The Knowledge Retention Algorithm

A closer look at the evidence behind spaced repetition

Epistemic Status: High confidence, based on years of studying the scientific literature on learning protocols and implementing them with concrete systems for personal use

Epistemic Effort: Medium to high, read through many papers, implemented the protocol for testing (daily usage since 2021)

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The mind is a system, and knowledge retention is an emergent property of the informational atoms you absorb and the software you use to hold onto those atoms.

You absorb countless facts and concepts, but without repeated activation of the neurons that encoded them, the internal representation will dissipate, as if you never absorbed them in the first place. This inefficiency is unacceptable. Attention is a finite resource and therefore has a return on investment (ROI). To maximize the ROI of paying attention to information with the intention to recall it later, an effective mental system is required.

The question is, what does this system look like? What algorithm optimizes long-term knowledge and attention utilization? These questions are best answered by the scientific method. It is comical to see how many students think their study habits are effective, when in fact they are suboptimal.

The rational path is to relinquish our subjective feelings about the effectiveness of learning protocols and turn toward the data. In this piece, I synthesize the literature on spaced repetition, one of the most well-established protocols for the long-term retention of acquired knowledge.

What is Spaced Repetition?

Spaced repetition, also referred to as spaced retrieval, is a powerful learning technique that involves distributing learning sessions across time in a repeated manner. It can also be conceptualized as the opposite of "cramming". For example, establishing a routine to practice textbook problems for 1 hour every other day is spaced repetition. The retrieval of learned information is spaced by two days and repeated consistently.

The typical student masses review material prior to an exam, so the review of information is crammed into a small number of sessions that run back-to-back. With this technique, there is no established repetition or spacing between study sessions. While this approach may work momentarily and result in adequate exam scores, the information will not be retained in the long term. This class-taking style of cramming information, vomiting information on exams, and forgetting information after the class ends runs antithetical to the purpose of educational institutions. The solution is spaced repetition.

The research done by psychologists on learning methods has convincingly demonstrated the immense superiority of spaced retrieval over "massed" retrieval, which is why students should abandon cramming. Research from Purdue University showed that spaced retrieval with long intervals between tests improved retention by 200% compared to cramming tests.¹ Another paper on student studying behaviors showed reviewing chapter material immediately after a lecture was one of the strongest predictors of worse exam grades.² In other words, reviewing chapter material after a lecture condenses studying into a short time interval, and this correlated with worse performance on exams.

Many studies have reached the same conclusion that distributing learning across time is more effective for long-term retention than condensing learning into tighter intervals.³ A monograph on learning techniques summarizes this point well:

"...students mass much of their study prior to tests and believe that this popular cramming strategy is effective... would students be better off spreading out their study of content? The answer to this question is a resounding 'yes.' The term distributed practice effect refers to the finding that distributing learning over time typically benefits long-term retention more than does massing learning opportunities back-to-back or in relatively close succession.''⁴

Why Does Spaced Repetition Work?

The reason spaced repetition works is that it disrupts Ebbinghaus' Forgetting Curve. In the 1880s, psychologist Hermann Ebbinghaus performed a set of classic experiments on his memory and was able to model his retention of information over time mathematically. This curve has been successfully replicated many times and has become a classic model of human forgetfulness in memory psychology.⁵ It shows that our retention decreases exponentially from the time initially exposed to the information.

What spaced retrieval does is disrupts this decay process. The repeated retrieval of information distributed over time induces active recall, and we "relearn" the information. Upon reviewing the information, the retention spikes back up to 100% and starts to decay again, but the decay curve becomes less steep. The act of relearning material stymies the subsequent drop in retention.

So with spaced repetition, the retention is routinely brought to 100% and the forgetting curve flattens out as more retrievals are performed. This results in enhanced long-term retention. The crammer will learn material immediately before the exam, but their retention of that material will decay exponentially after the exam. The spaced repetition practitioner will repeatedly disrupt the forgetting curve and establish a higher long-term retention rate.

