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

TL;DR

GeoX is a multi-modal model designed for geometric problem solving, integrating diagram understanding, reasoning, and verification, outperforming existing models on standard benchmarks.

Contribution

The paper introduces GeoX, a unified geometric reasoning model with unimodal pre-training, geometry-language alignment, and visual instruction tuning, addressing limitations of prior models.

Findings

GeoX outperforms existing models on GeoQA, UniGeo, Geometry3K, and PGPS9k benchmarks.

Unimodal pre-training enhances geometric diagram and symbol understanding.

Geometry-language alignment improves cross-modal reasoning capabilities.

Abstract

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.