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Equation 3 · Part 5 · How AI Inference Serving Actually Works

Denominator: bytes read and written

I=FLOPs performedbytes read and writtenI = \frac{\text{FLOPs performed}}{\text{bytes read and written}}
bytes read and written\text{bytes read and written}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division. Bytes measure the data moved or stored.

Its job in the formula

bytes read and written occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The standard way to make this precise is a piece of hardware-performance reasoning called the roofline model, and stating it once explains why every mitigation below targets one phase and not the other. Every accelerator has two ceilings: a peak arithmetic rate, in floating-point operations per second, and a peak memory-bandwidth rate, in bytes per second. Which one binds a given piece of work depends on that work’s arithmetic intensity — the ratio of arithmetic performed to bytes moved: I=FLOPs performedbytes read and writtenI = \frac{\text{FLOPs performed}}{\text{bytes read and written}}. A computation is compute-bound when I exceeds the hardware’s own ratio of FLOPs to bandwidth, and memory-bound when it falls below it. Prefill, processing every position of a prompt…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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