## AI 生成解读视频

AI抽取解析论文重点内容自动生成视频

AI解析本论文相关学术脉络

## AI 精读

AI抽取本论文的概要总结

We present a new algorithm to learn to solve algebra word problems

# Learn to Solve Algebra Word Problems Using Quadratic Programming

Conference on Empirical Methods in Natural Language Processing, (2015)

EI

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 ...更多

0

• An algebra word problem describes a mathematical problem which can be typically modeled by an equation system, as demonstrated in Figure 1.
• Using machine learning techniques to construct the solver has become a new trend (Kushman et al, 2014; Hosseini et al, 2014; Amnueypornsakul and Bhat, 2014; Roy et al, 2015)
• This is based on the fact that word problems derived from the same mathematical problem share some common semantic and syntactic features due to the same underlying logic.

• An algebra word problem describes a mathematical problem which can be typically modeled by an equation system, as demonstrated in Figure 1
• The experimental results show that our algorithm significantly outperforms the state-of-the-art baseline (Kushman et al, 2014)
• We present a new algorithm to learn to solve algebra word problems
• To reduce the possible derivations, we only consider filling the number slots of the equation system templates, and design effective features to describe the relationship between numbers and unknowns
• We use the max-margin objective to train the log-linear model. This results in a quadratic programming (QP) problem that can be efficiently solved via the constraint generation algorithm

• Assume n1 and n2 are two numbers in a word Dataset: The dataset used in the experiment is problem.
• The version of the parser is the max same as (Kushman et al, 2014).
• The performance of the algorithm is evaluated by comparing each nouni1∈N P1, nounj2∈N P2 s.t. nouni1=nounj2 ord nouni1 + ord nounj2 number of the correct answer with the calculated one, regardless of the ordering.
• The authors report the average accuracy of 5-fold cross-validation

• Experimental results show that the algorithm achieves 79.7% accuracy, about 10% higher than the state-of-the-art baseline (Kushman et al., 2014).
• Experimental results show that the algorithm significantly outperforms the state-of-the-art baseline (Kushman et al, 2014)

• The authors present a new algorithm to learn to solve algebra word problems.
• The authors use the max-margin objective to train the log-linear model.
• This results in a QP problem that can be efficiently solved via the constraint generation algorithm.
• The authors would like to compare the algorithm with the algorithms designed for specific word problems, such as (Hosseini et al, 2014)

• Table1: Features used in our algorithm
• Table2: Learning statistics
• Table3: Algorithm comparison
• Table4: Ablation study for fully supervised data
• Table5: The problems of our algorithm

• This work is supported by the National Basic Research Program of China (973 program No 2014CB340505)

• Bussaba Amnueypornsakul and Suma Bhat. 2014. Machine-guided solution to mathematical word problems.
• Yoshua Bengio, Rjean Ducharme, Pascal Vincent, and Christian Janvin. 2003. A neural probabilistic language model. Journal of Machine Learning Research, 3(6):1137–1155.
• Christopher M Bishop. 2006. Pattern recognition and machine learning. springer.
• Daniel G Bobrow. 196Natural language input for a computer problem solving system.
• Rong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, XiangRui Wang, and Chih-Jen Lin. 2008. Liblinear: A library for large linear classification. The Journal of Machine Learning Research, 9:1871–1874.
• Pedro F Felzenszwalb, Ross B Girshick, David McAllester, and Deva Ramanan. 2010. Object detection with discriminatively trained part-based models. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 32(9):1627–1645.
• Mohammad Javad Hosseini, Hannaneh Hajishirzi, Oren Etzioni, and Nate Kushman. 2014. Learning to solve arithmetic word problems with verb categorization. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 523–533.
• Daphne Koller and Nir Friedman. 2009. Probabilistic graphical models: principles and techniques. MIT press.
• Nate Kushman, Yoav Artzi, Luke Zettlemoyer, and Regina Barzilay. 2014. Learning to automatically solve algebra word problems. ACL (1), pages 271– 281.
• Christopher D. Manning, Mihai Surdeanu, John Bauer, Jenny Finkel, Steven J. Bethard, and David McClosky. 2014. The Stanford CoreNLP natural language processing toolkit. In Proceedings of 52nd Annual Meeting of the Association for Computational Linguistics: System Demonstrations, pages 55–60.
• Takuya Matsuzaki, Hidenao Iwane, Hirokazu Anai, and Noriko Arai. 2013. The complexity of math problems–linguistic, or computational. In Proceedings of the Sixth International Joint Conference on Natural Language Processing, pages 73–81.
• Tomas Mikolov, Wen Tau Yih, and Geoffrey Zweig. 2013. Linguistic regularities in continuous spaceword representations. In HLT-NAACL.
• Anirban Mukherjee and Utpal Garain. 2008. A review of methods for automatic understanding of natural language mathematical problems. Artificial Intelligence Review, 29(2):93–122.
• John C. Platt. 1999. Fast training of support vector machines using sequential minimal optimization. In B. Scho04lkopf, C. Burges and A. Smola (Eds.), Advances in kernel methods - Support vector learning.
• Subhro Roy, Tim Vieira, and Dan Roth. 20Reasoning about quantities in natural language. Transactions of the Association for Computational Linguistics, 3:1–13.
• Ben Taskar, Vassil Chatalbashev, Daphne Koller, and Carlos Guestrin. 2005. Learning structured prediction models: A large margin approach. In Proceedings of the 22nd international conference on Machine learning, pages 896–903. ACM.
• Vladimir Vapnik. 2013. The nature of statistical learning theory. Springer Science & Business Media.
• Tom Kwiatkowski, Luke Zettlemoyer, Sharon Goldwater, and Mark Steedman. 2010. Inducing probabilistic ccg grammars from logical form with higherorder unification. In Proceedings of the 2010 conference on empirical methods in natural language processing, pages 1223–1233. Association for Computational Linguistics.
• Iddo Lev, Bill MacCartney, Christopher D Manning, and Roger Levy. 2004. Solving logic puzzles: From robust processing to precise semantics. In Proceedings of the 2nd Workshop on Text Meaning and Interpretation, pages 9–16. Association for Computational Linguistics.
• Hang Li. 2014. Learning to rank for information retrieval and natural language processing. Synthesis Lectures on Human Language Technologies, 7(3):1– 121.

Shuaixiang Dai
Liwei Chen
0