Equation 36 · Part 12 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Ending index or upper bound: k

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

k

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionEnding index or upper bound: kArticle meaning

The passage around this formula

…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…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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