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Equation 13 · Part 9 · How AI Accelerator Architecture Actually Works

Denominator: L + r + c - 2

η≈LL+r+c−2.\eta \approx \frac{L}{L + r + c - 2}.
L+r+c−2L + r + c - 2

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

L + r + c - 2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

while the useful work performed is r ⋅\cdot c ⋅\cdot L multiply-accumulates — one per cell, once per streamed step, in steady state. Dividing useful work by the total cell-cycles available, r ⋅\cdot c ⋅\cdot T , gives an idealised utilization η≈LL+r+c−2\eta \approx \frac{L}{L + r + c - 2}. As the streamed sequence L grows large relative to the array’s dimensions, η\eta approaches one and the fill-and-drain overhead becomes negligible. But when L is comparable to r and c — a small batch, a short sequence, a matrix dimension that barely exceeds the array’s own size — the overhead is not a rounding error, it is a large fraction of every pass through the array. This is a simplified model, not a specification of any one…

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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.