$$L_{\text{total}} = L_{\text{enc}} + \sum_{i=1}^{k} \left( L_{\text{retrieve}}^{(i)} + L_{\text{LLM}}^{(i)} \right)$$

Equation 36 · AI Agents & Systems

Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A single latency model makes the difference between the first three rows and the last two concrete. Writing $L_{\text{enc}}$ for query encoding, and $L_{\text{retrieve}}^{(i)}$ and $L_{\text{LLM}}^{(i)}$ for the retrieval and generation cost of round 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…

Meanings in this article

• $L_{\text{enc}}$: the writing.

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