Geo-Code: A Code Framework for Reverse Code Generation from Geometric Images Based on Two-Stage Multi-Agent Evolution

2026-02-08

AI Summary

This work proposes the first multi-agent system–based inverse programming framework for geometric image reconstruction, addressing the challenge that existing inverse graphics methods struggle to preserve critical structural and semantic constraints in complex geometric imagery. The approach employs a two-stage pipeline: it first leverages visual operators and large language models to accurately extract pixel coordinates and visual attributes, then establishes a synthesis-rendering-verification loop where bidirectional visual feedback drives iterative code self-correction. Innovatively, the method decouples inverse generation into geometry modeling and metric-driven code evolution, orchestrated through a collaborative multi-agent mechanism. Experiments demonstrate significant improvements in geometric accuracy and visual consistency, with reconstructed outputs performing on par with original images in multimodal reasoning tasks. The authors also release the Geo-coder dataset (1,500+ samples) and the GeocodeLM model.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• 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

Program code serves as a bridge linking vision and logic, providing a feasible supervisory approach for enhancing the multimodal reasoning capability of large models through geometric operations such as auxiliary line construction and perspective transformation. Nevertheless, current inverse graphics methods face tremendous challenges in accurately reconstructing complex geometric details, which often results in the loss of key geometric constraints or structural distortion. To address this bottleneck, we propose Geo-coder -- the first inverse programming framework for geometric images based on a multi-agent system. Our method innovatively decouples the process into geometric modeling via pixel-wise anchoring and metric-driven code evolution: Stage 1 leverages the complementary advantages of visual operators and large models to achieve precise capture of pixel coordinates and visual attributes; Stage 2 introduces a synthesis-rendering-validation closed loop, where bidirectional visual feedback drives the self-correction of code. Extensive experiments demonstrate that Geo-coder achieves a substantial lead in both geometric reconstruction accuracy and visual consistency. Notably, by effectively preserving the core geometric semantics, the images reconstructed with our method exhibit equivalent performance to the original ones in multimodal reasoning tasks, which fully validates the robustness of the framework. Finally, to further reduce research costs, we have open-sourced the Geo-coder dataset constructed on the GeoCode framework, which contains more than 1,500 samples. On this basis, we have also open-sourced the GeocodeLM model, laying a solid data and model foundation for subsequent research in this field.

Problem

• inverse graphics
• geometric reconstruction
• geometric constraints
• structural distortion
• multimodal reasoning

Innovation

• multi-agent system
• inverse programming
• geometric reconstruction
• code evolution
• visual feedback loop