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Equation 1 · Part 2 · How AI Memory Systems and the Bandwidth Wall Actually Work

Symbol P_max

P  ≤  min⁡ ⁣(Pmax⁡,  I⋅B),I=FLOPsbytes movedP \;\le\; \min\!\left(P_{\max},\; I \cdot B\right), \qquad I = \frac{\text{FLOPs}}{\text{bytes moved}}
Pmax⁡P_{\max}

What this part means

the peak arithmetic rate of the device.

Its job in the formula

PmP_max is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

with Pmax⁡P_{\max} the peak arithmetic rate of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the attainable performance [ 11 ] .

The passage around this formula

…per byte it moves across the memory boundary that matters. Williams, Waterman and Patterson formalized the relationship between intensity and attainable performance as the roofline model: P  ≤  min⁡ ⁣(Pmax⁡,  I⋅B),I=FLOPsbytes movedP \;\le\; \min\!\left(P_{\max},\; I \cdot B\right), \qquad I = \frac{\text{FLOPs}}{\text{bytes moved}}. with Pmax⁡P_{\max} the peak arithmetic rate of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the attainable performance [ 11 ] . The two terms cross at a ridge point I∗I^{*} = Pmax⁡P_{\max}/B : below it, runtime is set by how many bytes must move, whatever the peak…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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