$$C_{\text{train}}(t) \approx C_0\, g^{\,t-t_0}$$

Equation 3 · Model Evaluation

The Frontier Model Landscape in 2035: Four Scenarios, Their Signals, and What Would Falsify Them

This equation gives an approximation: it relates the quantities while allowing an approximation.

Write $C_{\text{train}}(t)$ for the cost of the largest training run in year t . Epoch’s estimate is well approximated by simple exponential growth, $C_{\text{train}}(t) \approx C_0\, g^{\,t-t_0}$. with g between roughly two-point-four and three-point-five depending on method and window [ 5 , 6 ] . The form matters more than the exact rate: exponential cost growth does not by itself predict consolidation. It predicts a shrinking count of organisations able to clear an ever-rising bar only if the pool of adequately capitalised entrants grows more slowly than $g^{t}$ . Whether that pool keeps pace is a question about capital markets and state investment, not something the cost curve alone answers — which is exactly why axis…

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