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Equation 36 · Part 7 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

=

Ltotal=Lenc+∑i=1k(Lretrieve(i)+LLLM(i)).L_{\text{total}} = L_{\text{enc}} + \sum_{i=1}^{k} \left( L_{\text{retrieve}}^{(i)} + L_{\text{LLM}}^{(i)} \right).
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A single latency model makes the difference between the first three rows and the last two concrete. Writing LencL_{\text{enc}} for query encoding, and Lretrieve(i)L_{\text{retrieve}}^{(i)} and LLLM(i)L_{\text{LLM}}^{(i)} for the retrieval and generation cost of round i , Ltotal=Lenc+∑i=1k(Lretrieve(i)+LLLM(i))L_{\text{total}} = L_{\text{enc}} + \sum_{i=1}^{k} \left( L_{\text{retrieve}}^{(i)} + L_{\text{LLM}}^{(i)} \right). For naive and hybrid RAG, k = 1 by construction — the sum has exactly one term, and total latency is boundable in advance for any query. For iterative RAG, k is a small integer set by a heuristic or a step cap chosen by the system builder, so the worst case is known even though the typical case varies with question difficulty. For agentic RAG, k is a random variable generated by the policy itself at run time, and its…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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