Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning

TL;DR

This paper introduces Direction-Adaptive Self-Distillation (DASD), a novel method that improves LLM reasoning by adaptively guiding tokens based on their uncertainty, balancing exploration and accuracy.

Contribution

DASD redefines self-distillation by applying entropy-based directional supervision, enhancing reasoning performance over existing uniform approaches.

Findings

DASD achieves the best macro Avg@16 on six reasoning benchmarks.

DASD preserves exploration without sacrificing step accuracy.

Analysis shows improved reasoning health and generalization.

Abstract

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.