arXiv Machine Learning By Kaijian Zou, Emiliano Penaloza, MohammadHossein Rezaei, Anisha Gunjal, Mohit Raghavendra, Lu Wang, Yunzhong He, Anas Mahmoud

Predicting Privileged Information Effectiveness for On-Policy Self-Distillation

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The paper studies how different configurations of privileged information (PI) affect on‑policy self‑distillation (OPSD) for large language models. By evaluating 16 PI setups across three agentic benchmarks and multiple student models, it finds that PI effectiveness varies with content, generation source, and model scale, with information‑dense trajectories and stronger generators yielding larger gains. The authors also propose KL‑based metrics, particularly Δd−_err, to predict PI utility before training, showing that selecting PI with this metric improves post‑training performance and remains beneficial when combined with GRPO.

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