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Equation 4 · Part 1 · The Token Tax of Giving a Model More Tools

Symbol T

T(n)=τ0+∑i=1nsiT(n) = \tau_0 + \sum_{i=1}^{n} s_i
TT

What this part means

T is part of the quantity the equation computes from the expression on the right.

Its job in the formula

T is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is T(n)=τ0+∑i=1nsiT(n) = \tau_0 + \sum_{i=1}^{n} s_i. which, if schemas run at roughly a uniform average size sˉ\bar{s} , simplifies to T(n) ≈\approx τ0\tau_0 + nsˉ\bar{s} . Nothing about this term depends on whether the model calls any tool at all; it is the price of the menu, not the price of the order. And critically, because a stateless inference API resends its full input on every request, T(n) is not paid once at the start of a…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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