The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Verb-related Features <s> This paper presents a novel approach to learning to solve simple arithmetic word problems. Our system, ARIS, analyzes each of the sentences in the problem statement to identify the relevant variables and their values. ARIS then maps this information into an equation that represents the problem, and enables its (trivial) solution as shown in Figure 1. The paper analyzes the arithmetic-word problems “genre”, identifying seven categories of verbs used in such problems. ARIS learns to categorize verbs with 81.2% accuracy, and is able to solve 77.7% of the problems in a corpus of standard primary school test questions. We report the first learning results on this task without reliance on predefined templates and make our data publicly available. 1 <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Verb-related Features <s> This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as ALGES. We compare ALGES with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, ALGES overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Verb-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> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Verb-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> BIB004
Verbs are important indicators for correct operator determination. For example, "lose" is a verb indicating quantity loss for an entity and related to the subtraction operator. Given a quantity, we call the verb closest to it in the dependency tree as its dependent verb. BIB003 [27] BIB004  directly use dependent verb as one of the features. Another widely-adopted verb-related feature is a vector capturing the distance between the dependent verb and a small pre-defined collection of verbs that are found to be useful in categorizing arithmetic operations. Again, the remaining features come from the works BIB003 , BIB004 ,  . The features indicate whether two quantities have the same dependent verbs or whether their dependent verbs refer to the same verb mention. As we can see from the examples in Table 5 , the difference between these two types of features is the occurrence number of the dependent verb in the sentence. Dependent verb of a quantity BIB003 [27] [28]  the verb closest to the quantity in the dependency tree Distance vector between the dependent verb and a small collection of predefined verbs that are useful for arithmetic operator classification BIB001 [24] BIB002 Whether two quantities have the same dependent verbs BIB003 [28]  For "In the first round she scored 40 points and in the second round she scored 50 points", the quantities "40" and "50" both have the same verb "scored". Note that "scored" appeared twice in the sentence. Whether both dependent verbs refer to the same verb mention BIB003 [28]  For "She baked 4 cupcakes and 29 cookies.", the quantities "4" and "29" both shared the verb "baked". Note that "baked" appeared only once in the sentence.