Published equation contexts
Why this formula appears here
I define a compute-to-memory locality index, L , as the ratio of two bandwidth-per-joule figures: the realized random-access bandwidth a system can sustain across its full memory pool, divided by the power it costs to sustain that bandwidth, computed once for the optically unified case and once for the same total memory capacity attached the conventional way — as edge-limited HBM and DDR stacks wired electrically to a die of the same process generation. Here BW is realized, measured random-access bandwidth in bytes per second — not a marketing peak, not a sequential-streaming figure, since random access is what most large-model inference and any pooled-memory workload actually demands — and…
Read the representative guide
Symbol B
B is an input to the expression that computes the quantity on the left.
Read this term in its guide →Symbol W_opt
pt occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Symbol P_opt
pt occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Read this term in its guide →Symbol W_cu
u occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Symbol P_cu
u occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Denominator: BW_cu / P_cu
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 2 · AI Hardware & Semiconductors
An Optical Fabric Turns Off-Package Memory Into an Extension of the Die
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
I define a compute-to-memory locality index, L , as the ratio of two bandwidth-per-joule figures: the realized random-access bandwidth a system can sustain across its full memory pool, divided by the power it costs to sustain that bandwidth, computed once for the optically unified case and once for the same total memory capacity attached the conventional way — as edge-limited HBM and DDR stacks wired electrically to a die of the same process generation. Here BW is realized, measured random-access bandwidth in bytes per second — not a marketing peak, not a sequential-streaming figure, since random access is what most large-model inference and any pooled-memory workload actually demands — and…