H2SD: Hybrid Hindsight Self-Distillation

Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but scalar trajectory rewards offer limited guidance for token-level credit assignment. Existing self-distillation methods incorporate privileged teacher information through fixed strategies: direct distribution matching may destabilize successful behavior, while magnitude modulation provides limited corrective guidance after failure. We propose Hybrid Hindsight Self-Distillation (H2SD), which adapts both teacher context and update strategy to trajectory correctness. For successful trajectories, the teacher conditions on the verified student response and a rephrasing instruction to rescore the original tokens. These scores modulate reward-derived updates while preserving advantage signs. For failed trajectories, a verified reference hint guides corrective supervision through reverse KL distillation. Across Sudoku, Calcudoku, Arrow Maze, and mathematical reasoning with two Qwen3 models, H2SD achieves an overall average accuracy of 43.33%, outperforming the strongest baseline by 11.43 percentage points while maintaining stable optimization.