SM-2 Algorithm and How the Human Brain Learns

Learning is as much about recording information in the brain as it is about retrieving it when needed. However, the human brain naturally tends to forget unused information quickly. Established in the late 19th century by German psychologist Hermann Ebbinghaus, the "Forgetting Curve" scientifically proves how newly learned information fades away within days if not reviewed. So, how is it possible to reverse this forgetting process and transfer information to long-term memory? This is where Spaced Repetition and its most famous implementation, the SM-2 Algorithm, come into play.

Memory and Synaptic Connections

There are billions of neurons in our brain, and every piece of new information means the creation of new synaptic connections between these neurons. The connection established when we read information for the first time is quite weak. If the information is read repeatedly right after (cramming), the brain perceives this as temporary electrical activity and soon weakens the connection. However, if the brain attempts to recall the information just as it is about to be forgotten (when the connection is on the verge of breaking), it produces a signal that "this information is vital" and rebuilds the synaptic connection much stronger. Each successful spaced review exponentially extends the forgetting period.

Mathematical Logic of the SM-2 Algorithm

The SM-2 algorithm, which we actively use in our language learning application Polyvo under the Polimelo studio, was developed by Polish researcher Piotr Woźniak in the late 1980s. The algorithm calculates the next review time (Interval) for each word or flashcard based on the following variables:

• q (Quality): The score from 0 to 5 given to the card by the user. (0: Completely forgotten, 5: Perfect recall).
• EF (Easiness Factor): Represents how easy the card is to learn. The starting value is 2.5. It increases as the card gets easier and decreases as it gets harder.
• n (Repetition Count): The number of times the card has been successfully recalled in a row.

The next review interval (I) of a card, in days, is determined by the following formula:

I(1) = 1 day
I(2) = 6 days
For n > 2: I(n) = I(n-1) * EF

After each successful review (q >= 3), the Easiness Factor (EF) is updated using the following formula:

EF' = EF + (0.1 - (5 - q) * (0.08 + (5 - q) * 0.02))

If the user scores the card below 3 (q < 3), meaning they failed to recall it, the repetition count (n) is reset, and the card returns to the "learning phase." The interval starts again at 1 day, but the EF value is decreased to ensure the card appears more frequently.

Why Spaced Repetition Over Cramming?

Studying all night before an exam (cramming) piles information into short-term memory. A few days after the exam is over, almost all of this information is forgotten. The SM-2 algorithm, on the other hand, aims for maximum retention with minimum effort. Instead of studying for hours a day, you can save thousands of words to your memory for years by spending just 10-15 minutes on the day determined by the algorithm. The system we developed in Polyvo is based exactly on this scientific foundation, ensuring our users use their time most efficiently.