Researchers introduce mathematical primitives and a four-dimension benchmark, identify Discovery as the dominant bottleneck in LLM mathematical reasoning, and improve reasoning with a primitive-privileged self-distillation framework
The work introduces the notion of Mathematical Primitive and a benchmark that evaluates mathematical reasoning along four dimensions—Discovery, Generation, Digestion, and Execution—and a systematic diagnosis shows that solution accuracy masks distinct capability profiles, that primitives unlock substantial latent execution capacity, and that Discovery is the dominant bottleneck; building on the finding that discovery-limited failures are particularly amenable to repair, it proposes a primitive-privileged self-distillation framework that selectively transfers primitive-guided reasoning into the student model and consistently improves mathematical reasoning over baselines across model scales and challenging benchmarks.