The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models
This study addresses the reasoning bottlenecks large language models encounter due to their lack of structured mathematical understanding. To this end, it pioneers the conceptual framework of "mathematical primitives" and constructs a four-dimensional diagnostic benchmark to precisely identify model deficiencies. Building upon this foundation, we propose a primitive-privileged self-distillation framework that leverages probing techniques and targeted repair mechanisms to achieve fine-grained, primitive-based knowledge distillation. Experimental results demonstrate that our approach significantly enhances the mathematical reasoning capabilities of models across varying scales, effectively overcoming identified bottlenecks and comprehensively outperforming existing baselines. This work establishes a novel paradigm for augmenting the structured mathematical reasoning of large language models.