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Equation 29 · Part 4 · Locality Is the Whole Game: The Memory Hierarchy and What a Kernel Does Not Read

Symbol N^2

Ω(Nd+N2)\Omega(Nd + N^2)
N2N^2

What this part means

The square of N: multiply N by itself.

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.

The passage around this formula

…the forward pass so that attention can be recomputed on-chip, which the authors state is faster than reading the stored intermediate back from HBM. Their analysis gives O(N2N^2 d2d^2 M−1M^{-1}) HBM accesses against Ω(Nd+N2)\Omega(Nd + N^2) for standard attention, with a matching lower bound showing no exact algorithm can do asymptotically better across all SRAM sizes [ 1 ] . The reported results were a 7.6 times speedup on the attention computation itself for GPT-2, 15 per cent faster end-to-end BERT-large training against the…

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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

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