Sharpen Without Search: On-Policy Distillation of Sequence-Level Power Distribution
On-policy power distillation trains one-shot sharpened reasoning, lifting MATH500 by up to 23 points.
On-policy power distillation (OPPD) trains a language model to emit answers from a sequence-level power distribution in one generation, avoiding multi-candidate power sampling. A sequential Monte Carlo sampler has the student propose candidates while a frozen teacher's power distribution weights a maximum-likelihood update. Single-generation accuracy rises by up to 23.0 points on MATH500 and 27.3 on GSM8K, and exceeds 64-candidate power sampling by 2.4 and 3.5 points. Versus GRPO with verified rewards, OPPD is higher by 3.8, 4.0, and 5.4 points on MATH500, GSM8K, and AIME; combining them adds up to 9.3 points, and math-only training lifts HumanEval by up to 5.3.
- OPPD replaces multi-sample power search with one trained generation.
- MATH500 and GSM8K rise by up to 23.0 and 27.3 points.
- Beats GRPO by 3.8 to 5.4 points; stacking adds up to 9.3.
- A loss coefficient sets the absorbed exponent between 1.19 and 2.02.
- Math-only training raises HumanEval accuracy by up to 5.3 points.
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A language model can give a correct answer more probability than any single incorrect answer and still usually sample an incorrect one, because the incorrect answers together hold more probability. The power distribution raises each complete answer's probability to a power above one and renormalizes, shifting probability toward answers the model finds most likely (sharpening). Sampling from it improves reasoning without changing parameters, but needs many scored candidates per query. We show that a model can instead be trained to produce such answers in one generation. On-policy power distillation (OPPD) runs a sequential Monte Carlo sampler in which the model being trained generates candidates and a frozen teacher's power distribution weights them; the same probabilities weight each answer in a maximum-likelihood update. Training raises single-generation accuracy by up to 23.0 points on MATH500 and 27.3 on GSM8K over the untrained model at the same temperature, and one generation scores 2.4 and 3.5 points above published power sampling with 64 candidates, recovering 94 percent of the gain that 16 candidates give the untrained model. For context, against GRPO trained with verified rewards from the same checkpoint and budget, OPPD scores 3.8, 4.0 and 5.4 points higher on MATH500, GSM8K and AIME using no reference answers; the two are complementary, and OPPD applied after GRPO adds up to 9.3 points. Trained only on mathematics, OPPD raises HumanEval accuracy by up to 5.3 points. One loss coefficient moves the sharpening exponent the model absorbs between 1.19 and 2.02, against 1.14 for ordinary on-policy distillation, and it rises mostly on the model's own answers. Gains hold across model families and sizes, including a model already trained with verified rewards, where lowering the temperature gives nothing and OPPD adds 4.4 points on MATH500. Code: https://github.com/ArminAzizi98/OPPD.
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2610.06804