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Equation 15 · Part 5 · Comparing the Main Approaches to AI Agent Architecture

Symbol gamma

G=(V,E),v→v′ fires iff γ(v,v′)=1,G = (V, E), \qquad v \to v' \text{ fires iff } \gamma(v, v') = 1,
γ\gamma

What this part means

an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted.

Its job in the formula

gamma is an input to the expression that computes the quantity on the left.

Where the article explains it

where each node v ∈\in V is either a deterministic function or an invocation of some policy πv\pi_v , and γ\gamma is an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted.

The passage around this formula

Formally, this pattern replaces the time-indexed loop with execution over a graph: G=(V,E),v→v′ fires iff γ(v,v′)=1G = (V, E), \qquad v \to v' \text{ fires iff } \gamma(v, v') = 1. where each node v ∈\in V is either a deterministic function or an invocation of some policy πv\pi_v , and γ\gamma is an explicit gate on the edge — a test, a validation check, or a human approval — that must pass before the transition is permitted. That is the structural reason human approval is a first-class primitive in this pattern rather than a wrapper bolted around it from outside: approval is just one kind of γ\gamma , attached to one particular edge, rather than a blanket condition on the whole run.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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See this notation across published equations →

Sources cited in the article section

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