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Entropy-Aware On-Policy Distillation of Language Models

Paper · 2026 · Woogyeol Jin, Taywon Min, Yongjin Yang et al.

Summary

On-policy distillation (OPD) trains a small student on its own sampled outputs, using token-level feedback from a larger teacher. It is usually optimized with reverse KL. The authors argue that this mode-seeking objective harms the student where the teacher is uncertain. At those positions, reverse KL pushes the student toward one option, shrinks output diversity, and gives noisy gradients. They show this in two ways: an entropy analysis of a Qwen3-8B teacher against a distilled Qwen3-1.7B-Base student on AIME prompts, and a simplified categorical toy setting. Their fix is Entropy-Aware On-Policy Distillation (EOPD). It keeps reverse KL as the default loss but adds a forward KL term at token positions where teacher entropy exceeds a threshold. This lets the student cover several plausible continuations at decision points while still imitating the teacher closely elsewhere, with little extra cost. Across six math reasoning benchmarks, EOPD beat standard OPD for Qwen3-0.6B, 1.7B and 4B base students, and the gains grew with model size. The work shows that reasoning ability transfers better when the teacher's uncertainty is preserved.

Key points

  • Diversity collapse after standard OPD: high-entropy tokens (entropy ≥ 1.0) make up 6.8% of the distilled student's outputs, against 18.5% for the Qwen3-8B teacher.
  • Toy experiment (80-way categorical distribution): with a high-entropy teacher, the student's top-1 prediction changed about 84.0 times during training, against 7.3 with a low-entropy teacher. This points to unstable reverse-KL signals.
  • Average gains over OPD across six math benchmarks (Avg@8 / Pass@8):
    • Qwen3-0.6B-Base: +1.16 / +1.37
    • Qwen3-1.7B-Base: +0.99 / +2.39
    • Qwen3-4B-Base: +1.80 / +5.05
  • Placement of forward KL matters: with threshold τ = 0.8, forward KL is active on roughly 15–20% of tokens. Applying it to a random 20% of positions mostly underperformed both EOPD and full forward KL on MATH500, AMC23, AIME24 and AIME25. Pure forward-KL OPD also trailed reverse-KL OPD.
  • Availability: the paper appears at ICML 2026, and the code is released at github.com/WLS04/EOPD.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Fields, topics and concepts

Cite

Cite as Woogyeol Jin, Taywon Min, Yongjin Yang, Dennis Wei, Yi Zhou, Swanand Ravindra Kadhe, Nathalie Baracaldo and Kimin Lee. 2026. Entropy-Aware On-Policy Distillation of Language Models. arXiv:2603.07079.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2603.07079 · arXiv 2603.07079

@misc{jin2026entropy,
  title = {{Entropy-Aware On-Policy Distillation of Language Models}},
  author = {Woogyeol Jin, Taywon Min, Yongjin Yang, Dennis Wei, Yi Zhou, Swanand Ravindra Kadhe, Nathalie Baracaldo and Kimin Lee},
  year = {2026},
  doi = {10.48550/arxiv.2603.07079},
  eprint = {2603.07079},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2603.07079}
}

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