Equation 2 · Comparing the Main Approaches to AI Agent Architecture
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the observation history. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
where is the observation history, is whatever state the system has chosen to retain, and g is the task goal. Nothing here is specific to language models; it is the generic shape of a controller. What actually distinguishes the four patterns below is not this equation but what each one does with : whether it is one growing transcript, a plan object computed once and then held fixed, a set of disjoint per-worker histories that never touch each other directly, or a position in an explicit graph whose edges may or may not be permitted to fire. The rest of this article works through each shape in turn, using the tradeoffs their own architects have written down, not a synthetic…
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where is the observation history, is whatever state the system has chosen to retain, and g is the task goal. Nothing here is specific to language models; it is the generic shape of a controller. What actually distinguishes the four patterns below is not this equation but what each one does with : whether it is one growing transcript, a plan object computed once and then held fixed, a set of disjoint per-worker histories that never touch each other directly, or a position in an explicit graph whose edges may or may not be permitted to fire. The rest of this article works through each shape in turn, using the tradeoffs their own architects have written down, not a synthetic score.
Sources cited in the article section
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