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Equation 1 · Part 4 · How AI Accelerator Architecture Actually Works

=

I∗=Pmax⁡/βI^{*} = P_{\max} / \beta
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The roofline model’s ridge point, I∗I^{*} = Pmax⁡P_{\max} / β\beta , says whether a kernel’s arithmetic intensity is high enough that memory bandwidth is not the binding constraint [ 7 ] . It says nothing about whether the array can actually deliver Pmax⁡P_{\max} once that bar is cleared, because Pmax⁡P_{\max} itself assumes every cell is doing useful work on every cycle — and a real systolic pipeline spends some of its cycles filling and draining rather than computing.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.