Entropy-Aware On-Policy Distillation of Language Models

Woogyeol Jin, Taywon Min, Yongjin Yang, Dennis Wei, Yi Zhou, Swanand Ravindra Kadhe, Nathalie Baracaldo, Kimin Lee
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:53926-53943, 2026.

Abstract

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher’s high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student–teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of $+1.37$ for Qwen3-0.6B-Base, $+2.39$ for Qwen3-1.7B-Base, and $+5.05$ for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer. Our code is publicly available at https://github.com/WLS04/EOPD.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-jin26e, title = {Entropy-Aware On-Policy Distillation of Language Models}, author = {Jin, Woogyeol and Min, Taywon and Yang, Yongjin and Wei, Dennis and Zhou, Yi and Kadhe, Swanand Ravindra and Baracaldo, Nathalie and Lee, Kimin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {53926--53943}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/jin26e/jin26e.pdf}, url = {https://proceedings.mlr.press/v306/jin26e.html}, abstract = {On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher’s high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student–teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of $+1.37$ for Qwen3-0.6B-Base, $+2.39$ for Qwen3-1.7B-Base, and $+5.05$ for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer. Our code is publicly available at https://github.com/WLS04/EOPD.} }
Endnote
%0 Conference Paper %T Entropy-Aware On-Policy Distillation of Language Models %A Woogyeol Jin %A Taywon Min %A Yongjin Yang %A Dennis Wei %A Yi Zhou %A Swanand Ravindra Kadhe %A Nathalie Baracaldo %A Kimin Lee %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-jin26e %I PMLR %P 53926--53943 %U https://proceedings.mlr.press/v306/jin26e.html %V 306 %X On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher’s high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student–teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of $+1.37$ for Qwen3-0.6B-Base, $+2.39$ for Qwen3-1.7B-Base, and $+5.05$ for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer. Our code is publicly available at https://github.com/WLS04/EOPD.
APA
Jin, W., Min, T., Yang, Y., Wei, D., Zhou, Y., Kadhe, S.R., Baracaldo, N. & Lee, K.. (2026). Entropy-Aware On-Policy Distillation of Language Models. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:53926-53943 Available from https://proceedings.mlr.press/v306/jin26e.html.

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