BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction

2026-06-03

AI Summary

Existing approaches to geometric problem solving suffer from poor adaptability of symbolic systems, hallucination-prone neural models, and predominantly unidirectional neuro-symbolic architectures that struggle to correct early errors. This work proposes the first neuro-symbolic framework enabling bidirectional interaction, in which a multimodal large language model (MLLM) and a symbolic solver engage in a feedback loop to dynamically refine formal representations, generate auxiliary hypotheses, and collaboratively resolve symbolic inconsistencies. By transcending the limitations of conventional unidirectional pipelines, this mechanism substantially enhances the robustness, accuracy, and stability of complex geometric reasoning.

Abstract

Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions.

Problem

• geometry problem solving
• neuro-symbolic
• hallucination
• symbolic reasoning
• bidirectional interaction

Innovation

• Bidirectional Neuro-Symbolic Interaction
• Geometry Problem Solving
• Neuro-Symbolic Hybrid
• MLLM Adviser
• Symbolic Solver