Problem
Research questions and friction points this paper is trying to address.
language model reasoning
power distribution
probability sharpening
sampling efficiency
on-policy distillation
Sharpen Without Search: On-Policy Distillation of Sequence-Level Power Distribution
🤖 AI Summary
This study addresses the vulnerability of single-pass generation in language models to accumulated error probabilities and the high computational overhead of traditional Power sampling, which relies on scoring multiple candidates. We propose Online Policy Distillation (OPPD), a method that transfers the sharpened Power distribution knowledge from a teacher model to a student model via online policy distillation, sequential Monte Carlo sampling, and maximum likelihood estimation. OPPD achieves search-free inference gains equivalent to multi-candidate decoding in single-pass generation, with a loss coefficient enabling dynamic adjustment of the sharpening intensity. Empirically, OPPD improves performance by 23.0 and 27.3 points on MATH500 and GSM8K, respectively, surpassing 64-candidate Power sampling. Furthermore, it demonstrates complementary and superior performance relative to GRPO, alongside strong cross-model generalization and transferability from mathematical to code reasoning tasks.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
On-Policy Power Distillation
Power Distribution Sharpening
Sequential Monte Carlo
Sequence-Level Distillation
Reasoning
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