Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver

• URL: http://arxiv.org/abs/2409.04214v2
• Date: Mon, 9 Sep 2024 02:46:34 GMT
• Title: Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver
• Authors: Zeren Zhang, Jo-Ku Cheng, Jingyang Deng, Lu Tian, Jinwen Ma, Ziran Qin, Xiaokai Zhang, Na Zhu, Tuo Leng,
• Abstract summary: We introduce a new framework that integrates visual features, geometric formal language, and natural language representations. We propose a novel synthetic data approach and create a large-scale geometric dataset, SynthGeo228K, annotated with both formal and natural language captions. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.
• Score: 11.69164802295844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to understand geometric diagrams, performing no better in geometry problem solving than LLMs that only process text. This limitation is amplified by the lack of effective methods for representing geometric relationships. To address these issues, we introduce the Diagram Formalization Enhanced Geometry Problem Solver (DFE-GPS), a new framework that integrates visual features, geometric formal language, and natural language representations. We propose a novel synthetic data approach and create a large-scale geometric dataset, SynthGeo228K, annotated with both formal and natural language captions, designed to enhance the vision encoder for a better understanding of geometric structures. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.

Related papers

• GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models [10.443672399225983]
  Vision-parametric models (VLMs) have made significant progress in various multimodal tasks. They still struggle with geometry problems and are significantly limited by their inability to perform mathematical operations not seen during pre-training. We present GeoCoder, which leverages modular code-finetuning to generate and execute code using a predefined geometry function library.
  arXiv  Detail & Related papers  (2024-10-17T12:56:52Z)
• Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram [78.79651421493058]
  We propose a neural-symbolic model for plane geometry problem solving (PGPS) with three key steps: modal fusion, reasoning process and knowledge verification. For reasoning, we design an explicable solution program to describe the geometric reasoning process, and employ a self-limited decoder to generate solution program autoregressively. We also construct a large-scale geometry problem dataset called PGPS9K, containing fine-grained annotations of textual clauses, solution program and involved knowledge solvers.
  arXiv  Detail & Related papers  (2024-07-10T02:45:22Z)
• GOLD: Geometry Problem Solver with Natural Language Description [7.9345421580482185]
  We present the Geometry problem sOlver with natural Language Description (GOLD) model. GOLD enhances the extraction of geometric relations by separately processing symbols and geometric primitives within the diagram. It converts the extracted relations into natural language descriptions, efficiently utilizing large language models to solve geometry math problems.
  arXiv  Detail & Related papers  (2024-05-01T13:00:51Z)
• A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications [67.33002207179923]
  This paper presents a survey of data structures, models, and applications related to geometric GNNs. We provide a unified view of existing models from the geometric message passing perspective. We also summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.
  arXiv  Detail & Related papers  (2024-03-01T12:13:04Z)
• Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images [56.86175251327466]
  We introduce a novel approach to learn geometries such as depth and surface normal from images while incorporating geometric context. Our approach extracts geometric context that encodes the geometric variations present in the input image and correlates depth estimation with geometric constraints. Our method unifies depth and surface normal estimations within a cohesive framework, which enables the generation of high-quality 3D geometry from images.
  arXiv  Detail & Related papers  (2024-02-08T17:57:59Z)
• GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning [17.61621287003562]
  We evaluate vision language models (VLMs) along various axes through the lens of geometry problems. We procedurally create a synthetic dataset of geometry questions with controllable difficulty levels along multiple axes. The empirical results obtained using our benchmark for state-of-the-art VLMs indicate that these models are not as capable in subjects like geometry.
  arXiv  Detail & Related papers  (2023-12-19T15:25:39Z)
• G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model [124.68242155098189]
  Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities. G-LLaVA demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.
  arXiv  Detail & Related papers  (2023-12-18T17:36:20Z)
• GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning [172.36214872466707]
  We focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. We propose a Geometric Question Answering dataset GeoQA, containing 5,010 geometric problems with corresponding annotated programs.
  arXiv  Detail & Related papers  (2021-05-30T12:34:17Z)
• Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning [123.06420835072225]
  We construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem solver (Inter-GPS) Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step.
  arXiv  Detail & Related papers  (2021-05-10T07:46:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.