SMART: A Situation Model for Algebra Story Problems via Attributed Grammar

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 *situation model*, which originates from
psychology studies to represent the mental states of humans in problem-solving, and propose *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 *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.