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Equation 4 · Part 5 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

subscript

(rF/rB)5.5=(1.875)5.5≈32(r_F/r_B)^{5.5} = (1.875)^{5.5} \approx 32
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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