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Equation 13 · Part 8 · How AI Accelerator Architecture Actually Works

subtraction

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

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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