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Proc Natl Acad Sci U S A. 2019 Mar 5;116(10):3988-3993. doi: 10.1073/pnas.1815156116. Epub 2019 Jan 22.

Enhancing human learning via spaced repetition optimization.

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Networks Learning Group, Max Planck Institute for Software Systems, 67663 Kaiserslautern, Germany;
Empirical Inference Department, Max Planck Institute for Intelligent Systems, 72076 Tübingen, Germany.
Networks Learning Group, Max Planck Institute for Software Systems, 67663 Kaiserslautern, Germany.


Spaced repetition is a technique for efficient memorization which uses repeated review of content following a schedule determined by a spaced repetition algorithm to improve long-term retention. However, current spaced repetition algorithms are simple rule-based heuristics with a few hard-coded parameters. Here, we introduce a flexible representation of spaced repetition using the framework of marked temporal point processes and then address the design of spaced repetition algorithms with provable guarantees as an optimal control problem for stochastic differential equations with jumps. For two well-known human memory models, we show that, if the learner aims to maximize recall probability of the content to be learned subject to a cost on the reviewing frequency, the optimal reviewing schedule is given by the recall probability itself. As a result, we can then develop a simple, scalable online spaced repetition algorithm, MEMORIZE, to determine the optimal reviewing times. We perform a large-scale natural experiment using data from Duolingo, a popular language-learning online platform, and show that learners who follow a reviewing schedule determined by our algorithm memorize more effectively than learners who follow alternative schedules determined by several heuristics.


human learning; marked temporal point processes; memorization; spaced repetition; stochastic optimal control

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