Sharpen Without Search: On-Policy Distillation of Sequence-Level Power Distribution
On-policy power distillation trains models to sample sharpened answers once, lifting MATH500 by up to 23 points.
On-policy power distillation (OPPD) trains a language model to emit answers from a sharpened sequence-level power distribution in one generation, using a sequential Monte Carlo sampler weighted by a frozen teacher. Versus the untrained model at the same temperature, accuracy rises by up to 23.0 points on MATH500 and 27.3 on GSM8K, and one sample exceeds published 64-candidate power sampling by 2.4 and 3.5 points. Against GRPO from the same checkpoint and budget, OPPD is 3.8, 4.0 and 5.4 points higher on MATH500, GSM8K and AIME without reference answers, and applying OPPD after GRPO adds up to 9.3 points. A single loss coefficient sets the absorbed sharpening exponent between 1.19 and 2.02; math-only training also raises HumanEval by up to 5.3 points.
- OPPD trains the student with a teacher's power-weighted sequential Monte Carlo samples.
- Single-generation accuracy rises up to 23.0 points on MATH500 and 27.3 on GSM8K.
- One sample beats 64-candidate power sampling by 2.4 and 3.5 points.
- OPPD beats same-budget GRPO by 3.8, 4.0 and 5.4 points without reference answers.
- Math-only training also lifts HumanEval by up to 5.3 points.
Full article290 words · extracted from arxiv.org · click to collapse
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://arxiv.org/abs/2610.06804