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Register a new userA Meaning-based Statistical English Math Word Problem Solver
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Chao-Chun Liang
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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.
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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.
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.
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver (NS-Solver) to explicitly and seamlessly incorporate different levels of symbolic constraints by auxiliary tasks. Our NS-Solver consists of a problem reader to encode problems, a programmer to generate symbolic equations, and a symbolic executor to obtain answers. Along with target expression supervision, our solver is also optimized via 4 new auxiliary objectives to enforce different symbolic reasoning: a) self-supervised number prediction task predicting both number quantity and number locations; b) commonsense constant prediction task predicting what prior knowledge (e.g. how many legs a chicken has) is required; c) program consistency checker computing the semantic loss between predicted equation and target equation to ensure reasonable equation mapping; d) duality exploiting task exploiting the quasi duality between symbolic equation generation and problems part-of-speech generation to enhance the understanding ability of a solver. Besides, to provide a more realistic and challenging benchmark for developing a universal and scalable solver, we also construct a new large-scale MWP benchmark CM17K consisting of 4 kinds of MWPs (arithmetic, one-unknown linear, one-unknown non-linear, equation set) with more than 17K samples. Extensive experiments on Math23K and our CM17k demonstrate the superiority of our NS-Solver compared to state-of-the-art methods.
A practical automatic textual math word problems (MWPs) solver should be able to solve various textual MWPs while most existing works only focused on one-unknown linear MWPs. Herein, we propose a simple but efficient method called Universal Expression Tree (UET) to make the first attempt to represent the equations of various MWPs uniformly. Then a semantically-aligned universal tree-structured solver (SAU-Solver) based on an encoder-decoder framework is proposed to resolve multiple types of MWPs in a unified model, benefiting from our UET representation. Our SAU-Solver generates a universal expression tree explicitly by deciding which symbol to generate according to the generated symbols semantic meanings like human solving MWPs. Besides, our SAU-Solver also includes a novel subtree-level semanticallyaligned regularization to further enforce the semantic constraints and rationality of the generated expression tree by aligning with the contextual information. Finally, to validate the universality of our solver and extend the research boundary of MWPs, we introduce a new challenging Hybrid Math Word Problems dataset (HMWP), consisting of three types of MWPs. Experimental results on several MWPs datasets show that our model can solve universal types of MWPs and outperforms several state-of-the-art models.
Wikipedia is a goldmine of information; not just for its many readers, but also for the growing community of researchers who recognize it as a resource of exceptional scale and utility. It represents a vast investment of manual effort and judgment: a huge, constantly evolving tapestry of concepts and relations that is being applied to a host of tasks. This article provides a comprehensive description of this work. It focuses on research that extracts and makes use of the concepts, relations, facts and descriptions found in Wikipedia, and organizes the work into four broad categories: applying Wikipedia to natural language processing; using it to facilitate information retrieval and information extraction; and as a resource for ontology building. The article addresses how Wikipedia is being used as is, how it is being improved and adapted, and how it is being combined with other structures to create entirely new resources. We identify the research groups and individuals involved, and how their work has developed in the last few years. We provide a comprehensive list of the open-source software they have produced.
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