Equation 7 · Part 6 · What We Still Cannot Do: Open Problems in Frontier Model Systems

subscript

n_{\max} \approx \frac{\ln \tau}{\ln q}.

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

so the horizon that can be sustained at a target success rate $\tau$ is $n_{\max} \approx \frac{\ln \tau}{\ln q}$ . The derivative of $n_{\max}$ with respect to q is steep near q = 1 , which is the good news — small per-step gains buy disproportionate horizon. The bad news is the same expression read the other way: sustaining an order of magnitude more steps requires driving per-step error down by an order of magnitude, and every one of the six problems above is a term in that per-step error which scale is not reducing. Verification, calibration, and memory are precisely the mechanisms that break the exponential by resetting accumulated uncertainty. Without them, capability gains are spent buying a slowly lengthening…

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 →

The article lists its research sources here.