Equation 2 · RAG in 2035: Four Scenarios, Their Signals, and What Would Falsify Them
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the number of tokens. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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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 M tokens actually returned:
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