HMS: A Hierarchical Solver with Dependency-Enhanced Understanding for Math Word Problem

Automatically solving math word problems is a crucial task for exploring the intelligence levels of machines in the general AI domain. It is highly challenging since it requires not only natural language understanding but also mathematical expression inference. Existing solutions usually explore sequence-to-sequence models to generate expressions, where the problems are simply encoded sequentially. However, such models are generally far from enough for understanding problems as similar to humans and lead to incorrect answers. To this end, in this paper, we propose a novel Hierarchical Math Solver (HMS) to make deep understanding and exploitation of problems. In problem understanding, imitating human reading habits, we propose a hierarchical word-clause-problem encoder. Specifically, we first split each problem into several clauses and learn problem semantics from the local clause level to the global problem level. Then, in clause understanding, we propose a dependency-based module to enhance clause semantics with the dependency structure of the problem. Next, in expression inference, we propose a novel tree-based decoder to generate the mathematical expression for the answer. In the decoder, we apply a hierarchical attention mechanism to enhance the problem semantics with context from different levels, and a pointer-generator network to guide the model to copy existing information and infer extra knowledge. Extensive experimental results on two widely used datasets demonstrate that HMS achieves not only better answers but also more reasonable inference.