Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models

摘要

Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs’ abilities in constructive geometric problem-solving, – one of the most fundamental steps in developing human mathematical reasoning, revealing notable challenges in this domain. LLMs exhibit biases in variable names, struggle with 2D spatial relationships and planning, and hallucinate object placements. To this end, we introduce a framework that enhances LLMs’ reasoning potential through a multi-agent system conducting internal dialogue. This work underscores LLMs’ limitations in geometric reasoning and improves their capabilities through self-correction, collaboration, and diverse role specializations.