# Unbounded Human Learning: Optimal Scheduling for Spaced Repetition

arXiv: https://arxiv.org/abs/1602.07032 · HTML: https://mlsanity.com/paper/1602.07032/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2016.

## Built on by (most cited first, 12 of 12)

- [Mitigating Biases in Student Performance Prediction via Attention-Based Personalized Federated Learning](https://mlsanity.com/paper/2208.01182/) (2022)
- [Multi-Factors Aware Dual-Attentional Knowledge Tracing](https://mlsanity.com/paper/2108.04741/) (2021)
- [Multi-Layer Personalized Federated Learning for Mitigating Biases in Student Predictive Analytics](https://mlsanity.com/paper/2212.02985/) (2022)
- [Improving Artificial Teachers by Considering How People Learn and Forget](https://mlsanity.com/paper/2102.04174/) (2021)
- [SmartPhone: Exploring Keyword Mnemonic with Auto-generated Verbal and Visual Cues](https://mlsanity.com/paper/2305.10436/) (2023)
- [KARL: Knowledge-Aware Retrieval and Representations aid Retention and Learning in Students](https://mlsanity.com/paper/2402.12291/) (2024)
- [IntelliCode: A Multi-Agent LLM Tutoring System with Centralized Learner Modeling](https://mlsanity.com/paper/2512.18669/) (2025)
- [Least Squares Maximum and Weighted Generalization-Memorization Machines](https://mlsanity.com/paper/2308.16456/) (2023)
- [SRS-Stories: Vocabulary-constrained multilingual story generation for language learning](https://mlsanity.com/paper/2512.18362/) (2025)
- [WordCraft: Scaffolding the Keyword Method for L2 Vocabulary Learning with Multimodal LLMs](https://mlsanity.com/paper/2602.00762/) (2026)
- [A Dataset for Modeling Iterative Problem-Solving](https://mlsanity.com/paper/2609.00940/) (2026)
- [Interpretable Memory Models for Spaced Repetition](https://mlsanity.com/paper/2610.10548/) (2026)

## Abstract (arXiv)

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.