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Register a new userA Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers
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Added by
Chao-Chun Liang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We present ASDiv (Academia Sinica Diverse MWP Dataset), a diverse (in terms of both language patterns and problem types) English math word problem (MWP) corpus for evaluating the capability of various MWP solvers. Existing MWP corpora for studying AI progress remain limited either in language usage patterns or in problem types. We thus present a new English MWP corpus with 2,305 MWPs that cover more text patterns and most problem types taught in elementary school. Each MWP is annotated with its problem type and grade level (for indicating the level of difficulty). Furthermore, we propose a metric to measure the lexicon usage diversity of a given MWP corpus, and demonstrate that ASDiv is more diverse than existing corpora. Experiments show that our proposed corpus reflects the true capability of MWP solvers more faithfully.
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We introduce MeSys, a meaning-based approach, for solving English math word problems (MWPs) via understanding and reasoning in this paper. It first analyzes the text, transforms both body and question parts into their corresponding logic forms, and then performs inference on them. The associated context of each quantity is represented with proposed role-tags (e.g., nsubj, verb, etc.), which provides the flexibility for annotating an extracted math quantity with its associated context information (i.e., the physical meaning of this quantity). Statistical models are proposed to select the operator and operands. A noisy dataset is designed to assess if a solver solves MWPs mainly via understanding or mechanical pattern matching. Experimental results show that our approach outperforms existing systems on both benchmark datasets and the noisy dataset, which demonstrates that the proposed approach understands the meaning of each quantity in the text more.
Developing automatic Math Word Problem (MWP) solvers has been an interest of NLP researchers since the 1960s. Over the last few years, there are a growing number of datasets and deep learning-based methods proposed for effectively solving MWPs. However, most existing methods are benchmarked soly on one or two datasets, varying in different configurations, which leads to a lack of unified, standardized, fair, and comprehensive comparison between methods. This paper presents MWPToolkit, the first open-source framework for solving MWPs. In MWPToolkit, we decompose the procedure of existing MWP solvers into multiple core components and decouple their models into highly reusable modules. We also provide a hyper-parameter search function to boost the performance. In total, we implement and compare 17 MWP solvers on 4 widely-used single equation generation benchmarks and 2 multiple equations generation benchmarks. These features enable our MWPToolkit to be suitable for researchers to reproduce advanced baseline models and develop new MWP solvers quickly. Code and documents are available at https://github.com/LYH-YF/MWPToolkit.
Math word problem (MWP) solving is the task of transforming a sequence of natural language problem descriptions to executable math equations. An MWP solver not only needs to understand complex scenarios described in the problem texts, but also identify the key mathematical variables and associate text descriptions with math equation logic. Although recent sequence modeling MWP solvers have gained credits on the math-text contextual understanding, pre-trained language models (PLM) have not been explored for solving MWP, considering that PLM trained over free-form texts is limited in representing text references to mathematical logic. In this work, we introduce MWP-BERT to obtain pre-trained token representations that capture the alignment between text description and mathematical logic. Additionally, we introduce a keyword-based prompt matching method to address the MWPs requiring common-sense knowledge. On a benchmark Math23K dataset and a new Ape210k dataset, we show that MWP-BERT outperforms the strongest baseline model by 5-10% improvement on accuracy.
Turing test was long considered the measure for artificial intelligence. But with the advances in AI, it has proved to be insufficient measure. We can now aim to mea- sure machine intelligence like we measure human intelligence. One of the widely accepted measure of intelligence is standardized math and science test. In this paper, we explore the progress we have made towards the goal of making a machine smart enough to pass the standardized test. We see the challenges and opportunities posed by the domain, and note that we are quite some ways from actually making a system as smart as a even a middle school scholar.
We study the problem of generating arithmetic math word problems (MWPs) given a math equation that specifies the mathematical computation and a context that specifies the problem scenario. Existing approaches are prone to generating MWPs that are either mathematically invalid or have unsatisfactory language quality. They also either ignore the context or require manual specification of a problem template, which compromises the diversity of the generated MWPs. In this paper, we develop a novel MWP generation approach that leverages i) pre-trained language models and a context keyword selection model to improve the language quality of the generated MWPs and ii) an equation consistency constraint for math equations to improve the mathematical validity of the generated MWPs. Extensive quantitative and qualitative experiments on three real-world MWP datasets demonstrate the superior performance of our approach compared to various baselines.
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