While diverse question answering (QA) datasets have been proposed and contributed significantly to the development of deep learning models for QA tasks, the existing datasets fall short in two aspects. First, we lack QA datasets covering complex questions that involve answers as well as the reasoning processes to get them. As a result, the state-of-the-art QA research on numerical reasoning still focuses on simple calculations and does not provide the mathematical expressions or evidence justifying the answers. Second, the QA community has contributed a lot of effort to improve the interpretability of QA models. However, they fail to explicitly show the reasoning process, such as the evidence order for reasoning and the interactions between different pieces of evidence. To address the above shortcoming, we introduce NOAHQA, a conversational and bilingual QA dataset with questions requiring numerical reasoning with compound mathematical expressions. With NOAHQA, we develop an interpretable reasoning graph as well as the appropriate evaluation metric to measure the answer quality. We evaluate the state-of-the-art QA models trained using existing QA datasets on NOAHQA and show that the best among them can only achieve 55.5 exact match scores, while the human performance is 89.7. We also present a new QA model for generating a reasoning graph where the reasoning graph metric still has a large gap compared with that of humans, eg, 28 scores.
While the recent tree-based neural models have demonstrated promising results in generating solution expression for the math word problem (MWP), most of these models do not capture the relationships and order information among the quantities well. This results in poor quantity representations and incorrect solution expressions. In this paper, we propose Graph2Tree, a novel deep learning architecture that combines the merits of the graph-based encoder and tree-based decoder to generate better solution expressions. Included in our Graph2Tree framework are two graphs, namely the Quantity Cell Graph and Quantity Comparison Graph, which are designed to address limitations of existing methods by effectively representing the relationships and order information among the quantities in MWPs. We conduct extensive experiments on two available datasets. Our experiment results show that Graph2Tree outperforms the state-of-the-art baselines on two benchmark datasets significantly. We also discuss case studies and empirically examine Graph2Tree’s effectiveness in translating the MWP text into solution expressions.
Several deep learning models have been proposed for solving math word problems (MWPs) automatically. Although these models have the ability to capture features without manual efforts, their approaches to capturing features are not specifically designed for MWPs. To utilize the merits of deep learning models with simultaneous consideration of MWPs’ specific features, we propose a group attention mechanism to extract global features, quantity-related features, quantity-pair features and question-related features in MWPs respectively. The experimental results show that the proposed approach performs significantly better than previous state-of-the-art methods, and boost performance from 66.9% to 69.5% on Math23K with training-test split, from 65.8% to 66.9% on Math23K with 5-fold cross-validation and from 69.2% to 76.1% on MAWPS.
Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to automatic math word problem solving. Despite its simplicity, a drawback still remains: a math word problem can be correctly solved by more than one equations. This non-deterministic transduction harms the performance of maximum likelihood estimation. In this paper, by considering the uniqueness of expression tree, we propose an equation normalization method to normalize the duplicated equations. Moreover, we analyze the performance of three popular SEQ2SEQ models on the math word problem solving. We find that each model has its own specialty in solving problems, consequently an ensemble model is then proposed to combine their advantages. Experiments on dataset Math23K show that the ensemble model with equation normalization significantly outperforms the previous state-of-the-art methods.
To enrich vocabulary of low resource settings, we proposed a novel method which identify loanwords in monolingual corpora. More specifically, we first use cross-lingual word embeddings as the core feature to generate semantically related candidates based on comparable corpora and a small bilingual lexicon; then, a log-linear model which combines several shallow features such as pronunciation similarity and hybrid language model features to predict the final results. In this paper, we use Uyghur as the receipt language and try to detect loanwords in four donor languages: Arabic, Chinese, Persian and Russian. We conduct two groups of experiments to evaluate the effectiveness of our proposed approach: loanword identification and OOV translation in four language pairs and eight translation directions (Uyghur-Arabic, Arabic-Uyghur, Uyghur-Chinese, Chinese-Uyghur, Uyghur-Persian, Persian-Uyghur, Uyghur-Russian, and Russian-Uyghur). Experimental results on loanword identification show that our method outperforms other baseline models significantly. Neural machine translation models integrating results of loanword identification experiments achieve the best results on OOV translation(with 0.5-0.9 BLEU improvements)
To alleviate data sparsity in spoken Uyghur machine translation, we proposed a log-linear based morphological segmentation approach. Instead of learning model only from monolingual annotated corpus, this approach optimizes Uyghur segmentation for spoken translation based on both bilingual and monolingual corpus. Our approach relies on several features such as traditional conditional random field (CRF) feature, bilingual word alignment feature and monolingual suffixword co-occurrence feature. Experimental results shown that our proposed segmentation model for Uyghur spoken translation achieved 1.6 BLEU score improvements compared with the state-of-the-art baseline.