Implementation of SM-2 in DART.

SM-2 is a simple spaced repetition algorithm. It calculates the number of days to wait before reviewing a piece of information based on how easily the information was remembered today.

Links

• Spaced repetition on Wikipedia
• Official algorithm description
• Official implementation of SM-2 algorithm in SuperMemo 2
• http://www.supermemo.com
• http://www.supermemo.eu

The algorithm requires four inputs

The algorithm requires four inputs: quality, repetitions, previous ease factor, and previous interval. The last three inputs are taken from the output of a previous call to SM-2. (On the first call, default values are used.)

Quality

An integer from 0-5 indicating how easily the information was remembered today. This could correspond to a button such as "Difficult" or "Very Easy."

The official algorithm description explains the meaning of each number:

5 - perfect response
4 - correct response after a hesitation
3 - correct response recalled with serious difficulty
2 - incorrect response; where the correct one seemed easy to recall
1 - incorrect response; the correct one remembered
0 - complete blackout.

Repetitions (integer)

The number of times the information has been reviewed prior to this review. repetitions should equal zero for the first review.

SM-2 uses this value to define specific intervals for the first and second reviews. SM-2 will also reset this value to zero when quality is less than 3.

Previous ease factor (float)

A floating point number (≥ 1.3) generated by the last iteration of the SM-2 algorithm. previous ease factor should equal 2.5 for the first review.

The ease factor is used to determine the number of days to wait before reviewing again. Each call to SM-2 adjusts this number up or down based on quality.

Previous interval (integer)

Generated by the last iteration of the SM-2 algorithm. Indicates the number of days to wait between reviews.

This previous interval is used when calculating the new interval. previous interval should equal zero for the first review.

Outputs

The algorithm returns three outputs: interval, repetitions, and ease factor. All three values should be saved and passed to the next call to SM-2 as inputs.

Interval (integer)

An integer number indicating the number of days to wait before the next review.

Repetitions (integer)

The number of times the information has been reviewed as of this review.

This value is maintained between calls to the algorithm and used for calculating interval. The number increments after each successful review. SM-2 will reset repetitions to zero if quality is less than 3.

Ease factor

A floating point number (≥ 1.3) which is adjusted up or down based on how easily the information was remembered.

This value is maintained between calls to the algorithm and is used for calculating interval.

Steps

If quality is greater than or equal to 3, indicating a correct response:

1. If repetitions is 0 (first review), set interval to 1 day.
2. If repetitions is 1 (second review), set interval to 6 days.
3. If repetitions is greater than 1 (subsequent reviews), set interval to previous interval * previous ease factor. (See note about recursion below.)
4. Round interval up to the next whole number.
5. Increment repetitions by 1.
6. Set ease factor to previous ease factor + (0.1 - (5 - quality) * (0.08 + (5 - quality ) * 0.02)). (See formula description below.)

If quality is less than 3, indicating an incorrect response:

1. Set repetitions to 0.
2. Set interval to 1.
3. Set ease factor to previous ease factor (no change).

If ease factor is less than 1.3:

1. Set ease factor to 1.3.

Return interval, repetitions and ease factor.

Ease factor formula

After the first two reviews, ease factor is adjusted using this formula:

previous ease factor + (0.1 - (5 - quality) * (0.08 + (5 - quality) * 0.02))

The magic numbers come from the official algorithm description.

This increases ease factor when quality is 5, makes no change when quality is 4, and decreases ease factor by varying amounts when quality is lower than 4. The lower quality is, the more ease factor is decreased.