MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles
This provides a rigorous testbed for advancing compositional reasoning in AI, addressing a domain-specific challenge in vision and symbols.
The authors tackled the problem of evaluating visual symbolic compositional reasoning by introducing MathSticks, a benchmark with matchstick puzzles, and found that current vision-language models perform poorly, with humans achieving over 90% accuracy.
We introduce \textsc{MathSticks}, a benchmark for Visual Symbolic Compositional Reasoning (VSCR), which unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation that must be corrected by moving one or two sticks under strict conservation rules. The benchmark includes both text-guided and purely visual settings, systematically covering digit scale, move complexity, solution multiplicity, and operator variation, with 1.4M generated instances and a curated test set. Evaluations of 14 vision--language models reveal substantial limitations: closed-source models succeed only on simple cases, open-source models fail in the visual regime, while humans exceed 90\% accuracy. These findings establish \textsc{MathSticks} as a rigorous testbed for advancing compositional reasoning across vision and symbols. Our code and dataset are publicly available at https://github.com/Yuheng2000/MathSticks.