The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Context-related Features <s> We present an approach for automatically learning to solve algebra word problems. Our algorithm reasons across sentence boundaries to construct and solve a system of linear equations, while simultaneously recovering an alignment of the variables and numbers in these equations to the problem text. The learning algorithm uses varied supervision, including either full equations or just the final answers. We evaluate performance on a newly gathered corpus of algebra word problems, demonstrating that the system can correctly answer almost 70% of the questions in the dataset. This is, to our knowledge, the first learning result for this task. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Context-related Features <s> This paper presents a new algorithm to automatically solve algebra word problems. Our algorithm solves a word problem via analyzing a hypothesis space containing all possible equation systems generated by assigning the numbers in the word problem into a set of equation system templates extracted from the training data. To obtain a robust decision surface, we train a log-linear model to make the margin between the correct assignments and the false ones as large as possible. This results in a quadratic programming (QP) problem which can be efficiently solved. Experimental results show that our algorithm achieves 79.7% accuracy, about 10% higher than the state-of-the-art baseline (Kushman et al., 2014). <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Context-related Features <s> Little work from the Natural Language Processing community has targeted the role of quantities in Natural Language Understanding. This paper takes some key steps towards facilitating reasoning about quantities expressed in natural language. We investigate two different tasks of numerical reasoning. First, we consider Quantity Entailment, a new task formulated to understand the role of quantities in general textual inference tasks. Second, we consider the problem of automatically understanding and solving elementary school math word problems. In order to address these quantitative reasoning problems we first develop a computational approach which we show to successfully recognize and normalize textual expressions of quantities. We then use these capabilities to further develop algorithms to assist reasoning in the context of the aforementioned tasks. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Context-related Features <s> This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional annotations or predefined templates. We develop a theory for expression trees that can be used to represent and evaluate the target arithmetic expressions; we use it to uniquely decompose the target arithmetic problem to multiple classification problems; we then compose an expression tree, combining these with world knowledge through a constrained inference framework. Our classifiers gain from the use of quantity schemas that supports better extraction of features. Experimental results show that our method outperforms existing systems, achieving state of the art performance on benchmark datasets of arithmetic word problems. <s> BIB004 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Context-related Features <s> 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 . <s> BIB005
The information embedded in the text window centered at a particular quantity can also provide important clues for solving math word problems. To differentiate two quantities both in the numeric format, we can leverage the word lemmas, part of speech (POS) tags and dependence types within the window as the features. In this manner, quantities associated with the same operators would to likely to share similar context information. A trivial trick used in BIB004 [28]  is to examine whether there exists comparative adverbs. For example, terms "more", "less" and "than" indicate operators of {+, −}. Word lemma BIB001 [40]  For "Connie has 41.0 red markers.", the word lemmas around the quantity "41.0" are {Connie, have, red, marker}. POS tags BIB005 [39] BIB002 [45] BIB003 For "A chef needs to cook 16.0 potatoes.", the POS tags within a window of size 2 centered at the quantity "16.0" are {TO, VB, NNS}. Dependence type BIB001 [40]  For "Ned bought 14.0 boxes of chocolates candy.", we can detect multiple dependencies within the window of size 2 around the "14.0": (boxes, 14.0) → (num), (boxes, of)→ (prep), (bought, Ned) → (nsubj). The dependence root is "bought". Comparative adverbs BIB004 [28]  For "If she drank 25 of them and then bought 30 more.", "more" is a comparative term in the window of quantity "30".