← All parts of this equation

Equation 22 · Part 2 · The Main Technical Approaches to AI Alignment, Compared

Symbol f_w

PGR  =  perf(fw→s)−perf(fw)perf(fs→s)−perf(fw).\mathrm{PGR} \;=\; \frac{\mathrm{perf}(f_{w\to s}) - \mathrm{perf}(f_w)}{\mathrm{perf}(f_{s\to s}) - \mathrm{perf}(f_w)}.
fwf_w

What this part means

the writing.

Its job in the formula

fwf_w is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

Writing fwf_w for the weak supervisor, fw→sf_{w\to s} for the strong model fine-tuned on the weak model’s labels, and fs→sf_{s\to s} for the strong model fine-tuned on ground truth as an upper-bound ceiling, those two conditions pin down PGR  =  perf(fw→s)−perf(fw)perf(fs→s)−perf(fw)\mathrm{PGR} \;=\; \frac{\mathrm{perf}(f_{w\to s}) - \mathrm{perf}(f_w)}{\mathrm{perf}(f_{s\to s}) - \mathrm{perf}(f_w)}.

The passage around this formula

…recovered, defined by its two boundary conditions: it equals one under perfect weak-to-strong generalization and zero when the weak-to-strong model does no better than the weak supervisor it learned from [ 12 ] . Writing fwf_w for the weak supervisor, fw→sf_{w\to s} for the strong model fine-tuned on the weak model’s labels, and fs→sf_{s\to s} for the strong model fine-tuned on ground truth as an upper-bound ceiling, those two conditions pin down PGR  =  perf(fw→s)−perf(fw)perf(fs→s)−perf(fw)\mathrm{PGR} \;=\; \frac{\mathrm{perf}(f_{w\to s}) - \mathrm{perf}(f_w)}{\mathrm{perf}(f_{s\to s}) - \mathrm{perf}(f_w)}. The paper also reports that simple additional…

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 surrounding passage

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