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The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

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Briefings

This paper investigates whether Large Language Models possess genuine mathematical understanding or merely pattern matching. The authors propose a 'Mathematical Primitive' framework to measure structural reasoning capabilities, introducing a new benchmark with four dimensions: Discovery, Generation, Digestion, and Execution. Key findings indicate that solution accuracy often hides distinct capability profiles, with Discovery being the primary bottleneck. The study concludes that discovery-limited failures can be repaired using a primitive-privileged self-distillation framework, which improves reasoning across various model scales.

Key points

• The authors propose a 'Mathematical Primitive' framework to measure structural mathematical understanding in LLMs.
• A new benchmark evaluates mathematical reasoning across four dimensions: Discovery, Generation, Digestion, and Execution.

Context

LLMs show strong performance on frontier math problems but it is unclear if they possess underlying structural understanding. This research aims to diagnose capabilities and leverage findings for post-training improvements.

Limitations

Evidence is limited to the paper's findings; no additional background or external data is supplied. The study focuses on specific dimensions of reasoning and does not claim universal applicability to all mathematical tasks.

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