FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation

• URL: http://arxiv.org/abs/2607.12982v2
• Date: Tue, 21 Jul 2026 09:49:15 GMT
• Title: FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation
• Abstract summary: FormalAnalyticGeo is a framework for automatic generation of analytic geometry problems.<n>It bridges free-form problem text with precise diagram rendering via a Signed Distance Field (SDF) engine.<n>Applying FormalAnalyticGeo at scale yields AnalyticGeo7K, a dataset of over 7K verified multimodal problems.
• Score: 5.058793220027875
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Math reasoning has achieved significant progress with the rapid advancement of Multimodal Large Language Models (MLLMs), however analytic geometry remains largely underexplored, primarily due to the scarcity of annotated samples. Existing diagram generation approaches struggle with analytic geometry: template methods cannot handle constraint-driven layouts, and generative models lack the geometric precision to render annotated conic curves correctly. We present FormalAnalyticGeo, a scalable framework for fully automatic generation of multimodal analytic geometry problems. Leveraging the rigor of formal languages, we design the framework around CDL (Condition Description Language), a formal intermediate representation that bridges free-form problem text with precise diagram rendering via a Signed Distance Field (SDF) engine. The framework employs four specialized LLM components in sequence: a Generator that produces diverse analytic geometry problems, a Formalizer that converts each problem into CDL for SDF-based rendering, a Measurer that extracts ground-truth answers through vision-based measurement on the rendered diagrams, and a Quality Verifier that checks outputs at three stages. Structured feedback from the Quality Verifier drives automatic retry, forming a closed loop that eliminates any need for human annotation. Applying FormalAnalyticGeo at scale yields AnalyticGeo7K, a dataset of over 7K verified multimodal problems, each with aligned text, diagram, formal annotation, and ground truth.Experiments show that the generated problems achieve a median ground-truth relative error of 0.70\%, with 82.3\% of answers falling within 5\% of the exact symbolic solution. Our framework and dataset will be publicly released.

Related papers

• Euclean: Automated Geometry Problem Formalization with Unified Verification in Lean [7.28030691695892]
  Euclean is a framework for automatically formalizing geometry in native Mathlib.<n>Human evaluation shows 48.89% TOP1 and 73.33% TOP5 accuracy.
  arXiv  Detail & Related papers  (2026-06-17T15:27:17Z)
• VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verification [12.221274109590176]
  We introduce VeriGeo, a controllable geometry generation framework grounded in executable reasoning traces.<n>A three-stage pipeline checks numerical consistency, analytical realizability, and global consistency.<n>Supervised fine-tuning on 8.7k examples generated by VeriGeo achieves the best reported GeoQA performance.
  arXiv  Detail & Related papers  (2026-06-12T06:59:44Z)
• Agentic Large Language Models for Automated Structural Analysis of 3D Frame Systems [9.941684692042632]
  Large language models (LLMs) have emerged as powerful foundation models with strong reasoning capabilities across domains.<n>In structural engineering, recent efforts have developed agentic LLMs for automated analysis of plane frames.<n>This paper proposes an agentic LLM framework for automated structural analysis of 3D frames from natural inputs.
  arXiv  Detail & Related papers  (2026-06-02T20:34:11Z)
• GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving [55.14836667214487]
  GeoFocus is a novel framework comprising two core modules.<n>GeoFocus achieves a 4.7% accuracy improvement over leading specialized models.<n>It demonstrates superior robustness in MATHVERSE under diverse visual conditions.
  arXiv  Detail & Related papers  (2026-02-09T11:15:01Z)
• TangramPuzzle: Evaluating Multimodal Large Language Models with Compositional Spatial Reasoning [104.66714520975837]
  We introduce a geometry-grounded benchmark designed to evaluate compositional spatial reasoning through the lens of the classic Tangram game.<n>We propose the Tangram Construction Expression (TCE), a symbolic geometric framework that grounds tangram assemblies in exact, machine-verifiable coordinate specifications.<n>We conduct extensive evaluation experiments on advanced open-source and proprietary models, revealing an interesting insight: MLLMs tend to prioritize matching the target silhouette while neglecting geometric constraints.
  arXiv  Detail & Related papers  (2026-01-23T07:35:05Z)
• GeoRef: Referring Expressions in Geometry via Task Formulation, Synthetic Supervision, and Reinforced MLLM-based Solutions [45.70578816057097]
  We introduce the task of Referring Expression (REC) for geometric problems.<n>REC evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts.<n>We generate a large-scale synthetic training dataset using a structured geometric formal language.
  arXiv  Detail & Related papers  (2025-09-25T12:00:52Z)
• NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation [23.592137999309546]
  NeSyGeo is a novel neuro-symbolic framework for generating geometric reasoning data.<n>We release a new benchmark NeSyGeo-Test for evaluating geometric reasoning abilities in MLLMs.
  arXiv  Detail & Related papers  (2025-05-21T16:45:49Z)
• Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration [57.95306827012784]
  We propose GeoGen, a pipeline that can automatically generate step-wise reasoning paths for geometry diagrams.<n>By leveraging the precise symbolic reasoning, textbfGeoGen produces large-scale, high-quality question-answer pairs.<n>We train textbfGeoLogic, a Large Language Model (LLM), using synthetic data generated by GeoGen.
  arXiv  Detail & Related papers  (2025-04-17T09:13:46Z)
• 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)
• G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model [121.07873620883322]
  Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities.<n>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)
• Dense Non-Rigid Structure from Motion: A Manifold Viewpoint [162.88686222340962]
  Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. We show that our approach significantly improves accuracy, scalability, and robustness against noise.
  arXiv  Detail & Related papers  (2020-06-15T09:15:54Z)

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.