FSRS-4

FSRS-4 has 17 trainable weights and replaces the FSRS-3 exponential curve with a power forgetting curve.

See the Model overview for the shared symbols and Model contract.

Formula source

Forgetting curve and interval

 $R(t,S)=\left(1+\frac{t}{9S}\right)^{-1}$

 $I(r,S)=9S\left(\frac{1}{r}-1\right)$

 $S_0(G)=\operatorname{clamp}\left(w_{G-1},S_{min},S_{max}\right)$

 $D_0(G)=\operatorname{clamp}\left(w_4-(G-3)w_5,D_{min},D_{max}\right)$

 $D^*=D-w_6(G-3)$

 $D'=\operatorname{clamp}\left(w_7w_4+(1-w_7)D^*,D_{min},D_{max}\right)$

$H_G = w_{15}$ for Hard and $1$ otherwise; $E_G = w_{16}$ for Easy and $1$ otherwise.

 $S_f=w_{11}D^{-w_{12}}\left((S+1)^{w_{13}}-1\right)e^{w_{14}(1-R)}$

 $S_r=S\left[1+e^{w_8}(11-D)S^{-w_9}\left(e^{w_{10}(1-R)}-1\right)H_GE_G\right]$

 $S'_{raw}(G)= \begin{cases} S_f,&G=1\\ S_r,&G\in\{2,3,4\} \end{cases}$

The model then clamps $S'_{\mathrm{raw}}$ to the range from $S_{\min}$ to $S_{\max}$ .