Equation 4 · Part 5 · The Token Tax of Giving a Model More Tools

Symbol s_i

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

s_i

What this part means

the number of tokens.

Its job in the formula

$s_i$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol s_iArticle meaning

Where the article explains it

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

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) $\approx$ $\tau_0$ + n $\bar{s}$ . Nothing about this term depends on…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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