Equation 1 · Part 2 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol t

\frac{F(t)}{B(t)} = \frac{F_0}{B_0}\left(\frac{r_F}{r_B}\right)^{t/2}

t

What this part means

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

t is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Full expressionSymbol tArticle meaning

The passage around this formula

The structural fact behind every accelerator roadmap for a decade has been that peak arithmetic throughput has scaled roughly three times every two years while DRAM bandwidth has scaled roughly 1.6 times and interconnect bandwidth roughly 1.4 times over the same interval [ 1 ] . Analysis. Extending those three exponents unchanged from a 2024 baseline to 2035 — eleven years, or 5.5 doubling periods at the two-year cadence the source measures — gives a compact way to see how much the imbalance would compound if nothing structural intervenes: $\frac{F(t)}{B(t)} = \frac{F_0}{B_0}\left(\frac{r_F}{r_B}\right)^{t/2}$ . With $r_F$ $\approx$ 3.0 and $r_B$ $\approx$ 1.6 for DRAM bandwidth, ( $r_F$ / $r_B$ )^{5.5} = (1.875)^{5.5} $\approx$ 32 : the ratio of peak…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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