Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.
Recently many efforts have been devoted to interpreting the black-box NMT models, but little progress has been made on metrics to evaluate explanation methods. Word Alignment Error Rate can be used as such a metric that matches human understanding, however, it can not measure explanation methods on those target words that are not aligned to any source word. This paper thereby makes an initial attempt to evaluate explanation methods from an alternative viewpoint. To this end, it proposes a principled metric based on fidelity in regard to the predictive behavior of the NMT model. As the exact computation for this metric is intractable, we employ an efficient approach as its approximation. On six standard translation tasks, we quantitatively evaluate several explanation methods in terms of the proposed metric and we reveal some valuable findings for these explanation methods in our experiments.
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.