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Graph-to-tree learning for solving math word problems.

Zhang, Jipeng, Lei Wang, Roy Ka-Wei Lee, Yi Bin, Yan Wang, Jie Shao, and Ee-Peng Lim. ["

Association for Computational Linguistics, ACL, 2020.

Whats Unique This paper present a novel architecture where it has Graph Transformers as encoder and Tree preoder traversal decoder. It initialize embeddings for Graph Transformers using BI-LSTM. It uses Quantity Cell Graph, and Quantity Comparision Graph as two different kinds of graphs.

How It Works

  • It uses BI-LSTM network to initialize embeddings for each tokens.
  • It extract quantities and tokens from the input math word problem
  • Using dependency parse tree and POS tagging, it builds narrative words for each numeric quanity. This is Quantity Cell Graph.
  • Using numeric order between quantity, it builds another graph, Quantity Comparision Graph
  • It uses Graph Convolution Network in a setup similar to Transformers, with 4 heads, two head for Qunatity Cell Graph, and remaining two heads for Quanity comparision heads. Then it applys feed forward with residual connections.
  • Tree Decoder decodes the output mathematical expression in the pre-order traversal.
  • Tree decoder vocabolory only contains numerical quantities of the input, constants and operations.
  • The figure of architecture diagram is as below:

Source: Author

  • It outperforms other models on Math23K and MAWPS datasets.