"The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Framework

Chain-of-Thought (CoT) reasoning empowers Large Language Models (LLMs) with remarkable capabilities but typically requires prohibitive parameter scales. CoT distillation has emerged as a promising paradigm to transfer reasoning prowess into compact Student Models (SLMs), but existing approaches often rely on a solitary teacher, capping the student's potential since individual LLMs often exhibit distinct capability biases and may suffer from catastrophic forgetting. While leveraging diverse teachers seems appealing, effectively fusing their supervisions remains challenging: teacher-student incompatibility risks amplifying hallucinations, and passive supervision fails to ensure genuine logic internalization. To address this, we introduce COMPACT, a framework that adaptively fuses supervisions from different teachers by dynamically weighting teacher gradients based on the student's real-time compatibility evaluated by a multi-dimensional metric: (1) Graph-based Consensus to filter misleading rationales by identifying mainstream reasoning paths; (2) Mutual-Information-based Adaptability to detect "epiphany moments" for genuinely understanding the reasoning process rather than merely imitating; and (3) Loss-based Difficulty to assess student receptivity to the teacher's guidance and prevent negative transfer. Extensive experiments and latent space analysis demonstrate that COMPACT effectively integrates diverse reasoning capabilities without damaging the model's original knowledge structure, achieving state-of-the-art performance on various benchmarks while mitigating catastrophic forgetting.