PGPS9K: Plane Geometry Problem Solving Dataset

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Introduction

The Plane Geometry Problem Solving Dataset (PGPS9K) was constructed by the State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), Institute of Automation of Chinese Academy of Sciences (CASIA). The samples in PGPS9K are labeled with both fine-grained diagram annotation and interpretable solution program, where the diagram annotation is converted into structural clauses and semantic clauses to effectively describe multi-level information in geometry diagram.

Collection and Description

PGPS9K is composed of 9,022 geometry problems paired with non-duplicate 4,000 geometry diagrams, where 2,891 problems paired with 1,738 diagrams are selected from Geometry3K dataset, the rest of problems are collected from five popular textbooks across grades 6-12 on mathematics curriculum websites . Our PGPS9K is divided into 30 problem types as exhibited in Fig. 2, covering almost all problem types of plane geometry problem in corresponding grades.

As shown in Fig. 3, PGPS9K dataset has five properties, which make it focus on the challenges at geometric reasoning and alleviate the bias introduced by the text:

Theorem-based: Solving problems in PGPS9K need to apply geometric theorem knowledge to carry out algebraic calculation and get numerical results finally;

Diagram-dependent: Above 90% of problems must be solved using the diagrams because necessary conditions such as variable content and geometric structure are displayed via visual form instead of text;

Abstract: The diagram is integrated with basic geometric primitives (point, line, circle) and non-geometric primitives (text, symbol). No complex semantic scenarios are involved in textual problem except abstract geometric conditions;

Fine-grained: Problems with the same diagram vary in conditions or targets. Slight distinctions in textual problems usually lead to completely different solutions to problems;

Condition-redundancy: Lots of conditions in semantic clauses or textual problem are not needed in problem solving at hand. The statistics results show that on average, 1.9 conditions are not used in problem solving, 42% of problems have redundant conditions.

Citation

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@inproceedings{Zhang2023PGPS,
  title     = {A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram},
  author    = {Zhang, Ming-Liang and Yin, Fei and Liu, Cheng-Lin},
  booktitle = {IJCAI},
  year      = {2023},
}