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Equation 13 · Part 5 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

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Pattainable=min⁡(Pmax⁡,  β⋅I).P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right).
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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

with W operations and Q bytes. Let Pmax⁡P_{\max} be the machine’s peak arithmetic rate and β\beta its achievable memory bandwidth. Then attainable performance is bounded by Pattainable=min⁡(Pmax⁡,  β⋅I)P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right). That expression is the whole model, and it has one structural feature that matters more than the rest. The two bounds cross at a ridge point

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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.

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Sources cited in the article section

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