Incorporate Spaced Repetition in the Learning Process

There are two research-backed steps to take when incorporating spaced repetition into the learning workflow:

1. Induce active recall

2. Increase time between retrieval sessions (absolute spacing)

Spaced repetition is great for disrupting the forgetting curve, but it is a powerhouse strategy when used in conjunction with active recall, as YouTuber Ali Abdaal has championed in many of his viral videos. These two learning techniques have been well established in learning psychology as the best ways to learn and retain information, which is fundamentally how we accumulate knowledge.

To induce active recall in each learning session, information must be retrieved from the brain, not external sources. This challenges your brain to exert cognitive energy in extracting information, and in the process of doing so, neural pathways to that information are strengthened.⁶ The act of passively reviewing information from external sources like books, videos, and notes is not effective for learning.

On to the second point, increasing the absolute spacing interval (time between retrieval sessions) to raise the difficulty of retrieval is a very effective way to improve long-term retention. For example, given five study sessions, it is better to space them apart by 3 days as opposed to 1 day because 3 days is a larger spacing period. The amount of time and effort is the same, but the simple act of spacing your studying apart more can have profound effects on your ability to recall the information a month from now. The evidence overwhelmingly supports this claim.⁷

To further emphasize the importance of combining active recall with spaced repetition, let me briefly discuss an important study. A paper published in the journal Psychological Science in the Public Interest examined the experimental literature on learning techniques for students with the purpose of classifying the utility of various strategies.⁸ The authors determined utility by looking at the overall effectiveness of learning and the generalizability across learning conditions and student characteristics. Of the ten studying techniques they examined, they concluded the techniques with the highest utility are "practice testing" and "distributed practice", which are just different ways of describing active recall and spaced repetition since they involve actively retrieving information and leveraging the distributed-practice effect. Passive reviewing techniques like highlighting/underlining and rereading were deemed low utility. The significance of this paper is that they did not base their conclusions on one set of experiments. Rather, they aggregated the findings of hundreds of studies on learning and memory (their citations are 12 pages long) to evaluate each technique.

Relative Spacing vs Absolute Spacing

When it comes to spaced repetition, there are two classes of spacing intervals that have been rigorously studied in academia: relative spacing and absolute spacing.

• Absolute Spacing: the amount of time between retrieval sessions

• Relative Spacing: the amount of time between two retrieval sessions relative to the previous spacing period

If you learn information and wait three days to initiate retrieval, then the absolute spacing between these two repetitions is three days. If you initially space your study sessions by three days, but then increase the spacing period by 50% after each subsequent session, you are implementing an expanding relative spacing schedule. This schedule would go as follows:

1. Learn information

2. Wait three days... initiate active recall, relearn information

3. Wait four days... initiate active recall, relearn information

4. Wait six days... initiate active recall, relearn information

5. Wait nine days... initiate active recall, relearn information

6. And so on...

Relative spacing is broken down into three categories: expanding, equal, and contracting.

An expanding relative spacing is a schedule that increases the absolute spacing period after each retrieval, which consequently increases the difficulty of each retrieval over time.

Equal relative spacing is a schedule that spaces retrievals apart by a fixed amount, i.e. the absolute spacing does not change.

A contracting relative spacing is a schedule in which the absolute spacing shrinks after each retrieval. This specific schedule can only be implemented over a fixed time period, such as preparing for an exam because the absolute spacing interval eventually approaches zero.

Literature from learning and memory psychology has shown resounding evidence for the value of enlarging absolute spacing on long-term retention. However, there has been much conflicting evidence on the topic of relative spacing. Some studies suggest that an expanding relative spacing schedule is superior for retention,⁹ but other studies show no difference in long-term recall between expanding and equal spacing.¹⁰

An experiment performed by psychologists Jeffrey Karpicke and Althea Bauernschmidt showed that increasing absolute spacing produced greater retention for both short-term and long-term recall, but the relative spacing of retrievals had no discernible effect on retention.¹¹ There is also some data showing equal relative spacing to be the most effective.¹² The fact of the matter is that there is too much conflicting evidence to definitively claim one spacing pattern is superior to others.

While many influencers in the productivity space have advocated for expanding spacing as the most effective (probably because Anki is a popular software that runs an expanding relative spacing algorithm), this claim is heavily subject to scrutiny by intellectuals.

