A Trainable Spaced Repetition Model for Language Learning

Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, pages 1848–1858, Berlin, Germany, August 7-12, 2016. c⃝2016 Association for Computational Linguistics A Trainable Spaced Repetition Model for Language Learning Burr Settles∗ Duolingo Pittsburgh, PA USA burr@duolingo.com Brendan Meeder† Uber Advanced Technologies Center Pittsburgh, PA USA bmeeder@cs.cmu.edu Abstract We present half-life regression (HLR), a novel model for spaced repetition practice with applications to second language ac- quisition. HLR combines psycholinguis- tic theory with modern machine learning techniques, indirectly estimating the “half- life” of a word or concept in a student’s long-term memory. We use data from Duolingo — a popular online language learning application — to fit HLR models, reducing error by 45%+ compared to sev- eral baselines at predicting student recall rates. HLR model weights also shed light on which linguistic concepts are system- atically challenging for second language learners. Finally, HLR was able to im- prove Duolingo daily student engagement by 12% in an operational user study. 1 Introduction The spacing effect is the observation that people tend to remember things more effectively if they use spaced repetition practice (short study periods spread out over time) as opposed to massed prac- tice (i.e., “cramming”). The phenomenon was first documented by Ebbinghaus (1885), using himself as a subject in several experiments to memorize verbal utterances. In one study, after a day of cramming he could accurately recite 12-syllable sequences (of gibberish, apparently). However, he could achieve comparable results with half as many practices spread out over three days. The lag effect (Melton, 1970) is the related ob- servation that people learn even better if the spac- ing between practices gradually increases. For ex- ample, a learning schedule might begin with re- ∗Corresponding author. †Research conducted at Duolingo. view sessions a few seconds apart, then minutes, then hours, days, months, and so on, with each successive review stretching out over a longer and longer time interval. The effects of spacing and lag are well- established in second language acquisition re- search (Atkinson, 1972; Bloom and Shuell, 1981; Cepeda et al., 2006; Pavlik Jr and Anderson, 2008), and benefits have also been shown for gym- nastics, baseball pitching, video games, and many other skills. See Ruth (1928), Dempster (1989), and Donovan and Radosevich (1999) for thorough meta-analyses spanning several decades. Most practical algorithms for spaced repetition are simple functions with a few hand-picked pa- rameters. This is reasonable, since they were largely developed during the 1960s–80s, when people would have had to manage practice sched- ules without the aid of computers. However, the recent popularity of large-scale online learning software makes it possible to collect vast amounts of parallel student data, which can be used to em- pirically train richer statistical models. In this work, we propose half-life regression (HLR) as a trainable spaced repetition algorithm, marrying psycholinguistically-inspired models of memory with modern machine learning tech- niques. We apply this model to real student learn- ing data from Duolingo, a popular language learn- ing app, and use it to …

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