Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations

There is an increasing interest in the use of mathematical word problem (MWP) generation in educational assessment. Different from standard natural question generation, MWP generation needs to maintain the underlying mathematical operations between quantities and variables, while at the same time ensuring the relevance between the output and the given topic. To address above problem, we develop an end-to-end neural model to generate diverse MWPs in real-world scenarios from commonsense knowledge graph and equations. The proposed model (1) learns both representations from edge-enhanced Levi graphs of symbolic equations and commonsense knowledge; (2) automatically fuses equation and commonsense knowledge information via a self-planning module when generating the MWPs. Experiments on an educational gold-standard set and a large-scale generated MWP set show that our approach is superior on the MWP generation task, and it outperforms the SOTA models in terms of both automatic evaluation metrics, i.e., BLEU-4, ROUGE-L, Self-BLEU, and human evaluation metrics, i.e., equation relevance, topic relevance, and language coherence. To encourage reproducible results, we make our code and MWP dataset public available at https:// github.com/tal-ai/MaKE_EMNLP2021. MLP Prior Net Linear Posterior Net z p z q KL Equation-based Symbolic Graph Equation Node Embedding Commonsense Knowledge Graph CSKG Node Embedding Equation Graph Embedding CSKG Graph Embedding GGNN GGNN Mean Pooling Mean Pooling GGNN Chicken and rabbits … yard ? Gold-standard Sentence Embedding GRU GRU GRU GRU GRU ? h t+1 MLP EOS Linear Decoder h 0 c 1 BOS Linear h 1 Plan c 2 MLP Chicken … Chicken h 2 c 3 MLP and and h 3 c 4 MLP rabbits c t yard h t c t+1 MLP ?