CADENCE is an on-policy distillation framework designed to address cold-start collapse, state-agnostic KL scheduling, and sparse binary rewards. Its DRIFT objective mixes forward- and reverse-KL surrogates per token, while COVA adapts the transition using student coverage, FTB emphasizes high-entropy forking tokens, and CCD supplies numerical-proximity partial credit. On GSM8K and MATH-500, a 0.5B student reached 69.8% GSM8K pass@1 after distillation from a 1.5B teacher, compared with 48.7% pretrained, and experiments ran on a single 64GB Apple Mac Studio.
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