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Equation 1 · Part 6 · How AI Accelerator Architecture Actually Works

superscript

I∗=Pmax⁡/βI^{*} = P_{\max} / \beta
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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 exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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