This paper presents a framework to answer the questions that require various kinds of inference mechanisms (such as Extraction, Entailment-Judgement, and Summarization). Most of the previous approaches adopt a rigid framework which handles only one inference mechanism. Only a few of them adopt several answer generation modules for providing different mechanisms; however, they either lack an aggregation mechanism to merge the answers from various modules, or are too complicated to be implemented with neural networks. To alleviate the problems mentioned above, we propose a divide-and-conquer framework, which consists of a set of various answer generation modules, a dispatch module, and an aggregation module. The answer generation modules are designed to provide different inference mechanisms, the dispatch module is used to select a few appropriate answer generation modules to generate answer candidates, and the aggregation module is employed to select the final answer. We test our framework on the 2020 Formosa Grand Challenge Contest dataset. Experiments show that the proposed framework outperforms the state-of-the-art Roberta-large model by about 11.4%.
Current neural math solvers learn to incorporate commonsense or domain knowledge by utilizing pre-specified constants or formulas. However, as these constants and formulas are mainly human-specified, the generalizability of the solvers is limited. In this paper, we propose to explicitly retrieve the required knowledge from math problemdatasets. In this way, we can determinedly characterize the required knowledge andimprove the explainability of solvers. Our two algorithms take the problem text andthe solution equations as input. Then, they try to deduce the required commonsense and domain knowledge by integrating information from both parts. We construct two math datasets and show the effectiveness of our algorithms that they can retrieve the required knowledge for problem-solving.
With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not explicitly use the math formulas. As a result, the expression trees they produce are lengthy and uninterpretable because they need to use multiple operators and constants to represent one single formula. In this paper, we propose sequence-to-general tree (S2G) that learns to generate interpretable and executable operation trees where the nodes can be formulas with an arbitrary number of arguments. With nodes now allowed to be formulas, S2G can learn to incorporate mathematical domain knowledge into problem-solving, making the results more interpretable. Experiments show that S2G can achieve a better performance against strong baselines on problems that require domain knowledge.
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.
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.
This paper presents a meaning-based statistical math word problem (MWP) solver with understanding, reasoning and explanation. It comprises a web user interface and pipelined modules for analysing the text, transforming both body and question parts into their logic forms, and then performing 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 the extracted math quantity with its associated syntactic and semantic information (which specifies the physical meaning of that quantity). Those role-tags are then used to identify the desired operands and filter out irrelevant quantities (so that the answer can be obtained precisely). Since the physical meaning of each quantity is explicitly represented with those role-tags and used in the inference process, the proposed approach could explain how the answer is obtained in a human comprehensible way.