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GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training

ICLR 2025 · Vision-language and multimodal › Multimodal LLMs · approach: Spatial reasoning in VLMs · 0 citations (OpenAlex)

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Proposes GeoX, a geometry-centric MLLM trained in three stages (unimodal pre-training of a geometry ViT and LLEMMA-based symbol decoder, formal geometry-language alignment with GS-Former, and visual instruction tuning) that generates verifiable formal programs executed by a solver.

Problem

Multimodal LLMs struggle with automatic geometry problem solving because they are pre-trained on natural images and text, and their solutions cannot be automatically verified; existing geometry specialists are task-specific.

Approach

Pre-train a geometry-specific diagram encoder (Geo-ViT) and a math-specialized symbol decoder (Geo-LLM) unimodally, align diagrams with formal point-level collinear/concyclic descriptions via GS-Former (Geo-aware Query Generator plus Semantics-guided Geometry Sampler with Gumbel-Softmax patch dropping), then instruction-tune to output formal programs executed by a symbolic solver.

Key results

• GeoX reaches 54.9% top-1 on GeoQA and 54.4% top-1 on UniGeo calculation, versus 43.4% for GPT-4V on GeoQA.
• On Geometry3K and PGPS9K, GeoX achieves 58.6% and 52.7% Completion, compared with 34.8% and 33.3% for GPT-4V.
• Formal diagram-caption alignment beats natural-language captions by +2.9% Completion on Geometry3K (58.6 vs 55.7).

Measured effects reported in the paper

Surprising findings

• GPT-4o with 2-shot in-context learning often generates incorrect formal programs (wrong operations or variables), while GeoX predicts them correctly in complex cases.
• Previous MLLM-based methods (G-LLaVA, MAVIS) can reach correct answers despite erroneous solving processes, which motivated a separate solver-based comparison metric.

Limitations

• Relies on a symbolic solver and formal program vocabulary, so outputs are constrained to the solver's operations.
• Fine-tunes a separate model per dataset after unified pre-training, limiting the generality claim.
• Some comparisons use solver-free fairness adjustments and the appendix's generalization to natural images is only qualitatively shown.

Experimental setup

Datasets: GeoQA GeoQA+ UniGeo Geometry3K PGPS9K PGDP5K G-LLaVA MathVista

Benchmarks: GeoQA UniGeo Geometry3K PGPS9K MathVista-GEO

Metrics: top-1 accuracy top-10 accuracy Completion Choice Top-3

Baselines: GPT-4V GPT-4o Qwen-VL LLaVA-v1.5 mPLUG-Owl2 NGS Geoformer UniMath-T5 PGPSNet G-LLaVA MAVIS SCA-GPS

Builds on: BLIP-2 LLEMMA Masked autoencoder (MAE) Gumbel-Softmax LLaVA

Closest papers by meaning

• GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning (CVPR 2026 · similarity 0.91)
• GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation (ICLR 2026 · similarity 0.91)
• G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model (ICLR 2025 · similarity 0.90)
• Synthesizing Multimodal Geometry Datasets from Scratch and Enabling Visual Alignment via Plotting Code (ICML 2026 · similarity 0.90)
• Socratic-Geo: Synthetic Data Generation and Cross-Modal Geometric Reasoning via Multi-Agent Interaction (CVPR 2026 · similarity 0.89)
• Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning (CVPR 2026 · similarity 0.89)