Equation 25 · Part 1 · The Token Tax of Giving a Model More Tools
Symbol tau_0
What this part means
ta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
ta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol tau_0→Article meaning
The passage around this formula
Putting the pieces together gives a short, honest account of where a tool protocol’s overhead actually lives. A single request pays a fixed tool-use tax the moment any tool is attached, plus roughly tokens for every one of the n tools visible in that request, repeated on every turn because the underlying inference API carries no memory between calls. Lazy discovery — Anthropic’s Tool Search Tool, or a disciplined use of MCP’s own…
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.
Open the illustrated subscripts: which member of a family? guide →
See this notation across published equations →
The article lists its research sources here.