The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> Hough has proposed an interesting and computationally efficient procedure for detecting lines in pictures. This paper points out that the use of angle-radius rather than slope-intercept parameters simplifies the computation further. It also shows how the method can be used for more general curve fitting, and gives alternative interpretations that explain the source of its efficiency. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> Diagrams often use repetition to convey points and establish contrasts. This paper shows how MAGI, our model of repetition and symmetry detection, can model the cognitive processes humans use when reading repetition-based diagrams. MAGI, which is based on the Structure Mapping Engine, detects repetition by aligning both visual and conceptual relational structure. This lets visual regularity of form support an understanding of the conceptual regularity such forms often depict. We describe JUXTA, which uses this insight to critique a class of diagrams that juxtapose similar scenes to demonstrate physical laws. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> A method for extraction of straight-line-based primitives is proposed. It is based on a bottom-up approach that extracts linear primitives first, then line segments, that are grouped in straight lines. Based on the extracted lines, quadrangles are detected and further approximated by rectangles. The extracted primitives are used in object recognition. The proposed approach provides a good relation between the complexity of extracted primitives and the complexity of algorithm itself, that allows it to be used in industrial applications. <s> BIB003 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> A key problem in diagrammatic reasoning is understanding how people reason about qualitative relationships in diagrams. We claim that progress in diagrammatic reasoning is slowed by two problems: (1) researchers tend to start from scratch, creating new spatial reasoners for each new problem area, and (2) constraints from human visual processing are rarely considered. To address these problems, we created GeoRep, a spatial reasoning engine that generates qualitative spatial descriptions from line drawings. GeoRep has been successfully used in several research projects, including cognitive simulation studies of human vision. In this paper, we outline GeoRep’s architecture, explain the domainindependent and domain-specific aspects of its processing, and motivate the representations it produces. We then survey how GeoRep has been used in three different projects ‐a model of symmetry, a model of understanding juxtaposition diagrams of physical situations, and a system for reasoning about military courses of action. <s> BIB004 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> This chapter first surveys the early development of mechanical theorem proving in geometry. GTP was initially viewed as an artificial intelligence problem that many believed would be easily tackled by machines. However, the initial optimism soon vanished as various difficulties associated with the domain emerged and no significant results could be proved. The developments over the last twenty years or so though have led to a revolution in the field. We survey several of the powerful methods proposed and analyse our own choice for formalization in Isabelle. Concepts that are important to deal with the geometry of the Principia are also introduced. <s> BIB005 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> Manual selection of single particles in images acquired using cryo-electron microscopy (cryoEM) will become a significant bottleneck when a very large number of images are required to achieve three-dimensional reconstructions at near atomic resolution. Investigation of fast, accurate approaches for automatic particle detection has become one of the current challenges in the cryoEM community. At the same time, the investigation is hampered by the fact that few benchmark particles or image datasets exist in the community. The unavailability of such data makes it difficult to evaluate newly developed algorithms and to leverage expertise from other disciplines. The paper presents our recent contribution to this effort. It also describes our newly developed computational framework for particle detection, through the application of edge detection and a sequence of ordered Hough transforms. Experimental results using keyhole limpet hemocyanin (KLH) as a model particle are very promising. In addition, it introduces a newly established web site, designed to support the investigation of automatic particle detection by providing an annotated image dataset of KLH available to the general scientific community. <s> BIB006 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global Features <s> The problem of detecting rectangular structures in images arises in many applications, from building extraction in aerial images to particle detection in cryo-electron microscopy. This paper proposes a new technique for rectangle detection using a windowed Hough transform. Every pixel of the image is scanned, and a sliding window is used to compute the Hough transform of small regions of the image. Peaks of the Hough image (which correspond to line segments) are then extracted, and a rectangle is detected when four extracted peaks satisfy certain geometric conditions. Experimental results indicate that the proposed technique produced promising results for both synthetic and natural images. <s> BIB007 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global 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> BIB008 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global 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> BIB009 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global 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> BIB010 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> Global 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> BIB011
There are certain types of global features in the document-level proposed by existing solvers. BIB010 , BIB011 ,  use the number of quantities in the problem text as part of feature space. Unigrams and bigrams are also applied in BIB009 BIB008 . They may play certain effect in determining the quantities and their order. Note that the unigrams and bigrams are defined in the word level rather than the character level. Number of quantities mentioned in text BIB010 [28]  Unigrams and bigrams of sentences in the problem text BIB009 BIB008 presented an efficient characteristic pattern detection method by scanning the distribution of black pixels and generating feature points graph. In BIB004 , a structure mapping engine named GeoRep was proposed to generate qualitative spatial descriptions from line diagrams. After that, the visual elements can be formulated through a two-level representation architecture. This work was also applied to the repetition and symmetry detection model in MAGI BIB002 . Inspired by human cognitive process of reading juxtaposition diagrams, MAGI detects repetition by aligning visual and conceptual relational structure to analyze repetition-based diagrams. The problem of rectangle and parallelogram detection in diagram understanding has also received a considerable amount of interest. The proposed techniques fall into two main categories, either based on primitive or Hough transform BIB001 . The primitivebased methods combine line segments or curves to form possible edges of a quadrangle. For examples, Lin and Nevatia  proposed the approach of parallelogram detection from a single aerial image by linear feature extraction and formation of hypothesis following certain geometric constraints. Similarly, Lagunovsky and Ablameyko BIB003 studied the problem of rectangular detection based on line primitives. As to the Hough transform based techniques, BIB006 presented an approach for automatic rectangular particle detection in cryo-electron microscopy through Hough transform, but this method can only work well when all rectangles have the same dimensions and the dimensions must be aware in advance. Jung et.al. BIB007 proposed a window Hough transform algorithm to tackle the problem of rectangle detection with varying dimensions and orientations. Geometry theorem proving (GTP)  , BIB005 was initially viewed as an artificial intelligence problem that was expected to be easily tackled by machines. The difficulties of solving GTP problems lie in the visual reasoning in geometry and the generation of elegant and concise geometry proofs. Moreover, completing the proof requires the ingenuity and insights to the problem. The first automated GTP was developed by Gelernter  , which used the diagram as pruning heuristic. The system rejects geometry goals that fail to satisfy the diagram. Whereas the limitation of the method is the true sub-goal may be pruned erroneously due to the insufficient precise arithmetic applied to the diagram. Fleuriot et. al. BIB005 studied Newton's geometric reasoning procedures in his work Principia and presented theorem prover Isabelle to formalize and generate the style of reasoning performed by Newton. By combining the existing geometry theorem proving techniques and the concepts of Nonstandard Analysis, the prover Isabelle can produce proofs of lemmas and theorem in Principia. Readers can refer to the book chapter BIB005 for the survey of early development of GTP. In this survey, we are more interested to examine the math problems that are required to consider visual diagram and textual mentions simultaneously. As illustrated in Figure 5 , a typical geometry word problem contains text descriptions or attribute values of geometric objects. The visual diagram may contain essential information that are absent from the text. For instance, points O, B and C are located on the same line segment and there is a circle passing points A, B, C and D. To well solve geometry word problems, three main challenges need to be tackled: 1) diagram parsing requires the detection of visual mentions, geometric characteristics, the spatial information and the co-reference with text; 2) deriving visual semantics which refer to the textual information related to visual analogue involves the semantic and syntactic interpretation to the text; and 3) the inherent ambiguities lie in the task of mapping visual mentions in the diagram to the concepts in real world. 