Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration

2025-04-17

AI Summary

Multimodal large language models (MLLMs) exhibit unreliable geometric problem solving (GPS) due to scarcity of fine-grained annotated data and severe reasoning hallucinations. Method: This paper proposes GeoLogic, a neuro-symbolic collaborative framework. It introduces (1) GeoGen, the first automated method for generating high-quality synthetic data—including geometric diagrams and stepwise reasoning traces—and (2) a bidirectional natural language–symbolic verification mechanism integrating a procedural geometric theorem engine, multi-stage data synthesis, supervised fine-tuning, and runtime symbolic validation. Results: Evaluated on multiple geometric reasoning benchmarks, GeoLogic significantly outperforms state-of-the-art MLLMs, effectively mitigating hallucinations while improving answer accuracy, logical rigor, and interpretability of reasoning steps.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, extbf{GeoGen} produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train extbf{GeoLogic}, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

Problem

• Improving MLLMs' geometric problem-solving via symbolic-neural integration
• Generating high-quality geometry QA pairs to reduce hallucinations
• Enhancing logical reasoning by combining LLMs with symbolic tools

Innovation

• Automatically generates step-wise reasoning paths
• Integrates symbolic reasoning for high-quality data
• Trains LLM with synthetic data for verification