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GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning

CVPR 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Spatial reasoning in VLMs · 0 citations (OpenAlex)

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Builds GeoTikz-Base (2.5M image-tikz pairs) via iterative self-refinement with CLIP-filtered pseudo-labels and localized code transformation, trains GeoTikzBridge-Base/Instruct models, and uses generated tikz as plug-and-play reasoning input for MLLMs and LLMs.

Problem

MLLMs struggle to perceive fine-grained geometric structures (segments, angles, shape constraints), and there is little large-scale geometric image-to-code data for training them.

Approach

Use iterative self-refinement with CLIP-score filtering of model-generated tikz code on unlabeled geometric diagrams, augmented by randomly deleting code lines to force fine-grained learning, and extend to instruction-guided auxiliary-line code editing; the resulting tikz is fed to reasoning models as a training-free plug-in.

Key results

• GeoTikzBridge-Base-38B reaches CLIP-S 0.915 and FID 30.6 on MathVista-GPS, versus 0.884 / 42.5 for FigCodifier-8B (best open baseline on that set).
• Adding GeoTikzBridge-Base tikz codes raises Qwen3-VL-30B-A3B MathVista-GPS accuracy from 0.697 to 0.745 and GLM4.5V from 0.745 to 0.764.
• GeoTikzBridge-Instruct achieves SSIM 0.844 and CLIP 0.992 on auxiliary-line generation, versus SSIM 0.135 for FigCodifier.

Surprising findings

• Tikz codes from the 8B GeoTikzBridge-Base model help VLM reasoning more than tikz codes from larger VLMs such as Qwen2.5-VL-72B and InternVL3.
• Only about 2.45M of the candidate samples survive CLIP filtering at the chosen threshold, and a looser threshold (0.6) yields more data but lower CLIP scores, so data quality matters more than quantity.

Limitations

• Overlong tikz code was truncated during training, causing consistent degradation on complex figures.
• GeoTikzBridge-Instruct underperforms on parallel-line drawing due to strict directional constraints.
• Reasoning gains rely on a separate solver VLM; the approach is not end-to-end.

Experimental setup

Datasets: DaTikZ MMathCoT-1M GEOS MAVIS-Instruct Geo170k Geometry3K GeomVerse UniGeo

Benchmarks: DaTikZ MathVista-GPS GAOKAO-MM-Math RBench RBench-V EDUBenchmark GeoTikz-Instruct

Metrics: CLIP score FID compilation success rate MSE SSIM PSNR answer accuracy

Baselines: Qwen2.5-VL-32B Qwen2.5-VL-72B Qwen3-VL-30B-A3B InternVL3-78B InternVL3.5-38B GLM4.5V-106B-A12B FigCodifier-8B GPT-5.0

Builds on: DaTikZ FigCodifier

Closest papers by meaning

• Synthesizing Multimodal Geometry Datasets from Scratch and Enabling Visual Alignment via Plotting Code (ICML 2026 · similarity 0.92)
• GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation (ICLR 2026 · similarity 0.91)
• GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training (ICLR 2025 · similarity 0.91)
• Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions (CVPR 2026 · similarity 0.91)
• GeoSense: Internalizing Geometric Necessity Perception for Multimodal Reasoning (ICML 2026 · similarity 0.90)
• Socratic-Geo: Synthetic Data Generation and Cross-Modal Geometric Reasoning via Multi-Agent Interaction (CVPR 2026 · similarity 0.90)