Visual Graph Reasoning via Knowledge Compilation
Visual graph reasoning requires answering graph-theoretic questions directly from graph images, where graph topology and state are conveyed visually rather than given in symbolic form. Despite recent progress of vision-language models (VLMs), current approaches to visual graph reasoning still fail on simple visual graph problems. This reveals a fundamental limitation of existing approaches: they prioritize final-answer supervision over the intermediate recovery of an explicit graph representation that preserves graph topology and state from visual input. To address this limitation, we propose VGCompiler, a compilation-centric paradigm for visual graph reasoning via knowledge compilation. VGCompiler organizes reasoning around two compilers: a representation compiler that recovers a structure-preserving intermediate graph representation from visual input, and an operation compiler that compiles query intent under the recovered graph state into an executable graph operation. Specifically, we build VGCompiler on Qwen3-VL-8B and train it with reinforcement learning guided by a layered reward over executability, compiled graph validity, representation quality, and operation quality. VGCompiler uses a frozen observer to summarize graph and question conditions into lightweight signatures, enabling archive retrieval and code reuse across similar regimes. Experiments on three benchmarks GVLQA, VisionGraph, and VGCURE, show that Qwen-VGCompiler, built on an 8B backbone, surpasses the strongest closed-source VLM baseline by 28.9% and the strongest code-based baseline by 23.7%, while maintaining high efficiency. We further evaluate VGCompiler on three real-world domains, including metro routing, logistics delivery, and network fault assessment, where it generalizes across heterogeneous visual graphs and domain-grounded tasks.