← All parts of this equation

Equation 3 · Part 6 · Model Systems in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

Symbol g_F

I∗(t)=F(t)B(t)=I0∗(gFgB)t,I^{*}(t) = \frac{F(t)}{B(t)} = I^{*}_0 \left(\frac{g_F}{g_B}\right)^{t},
gFg_F

What this part means

the open question, not whether relief exists.

Its job in the formula

gFg_F occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

Whether the relief keeps pace with gFg_F is the open question, not whether relief exists.

The passage around this formula

Write F(t) for peak arithmetic throughput and B(t) for memory bandwidth. The quantity that matters for a serving system is their ratio, because it sets the arithmetic intensity — operations per byte moved — at which a machine becomes compute-bound rather than bandwidth-bound: I∗(t)=F(t)B(t)=I0∗(gFgB)tI^{*}(t) = \frac{F(t)}{B(t)} = I^{*}_0 \left(\frac{g_F}{g_B}\right)^{t}. 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

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

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