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Synthesizing Multimodal Geometry Datasets from Scratch and Enabling Visual Alignment via Plotting Code

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

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Synthesizes 18K multimodal geometry problems (GeoCode) via symbolic seeds, LLM instantiation, code-based rendering and multi-stage verification, and shows that supervising VLMs to predict plotting code improves diagram-to-structure alignment and geometry benchmark accuracy.

Problem

Vision-language models struggle with complex geometry diagrams because existing geometry datasets have limited structural diversity and difficulty, and visual-symbolic alignment is supervised only implicitly through answers or text.

Approach

Generate geometry problems from scratch using AlphaGeometry-derived symbolic seeds, LLM instantiation, and a Coder that emits executable construction code, then use the resulting plotting code as an explicit SFT target so the model reconstructs the diagram structure before reasoning.

Key results

• Qwen3-VL-7B-Instruct on OlympiadBench improves from 45.82 to 57.34 (+11.52) after training on GeoCode.
• On GeoCode Test-mini, Qwen3-VL-7B goes from 17.91% base to 26.49% after SFT and 37.68% after GRPO.
• Plotting-code supervision reaches 26.49% on Test-mini versus 17.91% with no alignment and 20.52% with caption+debias supervision.

Surprising findings

• Successful parsing of predicted plotting code shows little correlation with solving accuracy (37.9% parsable vs 36.7% non-parsable).
• Qwen2.5-VL-7B-Instruct's accuracy on Test-mini and the OlympiadBench result are low baseline, and Qwen2.5-VL drops on MathVista (-3.36).

Limitations

• Manual inspection covered only a random 1% of generated data.
• Evaluation on public benchmarks is restricted to plane-geometry subsets and the paper reports single-run greedy decoding.
• Pipeline depends on proprietary-scale or strong LLMs (GPT-OSS-120B) for generation and validation.

Experimental setup

Datasets: GeoCode (synthetic) Geometry3K GeoQA MathVerse MathVista OlympiadBench

Benchmarks: GeoCode Test-mini Geometry3K MathVerse MathVista GeoQA OlympiadBench

Metrics: accuracy segment-level F1

Baselines: Qwen3-VL-7B-Instruct Qwen2.5-VL-7B-Instruct Caption supervision Gemini-2.5-Pro GPT-5

Builds on: AlphaGeometry GRPO G-LLaVA MathCoder-VL GenesisGeo

Closest papers by meaning

• GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning (CVPR 2026 · similarity 0.92)
• Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions (CVPR 2026 · similarity 0.90)
• GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training (ICLR 2025 · similarity 0.90)
• GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models (CVPR 2026 · similarity 0.89)
• GeoSense: Internalizing Geometric Necessity Perception for Multimodal Reasoning (ICML 2026 · similarity 0.89)
• Socratic-Geo: Synthetic Data Generation and Cross-Modal Geometric Reasoning via Multi-Agent Interaction (CVPR 2026 · similarity 0.88)