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 fine-grained 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.