliminates both terms at once, which is exactly why the paper reports a design fix rather than a single ideal m : embedding-based shortlisting recovered 10 to 11 percentage points of F1 at full scale, consistently across three model families and two providers, and 10 to 17 percentage points on live production traffic, validated against 1,435 human-labeled utterances [ 11 ] . The fix is not “show fewer tools” as a blanket rule. It is choosing which few to show, per request, well.
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