Synthesis of Problems for Shaded Area Geometry Reasoning

Alvin, Chris; Gulwani, Sumit; Majumdar, Rupak; Mukhopadhyay, Supratik

doi:10.1007/978-3-319-61425-0_39

“…#qa #word #shape #goal #var grade operator type GeoShader (Alvin et al, 2017) 102 / 4 1 1 6-10 {+, −, ×, ÷, 2 2 , √ 2} GEOS 186 4,343 4 3 1 6-10 {+, −, ×, ÷, 2 2 , √ 2} GEOS++ 1,406 Unlike existing datasets that only collect the problem text and diagrams, we further annotate each data in Geometry3K with dense formal language descriptions that bridge the semantic gap between the textual and visual contents as well as benefit the symbolic problem solver. The annotated formal language is used to train and evaluate our proposed problem parsers.…”

Section: Datasetmentioning

confidence: 99%

“…Unlike existing methods Alvin et al, 2017;Sachan et al, 2020), Inter-GPS achieves the explicit symbolic reasoning with the theorem knowledge base and the humanreadable search process, shown in Figure 4.…”

Section: Geometry Problem Solvermentioning

confidence: 99%

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Lu¹,

Gong²,

Jiang³

et al. 2021

Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Confer

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Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new largescale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. 1

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“…Dataset #qa #word #shape #goal #var grade operator type GeoShader (Alvin et al, 2017) 102 / 4 1 1 6-10 {+, −, ×, ÷, 2 2 , √ 2} GEOS 186 4,343 4 3 1 6-10 {+, −, ×, ÷, 2 2 , √ 2} GEOS++ 1,406 / 4 3 1 6-10 {+, −, ×, ÷, 2 2 , √ 2} GEOS-OS Unlike existing datasets that only collect the problem text and diagrams, we further annotate each data in Geometry3K with dense formal language descriptions that bridge the semantic gap between the textual and visual contents as well as benefit the symbolic problem solver. The annotated formal language is used to train and evaluate our proposed problem parsers.…”

Section: Dataset Collectionmentioning

confidence: 99%

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Lu

¹

,

Gong

²

,

Jiang³

et al. 2021

Preprint

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Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new largescale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. 1 * Equal contribution. 1 The project with code and data is available at https: //lupantech.github.io/inter-gps.

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“…GeoShader [109], as the first tool to automatically handle geometry problem with shaded area, presents an interesting reasoning technique based on analysis hypergraph. The nodes in the graph represent intermediate facts extracted from the diagram and the directed edges indicate the relationship of deductibility between two facts.…”

Section: Gwp Solversmentioning

confidence: 99%

The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers

Zhang

¹

,

Wang

²

,

Zhang

³

et al. 2020

IEEE Trans. Pattern Anal. Mach. Intell.

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Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the 1960s, MWPs have regained intensive attention in the past few years with the advancement of Artificial Intelligence (AI). Solving MWPs successfully is considered as a milestone towards general AI. Many systems have claimed promising results in self-crafted and small-scale datasets. However, when applied on large and diverse datasets, none of the proposed methods in the literature achieves high precision, revealing that current MWP solvers still have much room for improvement. This motivated us to present a comprehensive survey to deliver a clear and complete picture of automatic math problem solvers. In this survey, we emphasize on algebraic word problems, summarize their extracted features and proposed techniques to bridge the semantic gap, and compare their performance in the publicly accessible datasets. We also cover automatic solvers for other types of math problems such as geometric problems that require the understanding of diagrams. Finally, we identify several emerging research directions for the readers with interests in MWPs.

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Synthesis of Problems for Shaded Area Geometry Reasoning

Cited by 17 publications

References 0 publications

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning

The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers

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