Prob2Vec: Mathematical Semantic Embedding for Problem Retrieval in Adaptive Tutoring

We propose a novel mathematical semantic embedding for problem retrieval in adaptive tutoring. The goal is to retrieve problems with similar mathematical concepts. There are two challenges: First, problems conducive to tutoring are never exactly the same in terms of underlying concepts: those problems often mix concepts in innovative ways. Second, it is difficult for human to determine a consistent similarity score across a large enough training set. To address these two challenges, we develop a hierarchical problem embedding algorithm, Prob2Vec, which consists of abstraction and embedding steps. Prob2Vec is able to distinguish very finegrained differences among problems, an ability humans need time and effort to acquire. In addition, the associated concept labeling is a multi-label problem with imbalanced training data set suffering from dimensionality explosion. Robust concept labeling is achieved with a novel negative pre-training algorithm that dramatically reduces false negative and positive ratios for classification. Experimental results show that Prob2Vec achieves 96.88% accuracy on a problem similarity test, in contrast to 75% from directly applying state-of-the-art sentence embedding methods.