In this paper, we propose a neural model EPT-X (Expression-Pointer Transformer with Explanations), which utilizes natural language explanations to solve an algebraic word problem. To enhance the explainability of the encoding process of a neural model, EPT-X adopts the concepts of plausibility and faithfulness which are drawn from math word problem solving strategies by humans. A plausible explanation is one that includes contextual information for the numbers and variables that appear in a given math word problem. A faithful explanation is one that accurately represents the reasoning process behind the model’s solution equation. The EPT-X model yields an average baseline performance of 69.59% on our PEN dataset and produces explanations with quality that is comparable to human output. The contribution of this work is two-fold. (1) EPT-X model: An explainable neural model that sets a baseline for algebraic word problem solving task, in terms of model’s correctness, plausibility, and faithfulness. (2) New dataset: We release a novel dataset PEN (Problems with Explanations for Numbers), which expands the existing datasets by attaching explanations to each number/variable.

Math word problem solving is an emerging research topic in Natural Language Processing. Recently, to address the math word problem-solving task, researchers have applied the encoder-decoder architecture, which is mainly used in machine translation tasks. The state-of-the-art neural models use hand-crafted features and are based on generation methods. In this paper, we propose the GEO (Generation of Equations by utilizing Operators) model that does not use hand-crafted features and addresses two issues that are present in existing neural models: 1. missing domain-specific knowledge features and 2. losing encoder-level knowledge. To address missing domain-specific feature issue, we designed two auxiliary tasks: operation group difference prediction and implicit pair prediction. To address losing encoder-level knowledge issue, we added an Operation Feature Feed Forward (OP3F) layer. Experimental results showed that the GEO model outperformed existing state-of-the-art models on two datasets, 85.1% in MAWPS, and 62.5% in DRAW-1K, and reached comparable performance of 82.1% in ALG514 dataset.

Solving algebraic word problems has recently emerged as an important natural language processing task. To solve algebraic word problems, recent studies suggested neural models that generate solution equations by using ‘Op (operator/operand)’ tokens as a unit of input/output. However, such a neural model suffered two issues: expression fragmentation and operand-context separation. To address each of these two issues, we propose a pure neural model, Expression-Pointer Transformer (EPT), which uses (1) ‘Expression’ token and (2) operand-context pointers when generating solution equations. The performance of the EPT model is tested on three datasets: ALG514, DRAW-1K, and MAWPS. Compared to the state-of-the-art (SoTA) models, the EPT model achieved a comparable performance accuracy in each of the three datasets; 81.3% on ALG514, 59.5% on DRAW-1K, and 84.5% on MAWPS. The contribution of this paper is two-fold; (1) We propose a pure neural model, EPT, which can address the expression fragmentation and the operand-context separation. (2) The fully automatic EPT model, which does not use hand-crafted features, yields comparable performance to existing models using hand-crafted features, and achieves better performance than existing pure neural models by at most 40%.