Robust Reasoning via Dynamic Token Selection for Distribution-Aligned Self-Distillation

On-policy distillation is an efficient alternative to reinforcement learning, offering dense token-level training signals. However, its reliance on a stronger external teacher has driven recent work on on-policy self-distillation, where the same model serves as both teacher and student under different prompt contexts. Yet, existing self-distillation methods largely reduce learning to KL matching toward the context-augmented teacher model. This approach often suffers from training instability and can degrade reasoning performance over time. Moreover, self-distillation from the same model with prompt augmentation lacks the exploratory diversity provided by a genuine external teacher. To address these limitations, we move beyond fixed-teacher KL matching and propose \textbf{P}reference-\textbf{B}ased \textbf{S}elf-\textbf{D}istillation (\textbf{PBSD}), which revisits on-policy self-distillation through a reward-regularized perspective. Instead of directly matching the teacher distribution, we derive a reward-regularized objective whose analytic optimum is a reward-reweighted teacher distribution, yielding a target policy provably superior to the original teacher under this objective. Practically, PBSD optimizes preference gaps between teacher and student samples while maintaining on-policy student sampling. We support this framework with a statistical analysis of the induced preference-learning problem, formally establishing when on policy self-distillation is preferable to learning from an external teacher in our setting. Experiments on mathematical reasoning and tool-use benchmarks across multiple model scales demonstrate that PBSD consistently achieves the strongest average performance among comparable baselines, showing improved training stability over prior self-distillation baselines while preserving token efficiency.

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.