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Equation 22 · Part 1 · The Main Technical Approaches to AI Alignment, Compared

Symbol f_wto s

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)}.
fw→sf_{w\to s}

What this part means

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

Its job in the formula

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

The passage around this formula

…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 interventions help: an auxiliary…

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

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Sources cited in the surrounding passage

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