Equation 7 · Part 2 · Model Systems in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

superscript

I^{*}

superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

Full expressionsuperscriptArticle meaning

The passage around this formula

with $g_F$ and $g_B$ the annual growth factors. When $g_F$ > $g_B$ , $I^{*}$ 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

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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