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Life sciences · Preprint
arXiv · September 30, 2026
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Role prompting elicits specialized behavior from large language models through an expert identity, offering a lightweight way to guide reasoning on demanding tasks. However, evaluating or distilling complete role-prompted answers can miss useful next-token preferences when the sampled solution remains incorrect. Transferring these preferences also requires an objective that reaches alternatives the student rarely predicts. We introduce OPSRD, which uses a fixed expert role as privileged teaching context for on-policy self-distillation without reference solutions. A role-free student generates a trajectory, and a frozen instance of the same base model supplies role-conditioned distributions on its exact prefixes, exposing alternatives beyond the sampled continuation. Teacher-weighted forward KL targets alternatives the student underestimates, with clipping to limit individual vocabulary contributions. Supervision is restricted to the highest-entropy half of student positions, concentrating learning where predictions are uncertain. Experiments on three competition-math benchmarks with Qwen3-1.7B, 4B, and 8B show improvements over the base models without role prompts at inference. Forward KL achieves the highest macro-averaged accuracy among the three evaluated divergences at every scale. Code is available at https://github.com/zhansan114514/OPSRD.