FSRS
https://github.com/open-spaced-repetition
/motoso/FSRS
SM2 algorithmと同類の間隔反復algorithm
機械学習を用いている
https://github.com/open-spaced-repetition/fsrs4anki/wiki/Spaced-Repetition-Algorithm:-A-Three‐Day-Journey-from-Novice-to-Expert
間隔反復algorithmの歴史
https://jp.quora.com/Ankiの学習効率をさらに%EF%BC%92%EF%BC%90-アップする次世代型スケジ
かなり詳しい日本語解説
流石にアルゴリズムの詳しい計算式は解説していない
計算式
https://github.com/open-spaced-repetition/fsrs4anki/wiki/The-Algorithm
DSR moelに基づく
variables
$ R: Retrievability (probability of recall)
次回出題時に正答する確率
$ SStability (interval when $ R=90\%)/day
Rが1から0.9まで下がるのに要する時間
$ S': new stability after a same-day review/day
$ S_r': new stability after recall/day
$ S_f': new stability after forgetting/day
$ D\pod{\in[1,10]} : Difficulty
$ D': new difficulty after review
$ G\pod{\in\{1,2,3,4\}}: Grade
equivalent to Rating (Anki)
1: again
2: hard
3: good
4: easy
$ w_\bullet: parameters
$ w_0=S_0(1)
$ w_1=S_0(2)
$ w_2=S_0(3)
$ w_3=S_0(4)
$ w_4=D_0(3)
equations (v5)
$ S_0:G\mapsto w_{G-1}
$ D_0:G\mapsto w_4-e^{(G-3)w_5}+1
$ w_5(G-3)=\ln(w_4+1-D_0(G))
$ \therefore w_5=\ln(D_0(3)-D_0(4)+1)
$ S':(S,G)\mapsto Se^{w_{17}(G-3+w_{18})}
$ D':(D,G)\mapsto w_7D_0(3)+(1-w_7)(D-w_6(G-3))
$ D''が不明
$ R:(t,S)\mapsto\frac1{\sqrt{{1+\frac{19}{81}\frac tS}}}
tには時間をdayで割ったものが入る
$ I:(r,S)\mapsto\frac{81}{19}S\left(\frac{1}{\sqrt r}-1\right)
$ S_r':(D,S,R,G)\mapsto S\left(e^{w_8}(11-D)S^{-w_9}\left(e^{w_{10}(1-R)}-1\right)w_{15}^{\llbracket G=2\rrbracket}w_{16}^{\llbracket G=4\rrbracket}+1\right)
$ S_f':(D,S,R)\mapsto w_{11}D^{-w_{12}}\left((S+1)^{w_{13}}-1\right)e^{w_{14}(1-R)}
ts-fsrs
#2024-10-09 22:04:12
#2024-09-17 21:22:05