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Equation 13 · Part 1 · How AI Accelerator Architecture Actually Works

Symbol eta

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

What this part means

eta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

eta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…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.…

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Sources cited in the surrounding passage

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