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Published equation contexts

error(m)  =  Pr⁡[tool⋆∉Sm]⏟retrieval gap, shrinks as m grows  +  Pr⁡[miscall∣tool⋆∈Sm]⏟confusion gap, grows as m grows\mathrm{error}(m) \;=\; \underbrace{\Pr[\mathrm{tool}^\star \notin S_m]}_{\text{retrieval gap, shrinks as } m \text{ grows}} \;+\; \underbrace{\Pr[\text{miscall} \mid \mathrm{tool}^\star \in S_m]}_{\text{confusion gap, grows as } m \text{ grows}}

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A separate, applied study on enterprise agent routing gives a way to decompose exactly what breaks as a real tool catalogue scales, rather than only that something does. Scaling from 10 to 110 candidate agents or tools, the authors report routing F1 on under-specified requests dropping 16 to 23 percentage points across the models tested, and split that drop with an oracle analysis into two distinct components: a retrieval gap , the model’s failure to surface the correct tool at all, and a confusion gap , a roughly 10-percentage-point reduction in the theoretical best-case score that persists even when retrieval is assumed perfect [ 11 ] . Written as a decomposition of the error a shortlist…

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Pr⁡\Pr

Probability operator

The probability operator gives the chance of the event named inside its brackets or parentheses.

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Published contexts (1)

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error(m)  =  Pr⁡[tool⋆∉Sm]⏟retrieval gap, shrinks as m grows  +  Pr⁡[miscall∣tool⋆∈Sm]⏟confusion gap, grows as m grows\mathrm{error}(m) \;=\; \underbrace{\Pr[\mathrm{tool}^\star \notin S_m]}_{\text{retrieval gap, shrinks as } m \text{ grows}} \;+\; \underbrace{\Pr[\text{miscall} \mid \mathrm{tool}^\star \in S_m]}_{\text{confusion gap, grows as } m \text{ grows}}

Equation 14 · AI Infrastructure

The Token Tax of Giving a Model More Tools

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A separate, applied study on enterprise agent routing gives a way to decompose exactly what breaks as a real tool catalogue scales, rather than only that something does. Scaling from 10 to 110 candidate agents or tools, the authors report routing F1 on under-specified requests dropping 16 to 23 percentage points across the models tested, and split that drop with an oracle analysis into two distinct components: a retrieval gap , the model’s failure to surface the correct tool at all, and a confusion gap , a roughly 10-percentage-point reduction in the theoretical best-case score that persists even when retrieval is assumed perfect [ 11 ] . Written as a decomposition of the error a shortlist…

Meanings in this article

  • SmS_m: the shortlist shown to the model: [displayed formula].
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