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Equation 24 · Part 1 · What an AI Accelerator Actually Is: Silicon, Packaging, and the Memory It Can Reach

Symbol t_step

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

What this part means

tst_step is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

tst_step is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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.

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