SMART: A Situation Model for Algebra Story Problems via Attributed Grammar
This work addresses the problem of improving the accuracy and interpretability of algebra story problem solvers for AI researchers and educators, offering a substantial gain in generalization.
This paper tackles the challenge of solving algebra story problems by introducing SMART, a situation model that uses attributed grammar to represent real-world situations. SMART significantly outperforms previous neural solvers on the ASP6.6k dataset and shows a 17% improvement in out-of-distribution generalization.
Solving algebra story problems remains a challenging task in artificial intelligence, which requires a detailed understanding of real-world situations and a strong mathematical reasoning capability. Previous neural solvers of math word problems directly translate problem texts into equations, lacking an explicit interpretation of the situations, and often fail to handle more sophisticated situations. To address such limits of neural solvers, we introduce the concept of a \emph{situation model}, which originates from psychology studies to represent the mental states of humans in problem-solving, and propose \emph{SMART}, which adopts attributed grammar as the representation of situation models for algebra story problems. Specifically, we first train an information extraction module to extract nodes, attributes, and relations from problem texts and then generate a parse graph based on a pre-defined attributed grammar. An iterative learning strategy is also proposed to improve the performance of SMART further. To rigorously study this task, we carefully curate a new dataset named \emph{ASP6.6k}. Experimental results on ASP6.6k show that the proposed model outperforms all previous neural solvers by a large margin while preserving much better interpretability. To test these models' generalization capability, we also design an out-of-distribution (OOD) evaluation, in which problems are more complex than those in the training set. Our model exceeds state-of-the-art models by 17\% in the OOD evaluation, demonstrating its superior generalization ability.