Research map / Large language models / Agents, code and math
GNS: Solving Plane Geometry Problems by Neural-Symbolic Reasoning with Multi-Modal LLMs
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes GNS, a neural-symbolic framework that fine-tunes MLLMs to predict geometry knowledge, parse diagrams into symbolic clauses, generate solution programs, and execute them with SymPy, plus a 260K-sample GNS-260K dataset.
Problem
Plane geometry problem solving requires joint understanding of diagrams and text plus precise computation, which general MLLMs handle poorly; prior data (e.g., Geo170K) lacks structured annotations for these subtasks.
Approach
Train MLLMs on multi-task annotations (knowledge prediction, symbolic clause parsing, reasoning, symbolic solutions) so they output symbolic solution programs that an external SymPy-based solver executes, rather than doing arithmetic in natural language.
Key results
- Phi3-Vision-based GNS reaches 63.9% on MathVista testmini GPS, the reported top result, above GPT-4o (60.6%).
- LLaVA-1.5-13B-based GNS reaches 67.0%+ new SOTA on GeoQA (68.3% reported in Table 2) and 27.1% on MathVerse testmini.
- Ablation with LLaVA-1.5-7B: removing symbolic computation drops accuracy from 62.0% to 57.2%; without symbolic parsing and knowledge prediction accuracy falls to 52.4%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train with GNS-260K and use the GNS framework | DeepSeek-VL-1.3B · MathVista testmini GPS | accuracy: 19.7 -> 55.3 | Helped |
| Train with GNS-260K and use the GNS framework | MiniCPM-Llama3-V2.5-8B · MathVista testmini GPS | accuracy: 43.3* -> 61.1 | Helped |
| Train with GNS-260K and use the GNS framework | LLaVA-1.5-7B · MathVista testmini GPS | accuracy: 25.0* -> 62.0 | Helped |
| Train with GNS-260K and use the GNS framework | LLaVA-1.5-13B · MathVista testmini GPS | accuracy: 30.3* -> 63.9 | Helped |
| Train with GNS-260K and use the GNS framework | Phi3-V-128k-Instruct-4.2B · MathVista testmini GPS | accuracy: 40.9* -> 63.9 | Helped |
| Train with GNS-260K and use the GNS framework | DeepSeek-VL-1.3B · MathVerse testmini | accuracy: 4.9* -> 13.5 | Helped |
| Train with GNS-260K and use the GNS framework | MiniCPM-Llama3-V2.5-8B · MathVerse testmini | accuracy: 15.6* -> 23.2 | Helped |
| Train with GNS-260K and use the GNS framework | LLaVA-1.5-13B · MathVerse testmini | accuracy: 7.6 -> 27.1 | Helped |
| Add symbolic computation (ablation) | GNS with LLaVA-1.5-7B · MathVista testmini GPS | accuracy: 55.8 -> 52.4; 62.0 -> 57.2 | Helped |
| Add symbolic parsing (ablation) | GNS with LLaVA-1.5-7B · MathVista testmini GPS | accuracy: 60.6 -> 55.8 | Helped |
| Add knowledge prediction (ablation) | GNS with LLaVA-1.5-7B · MathVista testmini GPS | accuracy: 60.6 -> 62.0 | Helped |
Surprising findings
- The GNS-trained DeepSeek-VL-1.3B (55.3% on MathVista GPS) is competitive with GPT-4-Turbo and G-LLaVA-13B despite its small size.
Limitations
- Symbolic parsing and reasoning annotations partly rely on GPT-4-generated natural language descriptions and rule-based conversions.
- Performance on MathVerse remains below GPT-4V, which the authors attribute to its scale and broader training data.
- Evaluation is limited to plane geometry; the approach is not tested on other math domains.
Experimental setup
Datasets: GNS-260K PGPS9K GeoQA+ Geo170K
Benchmarks: MathVista (GPS testmini) MathVerse testmini GeoQA Geometry3K
Metrics: accuracy ROUGE-1
Baselines: GPT-4o GPT-4V Gemini-1.5-Flash Gemini Ultra G-LLaVA-7B G-LLaVA-13B Inter-GPS DualGeoSolver FiLM-BART
Builds on: Geo170K G-LLaVA Inter-GPS PGPS9K
Closest papers by meaning
- G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model (ICLR 2025 · similarity 0.89)
- Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning (CVPR 2026 · similarity 0.88)
- GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training (ICLR 2025 · similarity 0.87)
- Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions (CVPR 2026 · similarity 0.87)
- SolidGeo: Measuring Multimodal Spatial Math Reasoning in Solid Geometry (NeurIPS 2025 · similarity 0.86)
- Do Large Language Models Truly Understand Geometric Structures? (ICLR 2025 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.