Equation 1 · Part 6 · From Origins to Frontier: A History of AI Memory Systems and the Bandwidth Wall
Numerator: compute(t)
What this part means
The complete quantity above the fraction bar.
Its job in the formula
compute(t) occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: compute(t)→Article meaning
The passage around this formula
The scale of that abstract argument, made concrete decades later, is stark. Gholami and colleagues, surveying twenty years of server hardware, report that peak hardware FLOPS scaled at roughly 3.0 times every two years while DRAM bandwidth scaled at only 1.6 times and interconnect bandwidth at 1.4 times over the same interval [ 13 ] . Those are compounding rates, and compounding rates diverge violently over long periods. If the two multipliers applied uniformly across a full twenty years — an extrapolation the source itself does not perform, offered here only to size the shape of the problem, not as a number the cited paper states — the ratio between available arithmetic and available…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.