Equation 5 · Part 1 · How Tool Protocols and the Model Context Protocol Actually Work

Symbol a_t

a_t = \pi_\theta(h_t \mid \mathcal{T}_t), \qquad o_t = \mathrm{Call}(a_t), \qquad h_{t+1} = h_t \oplus (a_t,\, o_t)

a_t

What this part means

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

Its job in the formula

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

Full expressionSymbol a_tArticle meaning

The passage around this formula

… $\mathcal{T}_t$ is the tool set most recently returned by tools/list , each member carrying its own schema; $\pi_\theta$ is the model, which is expected — but not forced by anything outside its own training — to emit a call $a_t$ whose name and arguments validate against some tool in $\mathcal{T}_t$ ; $\mathrm{Call}$ is dispatch through the client to the server and back, exactly as described above; and $h_{t+1}$ is the context the model reasons over on the next step, built by appending the call and its result to what came…

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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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