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

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. Our code is available at https://github.com/Alpha-Innovator/GeoX Published as a conference paper at ICLR 2025 Two Examples Comparing our GeoX and GPT-4V Two Examples Comparing our GeoX and GPT-4V If angle D is 50°, since the line from O to D would create an isosceles triangle with OC and OD being equal radii of the circle, angle ∠COD would correspond to the central angle subtending arc CD. Therefore, inscribed angle ∠CAD would be half the measure of the central angle ∠COD because an inscribed angle is half the measure of the corresponding central angle. Given ∠D is 50°, this means ∠CAD would be 25°. So, angle A (∠CAD) is 25.0°.The correct answer from the choices given is 20.0. g_minus C_3 C_2, g_minus V_0 N_0, g_half V_1 20