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Equation 8 · Part 4 · Model Systems in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

Symbol B

ttoken≳W+KB,t_{\mathrm{token}} \gtrsim \frac{W + K}{B},
BB

What this part means

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

Its job in the formula

B 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

with gFg_F and gBg_B the annual growth factors. When gFg_F > gBg_B , I∗I^{*} grows without bound, and the batch size required to keep the arithmetic units busy grows with it. Autoregressive decoding sits on the wrong side of this: generating one token requires streaming the weights and the accumulated key–value cache, so decode time is bounded below by ttoken≳W+KBt_{\mathrm{token}} \gtrsim \frac{W + K}{B}. where W is the weight bytes touched and K the cache bytes. Pope and colleagues formalised the partitioning analysis behind this and showed how latency, throughput and cost trade against one another under different sharding layouts [ 12 ] . The mitigations are well documented and all attack the numerator or the batch: grouped-query…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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