Equation 1 · Part 3 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol B

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

B

What this part means

B occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

B occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol BArticle 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…

Read this part in the article →

Learn the underlying idea

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

Open the illustrated functions: inputs become outputs guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.