Equation 1 · Part 8 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

=

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

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.

Full expression=Article 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

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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

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