Collaborative Reasoning Distillation via Cross-Feedback and Coherent Curation

Reasoning capabilities are critical for advancing Large Language Models, yet current approaches either require massive computational budgets or struggle to effectively distill reasoning to smaller models. Standard distillation methods rely on outcome-based rewards, failing to distinguish between sound reasoning and lucky guesses. We propose Collaborative Reasoning Distillation (CRD), a framework that enhances reasoning in compact models through three innovations: (1) interactive cross-feedback where teachers iteratively critique each other's reasoning, (2) fine-grained step-wise quality assessment capturing logical validity independent of final answers, and (3) coherence-aware step stitching that synthesizes complementary strengths. Students are trained via Reasoning Quality Optimization (RQO) with budget constraints. Our model, CRD-4B, achieves 97.3\% on MATH-500 and 70.3\% on AIME'25, surpassing baselines while using only 50K training examples, up to 12 times smaller than the datasets of comparable models.