Equation 36 · Part 11 · Naive, Graph, and Agentic: A Systems Comparison of RAG Architectures

Starting index or lower bound: i=1

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

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

The passage around this formula

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…

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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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