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Equation 18 · Part 1 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

Symbol I^*

I∗I^{*}
I∗I^{*}

What this part means

I∗I^* 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

I∗I^* 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

Now put the two scaling rates from the opening beside this. If Pmax⁡P_{\max} grows at 3.0x per two years and β\beta grows at 1.6x, then I∗I^{*} — the intensity threshold a workload must clear — grows at roughly 1.9x per two years [ 4 ] . Each hardware generation raises the bar for what counts as compute bound. This is why a kernel that was compute bound two generations ago is memory bound today without a line of its source changing, and it is the single most useful thing to know about accelerator roadmaps.

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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

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