SHAPE of Thinking: Mathematical Heuristics for Analyzing and Improving LLM Reasoning
Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet final-answer accuracy reveals little about the strategies they use. We introduce \texttt{SHAPE} (Structured Heuristic Analysis for Problem-solving Evolution), a framework grounded in mathematics-education research that characterizes local mathematical actions in reasoning trajectories using a problem-independent heuristic taxonomy. Using \texttt{SHAPE}, we examine two previously hypothesized phenomena in LLM reasoning. First, we revisit the hypothesis that LLMs reuse learned solution techniques under problem perturbations. Across six models on MATH-Perturb, perturbations requiring a different...
| Authors | Jonghyun Song, Sangjun Song, Minjae Oh et al. |
|---|---|
| Primary category | cs.AI |
| Published | 28 June 2026 |
| Last updated at source | 14 October 2026 |
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