← All parts of this equation

Equation 1 · Part 9 · How AI Memory Systems and the Bandwidth Wall Actually Work

subscript

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}}
subscript

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

Given a memory system built this way, the question for any specific piece of computation is simple to state and consequential to answer: for this kernel, is the bottleneck the arithmetic units or the memory system that feeds them? The quantity that answers it is arithmetic intensity , defined as the number of floating-point operations a kernel performs 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…

Read this part in the article →

Learn the underlying idea

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

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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