GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization

ArXi:2506.07160v3 Announce Type: replace Recent progress in large language models (LLMs) has boosted mathematical reasoning, yet geometry remains challenging where auxiliary construction is often essential. Prior methods either underperform or depend on very large models (e.g., GPT-4o), making them costly. We argue that reinforcement learning with verifiable rewards (e.g., GRPO) can train smaller models to couple auxiliary construction with solid geometric reasoning. However, naively applying GRPO yields unconditional rewards, encouraging indiscriminate and sometimes harmful constructions.