sm2-plus extended interval

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This is a JS implementation of a refined version of the SM2 space repetition learning algorithm invented by BlueRaja overcoming some of the inherent issues of the original version. Details about what these issuses are and how BlueRaja solved them can be found in this post.

The discribed algorithm has shown a maximal interval of 5 days even with a difficulty of 0 while other memory tools extend the interval to weeks or month. This can be prevented by adding to a dificulty weighted old interval instead of a constant.

Usage

import { WORST, BEST, calculate, getPercentOverdue } from 'sm2-plus';

const DAY_IN_MINISECONDS = 24 * 60 * 60 * 1000;
const getDaysSinceEpoch = () => (
    Math.round(new Date().getTime() / DAY_IN_MINISECONDS)
);

const TODAY = getDaysSinceEpoch();

const testWord = {
  word: 'test',
  update: TODAY - 17,    
  difficulty: 0.2,
  interval: 100
};

console.info(calculate(testWord, BEST, TODAY));

The output should be:

{ 
  difficulty: 0.19,    
  interval: 1,
  dueDate: TODAY+1,
  update: TODAY,
  word: 'test' 
  }

Among them dueDate is the date the next time when the item should be reviewed.

Simulation

It is good to be able to make a evaluation about how many times does the user has to study to totally remember a word in the best case.

Thus a simulation method was export to do this job.

The first argument is the initial difficulty and the second argument is the threshold below which a word can be seen as remembered.

import { simulate } from 'sm2-plus'
simulate(0.3, 0.1);

The output would be like this, meaning that in the best condition, a user has to remember a word and select BEST 4 times to make sure that he has mastered the word whose initial difficulty is 0.3.

Day	Index	Difficulty
0	1	0.3
1	2	0.24117647058823527
2	3	0.18235294117647055
3	4	0.12352941176470585
4	5	0.06470588235294114

Algorithm Abstract

Each item should be stored as the following structure:

• difficulty: How difficult the item is, from [0.0, 1.0]. Defaults to 0.3 (if the software has no way of determining a better default for an item).
• interval: How many days should occur between review attempts for this item.
• update: The last date this item was reviewed.

When reviewing item, choose a performanceRating from [0.0, 1.0], with 1.0 being the best. Set a cutoff point for the answer being “correct” (default is 0.6). Then the item data can be updated using the way described below:

• percentOverdue= (today - update) / interval) (2 <= percentOverdue)

• difficulty = difficulty + percentOverdue * (8 - 9 * performanceRating) / 17 (0 <= difficulty <= 1)

• difficultyWeight = 3 - 1.7 * difficulty

• interval =

  • Ceil((1-difficulty)^3 * oldinterval) + (difficultyWeight - 1) * percentOverdue (for correct answer)
  • 1 / difficultyWeight / difficultyWeight (for incorrect answer)