The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> GWP Solvers <s> Automatically solving geometry questions is a long-standing AI problem. A geometry question typically includes a textual description accompanied by a diagram. The first step in solving geometry questions is diagram understanding, which consists of identifying visual elements in the diagram, their locations, their geometric properties, and aligning them to corresponding textual descriptions. In this paper, we present a method for diagram understanding that identifies visual elements in a diagram while maximizing agreement between textual and visual data. We show that the method's objective function is submodular; thus we are able to introduce an efficient method for diagram understanding that is close to optimal. To empirically evaluate our method, we compile a new dataset of geometry questions (textual descriptions and diagrams) and compare with baselines that utilize standard vision techniques. Our experimental evaluation shows an F1 boost of more than 17% in identifying visual elements and 25% in aligning visual elements with their textual descriptions. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> GWP Solvers <s> This paper introduces GEOS, the first automated system to solve unaltered SAT geometry questions by combining text understanding and diagram interpretation. We model the problem of understanding geometry questions as submodular optimization, and identify a formal problem description likely to be compatible with both the question text and diagram. GEOS then feeds the description to a geometric solver that attempts to determine the correct answer. In our experiments, GEOS achieves a 49% score on official SAT questions, and a score of 61% on practice questions. 1 Finally, we show that by integrating textual and visual information, GEOS boosts the accuracy of dependency and semantic parsing of the question text. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> GWP Solvers <s> A shaded area problem in high school geometry consists of a figure annotated with facts such as lengths of line segments or angle measures, and asks to compute the area of a shaded portion of the figure. We describe a technique to generate fresh figures for these problems. Given a figure, we describe a technique to automatically synthesize shaded area problems. We demonstrate the efficacy of our synthesis techniques by synthesizing problems from fresh figures as well as figures from a corpus of problems from high-school geometry textbooks. <s> BIB003
GEOS BIB002 can be considered as the first work to tackle a complete geometric word problem as shown in Figure 5 . The method consists of two main steps: 1) parsing text and diagram respectively by generating a piece of logical expression to represent the key information of the text and diagram as well as the confidence scores, and 2) addressing the optimization problem by aligning the satisfiability of the derived logical expression in a numerical method that requires manually defining indicator function for each predicate. It is noticeable that G-ALINGER is applied in GEOS BIB001 for primitive detection. Despite the superiority of automated solving process, the performance of the system would be undermined if the answer choices are unavailable in a geometry problem and the deductive reasoning based on geometric axiom is not used in this method. A subsequent improver of GEOS is presented in  . It harvests an axiomatic knowledge from 20 publicly available math textbooks and builds a more powerful reasoning engine that leverages the structured axiomatic knowledge for logical inference. GeoShader BIB003 , as the first tool to automatically handle geometry problem with shaded area, presents an interesting reasoning technique based on analysis hypergraph. The nodes in the graph represent intermediate facts extracted from the diagram and the directed edges indicate the relationship of deductibility between two facts. The calculation of the shaded area is represented as the target node in the graph and the problem is formulated as finding a path in the hypergraph that can reach the target node.