DCSD decouples credit direction from magnitude in self-distillation, topping 11 benchmarks and lifting math reasoning by 8.45 points over base models
The work introduces Decoupled Credit Self-Distillation (DCSD), which uses belief-margin probing to set each reasoning step's credit direction and marginal information gain to quantify its contribution magnitude, leaving the privileged teacher to allocate credit only within steps; across 11 mathematical and multimodal reasoning benchmarks DCSD achieves the best overall scores against GRPO, OPSD, RLSD and RLCSD, improving overall score by 8.45 points on mathematical reasoning and 7.01 points on multimodal reasoning over base models, while correcting credit direction for about 6% of tokens and reducing token credit magnitude by roughly 1.5 times.