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Equation 3 · Part 2 · How AI Inference Serving Actually Works

=

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

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

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

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.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

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