On-policy self-distillation trains a reasoning model on its own rollouts while a teacher, often the same model conditioned on privileged context, provides dense token-level supervision. Existing objectives typically weight the teacher's token-level signal uniformly across a chain-of-thought sequence, despite substantial variation in the entropy of the teacher's predictive distribution. We propose EGRSD (Entropy-Guided Reinforced Self-Distillation), which unifies token-level updates through three signals: a reward-grounded direction, a teacher-student likelihood-ratio magnitude, and the proposed teacher-entropy confidence gate that down-weights high-entropy token positions while maintaining a nonzero lower bound on every token weight. We further introduce CL-EGRSD, a causal-lookahead variant that distinguishes sustained high-entropy spans from transient high-entropy positions whose following context rapidly becomes low entropy. Experiments with Qwen3-4B and Qwen3-8B in thinking mode show that EGRSD and CL-EGRSD advance the accuracy-length frontier among the compared trainable methods.
On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose \textbf{Direction-Adaptive Self-Distillation} (\textbf{DASD}), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@k, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.
On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with that under privileged context, typically a verified solution. However, we show that the resulting distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce shorter, more direct outputs. We term this pathology \emph{privilege-induced style drift}, which can destabilize training and shorten responses. To address this, we propose \textbf{RLCSD} (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing style shifts induced by hints regardless of correctness and yielding a signal more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods, with additional results on agentic tasks supporting broader applicability. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to broader cross-model on-policy distillation.
We study on-policy self-distillation (OPSD), where a language model improves its reasoning ability by distilling privileged teacher distributions along its own on-policy trajectories. Despite its promise, OPSD can suffer from training instability due to a pattern mismatch between teacher and student responses. Self-reflected teacher responses may introduce reflection-induced biases and response templates that miscalibrate token-level supervision, ultimately harming the student's reasoning ability. To mitigate this issue, we propose OGLS-SD, an outcome-guided logit-steering framework that leverages verifiable outcome rewards to calibrate privileged teacher logits. Specifically, OGLS-SD contrasts teacher logits induced by successful and failed on-policy trajectories, constructing an outcome-discriminative steering direction for token-level guidance. Experiments on mathematical reasoning benchmarks show that OGLS-SD stabilizes self-distillation and improves performance over standard OPSD and other variants.