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Published equation contexts

Ttok≥WBT_{\mathrm{tok}} \ge \frac{W}{B}

Why this formula appears here

Autoregressive decoding sits at the far left of that graph. Generating one token requires reading essentially every weight and the accumulated key-value cache once, and performing roughly two arithmetic operations per parameter. At one byte per weight the intensity is about two operations per byte; at four bits per weight, about four. Pope and colleagues formalised this partitioning problem for large transformers and showed how latency, throughput and cost trade off under different sharding strategies, with generation and prefill behaving as different regimes [ 3 ] . The bound that matters on a device follows immediately: if W bytes of weights and cache must cross the memory bus for each…

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TtokT_{\mathrm{tok}}

Symbol T_tok

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

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

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Ttok≥WBT_{\mathrm{tok}} \ge \frac{W}{B}

Equation 8 · Small & Edge Models

The Deployment Envelope: Small Models Where the Power Is Not

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

Autoregressive decoding sits at the far left of that graph. Generating one token requires reading essentially every weight and the accumulated key-value cache once, and performing roughly two arithmetic operations per parameter. At one byte per weight the intensity is about two operations per byte; at four bits per weight, about four. Pope and colleagues formalised this partitioning problem for large transformers and showed how latency, throughput and cost trade off under different sharding strategies, with generation and prefill behaving as different regimes [ 3 ] . The bound that matters on a device follows immediately: if W bytes of weights and cache must cross the memory bus for each…

Meanings in this article

  • WW: the halving the bits per weight halves.
  • BB: the achievable memory bandwidth and I the operational intensity of the kernel.
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