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Equation 3 · Part 2 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

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rB≈1.6r_B \approx 1.6
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

With rFr_F ≈\approx 3.0 and rBr_B ≈\approx 1.6 for DRAM bandwidth, (rFr_F/rBr_B)^{5.5} = (1.875)^{5.5} ≈\approx 32 : the ratio of peak arithmetic to memory bandwidth would be roughly 32 times higher in 2035 than in 2024 if the historical exponents hold exactly. Swap in interconnect bandwidth’s 1.4x rate and the same arithmetic gives (3.0/1.4)^{5.5} ≈\approx 66 . Neither number is a forecast; both are what the stated assumption implies, and the assumption — that both exponents stay fixed for eleven more years — is exactly the thing worth doubting. HBM4’s own arrival already shows one departure from smooth continuation: doubling per-stack bandwidth required doubling channel count as well as pin rate, and…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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