SHAPE of Chain-of-Thought in Math Reasoning
Quick summary
arXiv:2608.28600v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their reasoning remain underexplored. We introduce \texttt{SHAPE}, a framework that analyzes Chain-of-Thought (CoT) trajectories through two lenses developed in mathematics education: (1) semantic spaces: the model's evolving mathematical interpretations of a problem (e.g., algebraic, geometric), and (2) heuristics: the specific mathematical actions taken within those spaces (e.g., simplifying the probl
Key takeaways
- arXiv:2608.28600v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their reasoning remain underexplored.
- We introduce \texttt{SHAPE}, a framework that analyzes Chain-of-Thought (CoT) trajectories through two lenses developed in mathematics education: (1) semantic spaces: the model's evolving mathematical interpretations of a problem (e.g., algebraic, geometric), and (2) heuristics: the specific mathematical actions taken within those spaces (e.g., simplifying the probl
Why it matters
This model development creates a new option for users and a new testing obligation for developers. A fixed evaluation set comparing quality, cost and failure behavior is more useful than launch claims.
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