The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Enhancing human learning via spaced repetition optimization
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Matching Methods for Causal Inference: A Review and a Look Forward
Stuart, E. A. (2010) · Statistical Science · doi:10.1214/09-sts313 · Cited by 5,478
Test-Enhanced Learning: Taking Memory Tests Improves Long-Term Retention
Roediger, H. L., & Karpicke, J. D. (2006) · Psychological Science · doi:10.1111/j.1467-9280.2006.01693.x · Cited by 2,867
Memory: A Contribution to Experimental Psychology
Ebbinghaus, H. (2013) · Annals of Neurosciences · doi:10.5214/ans.0972.7531.200408 · Cited by 2,827
Distributed practice in verbal recall tasks: A review and quantitative synthesis.
Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006) · Psychological Bulletin · doi:10.1037/0033-2909.132.3.354 · Cited by 1,888 · cited 1×
“[6] Then, to derive the HJB equation, we differentiate J with respect to time t , m(t), and n(t) using SI Appendix, section 2, Lemma 1:”
MethodSpacing Effects in Learning: A Temporal Ridgeline of Optimal Retention
Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008) · Psychological Science · doi:10.1111/j.1467-9280.2008.02209.x · Cited by 631
Bloom, K. C., & Shuell, T. J. (1981) · The Journal of Educational Research · doi:10.1080/00220671.1981.10885317 · Cited by 243 · cited 1×
“…), t ) is defined as the minimum of the expected value of the cost of going from state ( m ( t ), n ( t )) at time t to the final state at time t f : [5] Now Then, to derive the HJB equation, we differentiate J with respect to time t , m ( t ) , and n ( t ) using SI Appendix , section 2, Lemma 1 :…”
MethodLeveraging the Crowd to Detect and Reduce the Spread of Fake News and Misinformation
Kim, J., Tabibian, B., Oh, A., Schölkopf, B., & Gomez-Rodriguez, M. (2018) · Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining · doi:10.1145/3159652.3159734 · Cited by 230
Self-citationThe Wickelgren Power Law and the Ebbinghaus Savings Function
Wixted, J. T., & Carpenter, S. K. (2007) · Psychological Science · doi:10.1111/j.1467-9280.2007.01862.x · Cited by 130
Cited by
"Why is 'Chicago' deceptive?" Towards Building Model-Driven Tutorials for Humans
Lai, V., Liu, H., & Tan, C. (2020) · Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3313831.3376873 · Cited by 123
A Meta-Analytic Review of the Benefit of Spacing out Retrieval Practice Episodes on Retention
Latimier, A., Peyre, H., & Ramus, F. (2021) · Educational Psychology Review · doi:10.1007/s10648-020-09572-8 · Cited by 96
The Evolving Importance of Artificial Intelligence and Radiology in Medical Trainee Education
Fischetti, C., Bhatter, P., Frisch, E., Sidhu, A., Helmy, M., Lungren, M., & Duhaime, E. (2022) · Academic Radiology · doi:10.1016/j.acra.2021.03.023 · Cited by 47
Vagha, K., Choudhari, S., Taksande, A., Tembhurne, J., Vagha, J., & Vagha, S. (2025) · Frontiers in Medicine · doi:10.3389/fmed.2025.1601614 · Cited by 7
Azim, H. M., Santare, J. A., Sprague, A. V., Murphy, R. J., Miller, L. C., Perrotta, S. E., Maddahi, Y. N., & Record, M. J. (2025) · BMC Medical Education · doi:10.1186/s12909-025-07021-0 · Cited by 5
Metadata
- Authors
- Tabibian, B., Upadhyay, U., De, A., Zarezade, A., Schölkopf, B., & Gomez-Rodriguez, M.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2019-01-22
- Volume
- 116
- Issue
- 10
- Pages
- 3988-3993
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2914319828
- Cited by
- 178
- References
- 8
- FWCI
- 11.22
- Type
- journal article
- Language
- en
- Open access
- hybrid
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Enhancing human learning via spaced repetition optimization. https://app.cochat.ai/papers/10.1073/pnas.1815156116
- The paper
- Tabibian, B., Upadhyay, U., De, A., Zarezade, A., Schölkopf, B., & Gomez-Rodriguez, M. (2019). Enhancing human learning via spaced repetition optimization. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.1815156116
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
