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Equation 10 · Part 2 · Comparing the Main Approaches to AI Agent Architecture

superscript

h(j)h^{(j)}
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Because h(i)h^{(i)} and h(j)h^{(j)} are disjoint by construction, worker i ’s error cannot enter worker j ’s context directly — it can only reach the supervisor, and only in whatever compressed form the worker chooses to report. That disjointness is the formal reason this pattern offers stronger containment than the single loop for genuinely independent subtasks, and it is also exactly why the pattern is documented to struggle when subtasks are not independent: the architecture has no channel for worker i to see worker j ’s intermediate state even when the task actually requires it. Cost rises with the documented multiplier, latency improves only to the extent that subtasks are truly parallelizable,…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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