> For AI agents: the complete documentation index is available at https://open-spaced-repetition.github.io/ts-fsrs/zh-TW/llms.txt, the full documentation bundle is available at https://open-spaced-repetition.github.io/ts-fsrs/zh-TW/llms-full.txt.

# FSRS-4.5

FSRS-4.5 有 17 個可訓練權重。它修改了 FSRS-4 的遺忘曲線，同時保留相同的難度和成功回憶更新結構。

共用符號和 Model 契約請參閱[模型概覽](https://open-spaced-repetition.github.io/ts-fsrs/zh-TW/guide/model.md)。

:::info 公式來源
已依據 [awesome-fsrs Wiki — FSRS-4.5](https://github.com/open-spaced-repetition/awesome-fsrs/wiki/The-Algorithm#fsrs-45) 核對。
:::

## 遺忘曲線與間隔

```math
R(t,S)=\left(1+\frac{19t}{81S}\right)^{-1/2}
```

```math
I(r,S)=\frac{81S}{19}\left(r^{-2}-1\right)
```

## 初始記憶

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

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

## 難度

```math
D^*=D-w_6(G-3)
```

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

## 複習後的穩定性

Hard 時 `math:H_G = w_{15}`，否則為 `math:1`；Easy 時 `math:E_G = w_{16}`，否則為 `math:1`。

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

```math
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]
```

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

Again 分支會避免遺忘後的穩定性超過複習前的 `math:S`。最後，模型透過 `clamp` 將 `math:S'_{\mathrm{raw}}` 限制在 `math:S_{\min}` 到 `math:S_{\max}` 之間。