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Equation 1 · Part 7 · The Deployment Envelope: Small Models Where the Power Is Not

subscript

Rattainable=min⁡(Rpeak,B⋅I)R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I)
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

The general form of the argument is old and well posed. Williams, Waterman and Patterson built the roofline model on the premise that “for the recent past and foreseeable future, off-chip memory bandwidth will often be the constraining resource”, and defined operational intensity as operations per byte of DRAM traffic [ 1 ] . Their bound is one line, and it is the single most useful line in this whole subject: Rattainable=min⁡(Rpeak,B⋅I)R_{\mathrm{attainable}} = \min(R_{\mathrm{peak}}, B \cdot I). with RpeakR_{\mathrm{peak}} the peak arithmetic rate, B the achievable memory bandwidth and I the operational intensity of the kernel. If I is small, the second term wins and the accelerator’s headline throughput is irrelevant.

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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.