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Published equation contexts

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

Why this formula appears here

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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cfullc_{\text{full}}

Symbol c_full

cfc_full is part of the quantity the equation computes from the expression on the right.

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cretrievec_{\text{retrieve}}

Symbol c_retrieve

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

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Published contexts (1)

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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.

Equation 6 · AI Agents & Systems

RAG in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

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

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:…

Meanings in this article

  • MM: the number of tokens.
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