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Equation 6 · Part 3 · What Actually Happens Inside a Very Long Claude Context Window

Symbol n^2

CLC∼O(n2⋅d),CRAG∼O(k2⋅d),k≪n.C_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n.
n2n^2

What this part means

the square of n; the writing.

Its job in the formula

n2n^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Where the article explains it

Writing n for the number of tokens placed directly in context and k for the number of tokens a retriever would instead have selected, the quadratic cost derived above means the two approaches sit in different complexity regimes for handling the same underlying material: CLC∼O(n2⋅d),CRAG∼O(k2⋅d),k≪nC_{\mathrm{LC}} \sim O(n^2 \cdot d), \qquad C_{\mathrm{RAG}} \sim O(k^2 \cdot d), \qquad k \ll n.

The passage around this formula

It is worth being precise about what “just use a longer context” actually replaces, because the alternative is not vague. Retrieval-augmented generation, as originally formalised by Patrick Lewis and colleagues, pairs a parametric model with a separate non-parametric retrieval step: a retriever selects a small number of passages likely to be relevant to a query from a much larger corpus, and only those selected passages, not the whole corpus, are placed in the model’s context for generation [ 14 ] . This publication’s own reporting on retrieval-augmented systems covers that mechanism, its indexing choices, and its failure modes at length elsewhere; the point relevant here is narrower and…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.