Equation 4 · Part 2 · The Token Tax of Giving a Model More Tools

Symbol n

T(n) = \tau_0 + \sum_{i=1}^{n} s_i

n

What this part means

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionSymbol nArticle meaning

The passage around this formula

Call this fixed, tool-independent charge $\tau_0$ . On top of it sits the actual content of the catalogue: for n tools attached to a request, each with a schema costing $s_i$ tokens for its name, description, and JSON Schema of parameters, the tool-visibility component of a single request’s input is $T(n) = \tau_0 + \sum_{i=1}^{n} s_i$ . which, if schemas run at roughly a uniform average size $\bar{s}$ , simplifies to T(n)…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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