  Math word problems provide a natural abstraction to a range of natural
language understanding problems that involve reasoning about quantities, such
as interpreting election results, news about casualties, and the financial
section of a newspaper. Units associated with the quantities often provide
information that is essential to support this reasoning. This paper proposes a
principled way to capture and reason about units and shows how it can benefit
an arithmetic word problem solver. This paper presents the concept of Unit
Dependency Graphs (UDGs), which provides a compact representation of the
dependencies between units of numbers mentioned in a given problem. Inducing
the UDG alleviates the brittleness of the unit extraction system and allows for
a natural way to leverage domain knowledge about unit compatibility, for word
problem solving. We introduce a decomposed model for inducing UDGs with minimal
additional annotations, and use it to augment the expressions used in the
arithmetic word problem solver of (Roy and Roth 2015) via a constrained
inference framework. We show that introduction of UDGs reduces the error of the
solver by over 10 %, surpassing all existing systems for solving arithmetic
word problems. In addition, it also makes the system more robust to adaptation
to new vocabulary and equation forms .
