For the past year or so I've been trying to learn German, and the most difficult part in language learning is certainly vocabulary learning. The existing apps do a pretty good job at helping with vocabulary learning, with the only issue that creating the flashcards is a big time sink. Initially the idea was to have a pool of words one wants to learn, and then the app would just quiz the user and try to maximize the learning of the user. Context: When learning new vocabulary, it is very useful to learn words in context, for example pictures and related words. If we could group related words and pictures together, the learning would (ideally) be more efficient.

In the study of human learning, there is broad evidence that our ability to retain information improves with repeated exposure and decays with delay since last exposure. This plays a crucial role in the design of educational software, leading to a trade-off between teaching new material and reviewing what has already been taught. A common way to balance this trade-off is spaced repetition, which uses periodic review of content to improve long-term retention. Though spaced repetition is widely used in practice, e.g., in electronic flashcard software, there is little formal understanding of the design of these systems. Our paper addresses this gap in three ways. First, we mine log data from spaced repetition software to establish the functional dependence of retention on reinforcement and delay. Second, we use this memory model to develop a stochastic model for spaced repetition systems. We propose a queueing network model of the Leitner system for reviewing flashcards, along with a heuristic approximation that admits a tractable optimization problem for review scheduling. Finally, we empirically evaluate our queueing model through a Mechanical Turk experiment, verifying a key qualitative prediction of our model: the existence of a sharp phase transition in learning outcomes upon increasing the rate of new item introductions.