What does this equation mean?

They quantify how much of the gap this recovers with a metric called performance gap 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 $f_w$ for the weak supervisor, $f_{w\to s}$ for the strong model fine-tuned on the weak model’s labels, and $f_{s\to s}$ for the strong model fine-tuned on ground truth as an upper-bound ceiling, those two conditions pin down $\mathrm{PGR} \;=\; \frac{\mathrm{perf}(f_{w\to s}) - \mathrm{perf}(f_w)}{\mathrm{perf}(f_{s\to s}) - \mathrm{perf}(f_w)}$. The paper also reports that simple additional interventions help: an auxiliary confidence loss recovered performance closer to GPT-3.5 level using only GPT-2-level supervision on GPT-4, a substantially larger fraction of the gap than naive fine-tuning alone closed [ 12 ] .