Skip to content

Latest commit

 

History

History
30 lines (22 loc) · 2.26 KB

SAU_solver.md

File metadata and controls

30 lines (22 loc) · 2.26 KB
Raw

Semantically-aligned universal tree-structured solver for math word problems.

Jinghui Qin, Lihui Lin, Xiaodan Liang, Rumin Zhang, and Liang Lin. 2020.

In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 3780–3789.

Whats Unique This paper brings three novelties, 1) Universal Expression Tree to handle multiple equations, 2) New challanging Hybrid Math Word Problems dataset, 3) Semantically algined new tree-structure decoder.

How Does It Work

  • Universal Expression Tree: As can be seen in the figure below, different equations are concatenated in the tree with the special symbol ";". It also introduces multiple unknowns like x, y etc.

Source: Author

  • Semantically aligend Tree-structued decoder: SAU Solver As shown in the figure below, a new token is generated by attending its parent, or subtree from the sibling and attention weighted encoder represnetation on the problem.

Source: Author

  • Semantically aligned regularization: It generates attention weighed encoder representation for a subtree representation. It transforms both into a vector space, where they should be semantically aligned.

    \mathbf{e}_{s a}=\mathbf{W}_{e 2} \tanh \left(\mathbf{W}_{e 1} \mathbf{a}\right)\\ \mathbf{d}_{s a}=\mathbf{W}_{d 2} \tanh \left(\mathbf{W}_{d 1} \mathbf{t}\right)\\ \mathcal{L}_{s a}(T \mid P)=\frac{1}{m} \sum_{i=1}^{m}\left\|\mathbf{d}_{s a}-\mathbf{e}_{s a}\right\|_{2}

  • It demonstrates the improvement across different datasets like HMWP, ALG514, Math23K, Dolphin18K etc.