The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Quantity-pair Features <s> A program was written to solve calculus word problems. The program, CARPS (CAlculus Rate Problem Solver), is restricted to rate problems. The overall plan of the program is similar to Bobrow's STUDENT, the primary difference being the introduction of "structures" as the internal model in CARPS. Structures are stored internally as trees, each structure holding the information gathered about one object. ::: ::: It was found that the use of structures made CARPS more powerful than STUDENT in several respects. ::: ::: 1) CARPS is better able to recognize that two phrases describe the same object. (e.g., CONICAL PILE and PILE OF SAND) 2) Information about an object can be gathered in piecemeal fashion. In calculus word problems it is not uncommon to have two or three sentences providing information for one equation. 3) CARPS to a limited degree is able to use its knowledge to parse its input sentences. For example, in a problem about a filter, ALTITUDE was interpreted as ALTITUDE OF THE FILTER because CARPS knew that since the filter was a cone and cones have altitudes the filter had an altitude. ::: ::: The program has solved 14 calculus problems, most taken (sometimes with slight modifications) from standard calculus texts. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Quantity-pair 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> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Quantity-pair 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> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Quantity-pair 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> Quantity-pair 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 relationship between two quantities is helpful to determine their associated operator. A straightforward example is that if two quantities are associated with the same unit, they can be applied with addition and subtraction BIB004 BIB005 [15] BIB003 . If one quantity is related to a rate and the other is associated with a unit that is part of the rate, their operator is likely to be multiplication or division BIB004 [27] [28]  . Numeric relation and context similarity are two types of quantity-pair features proposed in BIB003  . The former obtains two sets of nouns located within the same sentence as the two quantities and sorts them by the distance in the dependency tree. Then, a scoring function is defined to measure the similarity between these two sorted noun lists. Higher similarity implies that the two quantities are more likely to be connected by addition or subtraction operators. The latter extracts features for equation template classifier. It is observed that the contextual information between two numbers is similar, they are likely to be located within in a template with symmetric number slots. For example, given a template n 1 × u 1 + n 2 × u 2 , "n 1 " and "n 2 " are symmetric. The context similarity is measured by the Jaccard similarity on two sets of words among the context windows. Given a problem text "A plum costs 2 dollars and a peach costs 1 dollars", "2" and "1" are two quantities with similar context. Two types of quantity-pair features were both adopted in the template-based solutions to equation set problems BIB002 BIB003 . The first type is the dependency path between a pair of quantities. Their similarity may be helpful to determine the corresponding positions (or number slots) in the equation template. For example, given a sentence "2 footballs and 3 soccer balls cost 220 dollars", the dependency paths between two quantity pairs (2, 220) and BIB001 220) are identical, implying that 2 and 3 refer to similar types of number slots in the template. The other feature is whether two quantities appear in the same sentence. If so, they are likely to appear in the same equation of the template. Finally, a popular quantity-pair feature used in BIB004 [28]  [39] BIB003 [45] examines whether the value of one quantity is greater than the other, which is helpful to determine the correct operands for subtraction operator. Whether both quantities have the same unit BIB004 [28] [15] BIB003 For "Student tickets cost 4 dollars and general admission tickets cost 6 dollars", quantities "4" and "6" have the same unit. If one quantity is related to a rate and the other is associated with a unit that is part of the rate BIB004 [27] [28]  For "each box has 9 pieces" and "Paul bought 6 boxes of chocolate candy", "9" is related to a rate ( i.e., pieces/box) and "6" is associated to the unit "box". Numeric relation of two quantities BIB003  For each quantity, the nouns around it are extracted and sorted by the distance in the dependency tree. Then, a scoring function is defined on the two sorted lists to measure the numeric relation. Context similarity between two quantities BIB003  The context is represented by the set of words around the quantity. Dependency path between two quantities. [39] BIB003 For "2 footballs and 3 soccer balls cost 220 dollars", the dependency path for the quantity pair (2, 3) is num(footballs,2) conj(footballs, balls)num(balls, 3). Whether both quantities appear in the same sentence BIB002 BIB003 Whether the value of the first quantity is greater than the other [  For the question "How many apples are left in the box?" and a quantity 77 that appears in "77 apples in a box", there are two matching tokens ("apples" and "box"). Number of quantities which happen to have the maximum number of matching tokens with the question BIB004 [28]  For "Rose have 9 apples and 12 erasers. ... 3 friends. How many apples dose each friend get?", the number of matching tokens for quantities 9, 12 and 3 is 1, 0 and 1. Hence, there are two quantities with the maximum matching token number. Whether any component of the rate is present in the question BIB004 [28]  Given a question "How many blocks does George have?" and a quantity 6 associated with rate "blocks/box", the feature indicator is set to 1 since block appears in the question. Whether the question contains terms like "each" or "per" BIB004 [28]  Whether the question contains comparison-related terms like "more" or "less" BIB004 [28]  Whether the question contains terms like "how many" BIB002 BIB003 [45]  It implies that the solution is positive.