SHAPE of Chain-of-Thought in Math Reasoning
The paper argues that what matters in math CoT is the heuristic path, not just the surface shape of the explanation.
SHAPE analyzes model reasoning through mathematical “semantic spaces” and the heuristics used inside them. The authors report that heuristic use explains final-answer correctness better than traditional CoT features. Correct solutions tended to keep effort within a few semantic spaces instead of jumping across many. They also find reinforcement learning pushes models toward mode-seeking heuristic behavior, while training for more diverse heuristics improves accuracy. HF Daily Papers' note
SHAPE analyzes model reasoning through mathematical “semantic spaces” and the heuristics used inside them. The authors report that heuristic use explains final-answer correctness better than traditional CoT features. Correct solutions tended to keep effort within a few semantic spaces instead of jumping across many. They also find reinforcement learning pushes models toward mode-seeking heuristic behavior, while training for more diverse heuristics improves accuracy. HF Daily Papers' note
score 4