The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> CONCLUSIONS AND FUTURE DIRECTIONS <s> Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural machine translation often belong to a family of encoder-decoders and consists of an encoder that encodes a source sentence into a fixed-length vector from which a decoder generates a translation. In this paper, we conjecture that the use of a fixed-length vector is a bottleneck in improving the performance of this basic encoder-decoder architecture, and propose to extend this by allowing a model to automatically (soft-)search for parts of a source sentence that are relevant to predicting a target word, without having to form these parts as a hard segment explicitly. With this new approach, we achieve a translation performance comparable to the existing state-of-the-art phrase-based system on the task of English-to-French translation. Furthermore, qualitative analysis reveals that the (soft-)alignments found by the model agree well with our intuition. <s> BIB001 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> CONCLUSIONS AND FUTURE DIRECTIONS <s> The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of stateof-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away. <s> BIB002 </s> The Gap of Semantic Parsing: A Survey on Automatic Math Word Problem Solvers <s> CONCLUSIONS AND FUTURE DIRECTIONS <s> A long-standing goal of artificial intelligence is an algorithm that learns, tabula rasa, superhuman proficiency in challenging domains. Recently, AlphaGo became the first program to defeat a world champion in the game of Go. The tree search in AlphaGo evaluated positions and selected moves using deep neural networks. These neural networks were trained by supervised learning from human expert moves, and by reinforcement learning from self-play. Here we introduce an algorithm based solely on reinforcement learning, without human data, guidance or domain knowledge beyond game rules. AlphaGo becomes its own teacher: a neural network is trained to predict AlphaGo's own move selections and also the winner of AlphaGo's games. This neural network improves the strength of the tree search, resulting in higher quality move selection and stronger self-play in the next iteration. Starting tabula rasa, our new program AlphaGo Zero achieved superhuman performance, winning 100-0 against the previously published, champion-defeating AlphaGo. <s> BIB003
In this paper, we present a comprehensive survey to review the development of math word problem solvers in recent years. The topics discussed in this survey cover arithmetic word problems, equation set problems, geometry word problems and miscellaneous others related to math. We compared the techniques proposed for each math task, provided a rational categorization, and conducted accountable experimental analysis. Moreover, we took a close examination on the subject of feature engineering proposed for MWP solvers and summarized the diversified proposal of syntactic features. Overall speaking, the current status of MWP solvers is far from promising and has great room for improvement. There is no doubt that the topic would continue to attract more and more research attention in the next few years, especially after the public release of large-scale datasets such as Dolphin18K and Math23K. In the following, we present a number of future directions that may be of interest to the community and worth further exploration. Firstly, DNS  was the first attempt that used deep learning models in MWP solvers so as to avoid non-trivial feature engineering. This work shed light on the feasibility of designing end-to-end models to enhance the accuracy and reduce human intervention. Considering that DNS only uses a basic seq-to-seq network structure, with LSTM and GRU as the encoding and decoing units, we expect more advanced networks to be developed. Moreover, as a common practice, these models can be integrated with attention mechanism BIB001 for performance advancement. Secondly, aligning visual understanding with text mention is an emerging direction that is particularly important to solve geometry word problems. However, this challenging problem has only been evaluated in self-collected and small-scale datasets, similar to those early efforts on evaluating the accuracy of solving algebra word problem. There is a chance that these proposed aligning methods fail to work well in a large and diversified dataset. Hence, it calls for a new round of evaluation for generality and robustness with a better benchmark dataset for geometry problems. Thirdly, intepretability plays a key role in measuring the usability of MWP solvers in the application of online tutoring, but may pose new challenges for the deep learning based solvers  . For instance, AlphaGo BIB002 and AlphaZero BIB003 have achieved astonishing superiority over human players, but their near-optimal actions could be difficult for human to interpret. Similar issues may occur in the domain of automatic math problem solver and they deserve an early examination. Last but not the least, solving math word problems in English plays a dominating role in the literature. We only observed a very rare number of math solvers proposed to cope with other languages. This research topic may grow into a direction with significant impact. To our knowledge, many companies in China have harvested an enormous number of word problems in K12 education. As reported in 2015 2 , Zuoyebang, a spin off from Baidu, has collected 950 million questions and solutions in its database. When coupled with deep learning models, this is an area with immense imagination and exciting achievements can be expected.