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Equation 5 · Part 4 · How Tool Protocols and the Model Context Protocol Actually Work

Symbol T_t

at=πθ(ht∣Tt),ot=Call(at),ht+1=ht⊕(at, ot)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)
Tt\mathcal{T}_t

What this part means

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

Its job in the formula

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

The passage around this formula

It helps to write the whole loop down once, because the assumption buried in it is the one the rest of this article is about: at=πθ(ht∣Tt),ot=Call(at),ht+1=ht⊕(at, ot)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). Here Tt\mathcal{T}_t is the tool set most recently returned by tools/list , each member carrying its own schema; πθ\pi_\theta is the model, which is expected — but not forced by anything outside its own training — to emit a call ata_t whose name and arguments validate against some tool in Tt\mathcal{T}_t ;…

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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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