The research on absolute spacing and relative spacing is summed up quite wonderfully by Karpicke and Bauernschmidt in discussing their experimental results.

"This would appear to be good news for students, educators, and researchers interested in implementing spaced retrieval practice because it leads to a straightforward recommendation: Increasing the absolute spacing of retrieval attempts has clear value for learning, but how tests are spaced relative to one another may not be critical."¹³

Implement Spaced Repetition

The most effective (and popular) software for implementing spaced retrieval, as far as I can tell, is Anki, which is a flashcards application that presents cards for review based on an expanding relative spacing schedule. The algorithm can be adjusted by users to tailor the review schedule to their specific learning conditions (studying for an exam is a lot different than general knowledge building).

While the evidence backing the superiority of this type of relative spacing is clouded by other studies reaching contradictory conclusions, it is still the best spaced repetition schedule in my opinion because it provides for scalable learning.

If you implement an equal relative spacing schedule, your spaced repetition system will become cluttered with cards that are due for review as you continue to add cards. By increasing the spacing between reviews over time, the system can scale to years of learning because cards need to be reviewed less frequently over time, allowing for the addition of new cards.

The benefit of this approach is that you can achieve scale without sacrificing long-term retention. Even though scientific findings on relative spacing contradict each other, the vast majority of studies reveal that expanding relative spacing is not worse than the alternatives. At worst, it does not improve retention over equal spacing, and at best, it enhances retention.

I will follow up this post with a deeper dive into Anki, my personal implementation, and my knowledge retention protocols.

Recap

• Spaced repetition describes a learning technique employed to improve retention of information by repeatedly retrieving the information in spaced intervals over time.

• This technique is heavily backed by literature from memory and learning psychology to be one of the most effective methods for retaining learned information

• The two best ways to enhance the results of spaced repetition are to induce active recall and increase the time between retrieval sessions

• A vast body of evidence shows that long-term retention is significantly enhanced by increasing the absolute spacing interval (time between reviews), but the data is contradictory on the effects of relative spacing intervals (expanding vs equal vs contracting) on long-term retention

References

1. Jeffrey D. Karpicke, Althea Bauernschmidt. (2011). Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing.

2. Regan A R Gurung, Janet Weidert, Amanda Jeske. (2010). Focusing on how students study.

3. Greene, R. L. (2008). Repetition and spacing effects. In H. L. Roediger (Ed.), Learning and memory: A comprehensive reference. Vol. 2: Cognitive psychology of memory (pp. 65–78)

4. John Dunlosky, Katherine Rawson, Elizabeth Marsh, Mitchell Nathan, Daniel Willingham. (2013). Improving Students' Learning With Effective Learning Techniques: Promising Directions From Cognitive and Educational Psychology.

5. Jaap M. J. Murre, Joeri Dros. (2015). Replication and Analysis of Ebbinghaus’ Forgetting Curve.

6. J. D. Karpicke, J. R. Blunt. (2011). Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping.

7. Jeffrey D. Karpicke, Althea Bauernschmidt. (2011). Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing.

8. John Dunlosky, Katherine Rawson, Elizabeth Marsh, Mitchell Nathan, Daniel Willingham. (2013). Improving Students' Learning With Effective Learning Techniques: Promising Directions From Cognitive and Educational Psychology.

9. Storm, B. C., Bjork, R. A., & Storm, J. C. (2010). Optimizing retrieval as a learning event: When and why expanding retrieval practice enhances long-term retention.

10. Carpenter, S. K., & DeLosh, E. L. (2005). Application of the testing and spacing effects to name learning. Applied Cognitive Psychology, 19, 619–636.

11. Jeffrey D. Karpicke, Althea Bauernschmidt. (2011). Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing.

12. Logan, J. M., & Balota, D. A. (2008). Expanded vs. equal interval spaced retrieval practice: Exploring different schedules of spacing and retention interval in younger and older adults. Aging, Neuropsychology, and Cognition, 15, 257–280

13. Jeffrey D. Karpicke, Althea Bauernschmidt. (2011). Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing.