title: GeoX: Geometric Problem Solving Through Unified Formalized
    Vision-Language Pre-training
summary: 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.
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paper_authors.name: Xinyu Cai
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paper_title: GeoX: Geometric Problem Solving Through Unified Formalized
    Vision-Language Pre-training
paper_summary: 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.
paper_ai_keywords: Multi-modal Large Language Models (MLLMs) Automatic Geometry Problem Solving (GPS) Diagram encoder Symbol decoder Unimodal pre-training Geometry-language alignment Generator-And-Sampler Transformer (GS-Former) Discriminative queries Visual instruction tuning Verifiable solutions GeoQA UniGeo Geometry3K PGPS9k