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Equation 6 · Part 3 · RAG in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

Symbol Theta

cfull(M)=Θ(M),cretrieve(M)=O(log⁡M)+Θ(k),k≪M.c_{\text{full}}(M) = \Theta(M), \qquad c_{\text{retrieve}}(M) = O(\log M) + \Theta(k), \qquad k \ll M.
Θ\Theta

What this part means

Theta is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

Theta is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

The two axes are related but not reducible to one another, and the coupling has an economic root worth making explicit. Autoregressive decoding is bounded by how much has to be read from memory to produce each token — the weights, plus whatever context has accumulated — and Pope and colleagues formalized exactly this partitioning of cost between arithmetic and memory movement in transformer serving [ 5 ] . Write n for the number of tokens a system must hold in an answer’s working set. Pasting a whole corpus of size M into context puts a floor under n near M itself; retrieving costs roughly the price of an index lookup plus the price of reasoning over the k ≪\ll M tokens actually returned:…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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