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Equation 4 · Part 3 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

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(rF/rB)5.5=(1.875)5.5≈32(r_F/r_B)^{5.5} = (1.875)^{5.5} \approx 32
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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