Symbol r_F
is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
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Why this formula appears here
With 3.0 and 1.6 for DRAM bandwidth, (/)^{5.5} = (1.875)^{5.5} 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} 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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Symbol r_B
is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
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Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 4 · Semiconductors
AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions
This equation gives an approximation: it relates the quantities while allowing an approximation.
With 3.0 and 1.6 for DRAM bandwidth, (/)^{5.5} = (1.875)^{5.5} 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} 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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