Under convexity and realizability, reverse-KL fine-tuning on weak supervision reduces strong-model error by at least its disagreement with the weak model.
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This inequality indicates that the weakly-supervised strong model improves upon the weak model by at least the magnitude of their disagreement,
Theorem 5.1: under convexity of the strong fine-tuning class and realizability, with reverse KL output distribution divergence, d(F*,F_sw) ≤ d(F*,F_w) − d(F_sw,F_w); extends Charikar et al. (2024) from squared loss.
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