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Equation 16 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

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Pmax⁡P_{\max}

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the machine’s peak arithmetic rate. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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Pmax⁡P_{\max}

Symbol P_max

the machine’s peak arithmetic rate.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

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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