← All parts of this equation

Equation 24 · Part 9 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

Numerator: B_weights + B_kv

tstep≥Bweights+Bkvβ,t_{\mathrm{step}} \ge \frac{B_{\mathrm{weights}} + B_{\mathrm{kv}}}{\beta},
Bweights+BkvB_{\mathrm{weights}} + B_{\mathrm{kv}}

What this part means

The complete quantity above the fraction bar.

Its job in the formula

BwB_weights + BkB_kv occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Bandwidth-limited throughput is the regime where achieved FLOPS is irrelevant because β\beta ⋅\cdot I is the binding term. Autoregressive decoding in a served language model is the clearest case: generating a single token requires streaming the model weights and the accumulated key-value cache out of memory, and performs only a small number of operations per byte read. The time per decoding step obeys tstep≥Bweights+Bkvβt_{\mathrm{step}} \ge \frac{B_{\mathrm{weights}} + B_{\mathrm{kv}}}{\beta}. a floor set entirely by memory traffic, in which peak arithmetic does not appear. This is why batching improves throughput so dramatically — the same weight bytes are amortised across many sequences, raising I — and why it does not improve single-stream latency at all.

Read this part in the article →

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 article section

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