FSRS-3

FSRS-3 has 13 trainable weights and uses an exponential forgetting curve. Its stability updates use the newly calculated difficulty $D'$ .

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

Formula source

Forgetting curve and interval

 $R(t,S)=0.9^{t/S}$

 $I(r,S)=S\frac{\ln r}{\ln 0.9}$

 $S_0(G)=\operatorname{clamp}\left(w_0+(G-1)w_1,S_{min},S_{max}\right)$

 $D_0(G)=\operatorname{clamp}\left(w_2+(G-3)w_3,D_{min},D_{max}\right)$

 $D^*=D+w_4(G-3)$

 $D'=\operatorname{clamp}\left(w_5w_2+(1-w_5)D^*,D_{min},D_{max}\right)$

 $S_f=w_9(D')^{w_{10}}S^{w_{11}}e^{w_{12}(1-R)}$

 $S_r=S\left[1+e^{w_6}(11-D')S^{w_7}\left(e^{w_8(1-R)}-1\right)\right]$

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

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