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7 changes: 3 additions & 4 deletions LLM-tutorial/M.人类偏好对齐训练.md
Original file line number Diff line number Diff line change
Expand Up @@ -269,12 +269,11 @@ KTO引入了前景理论(prospect theory),该理论解释了为什么人
前景理论中,Tversky & Kahneman 用以下效用方程建模了人类价值

$$
v(z, z_{\text{ref}};\alpha, \lambda) = \left\{
\begin{array}{ll}
v(z, z_{\text{ref}};\alpha, \lambda) =
\begin{cases}
(z - z_{\text{ref}})^{\alpha} & \quad \text{if } z \geq z_{\text{ref}} \\
-\lambda(z_{\text{ref}} - z)^{\alpha} & \quad \text{if } z < z_{\text{ref}}
\end{array}
\right.
\end{cases}
$$

价值函数 $v:z \to R$ 将一个输出 $z$ 相对一个参考值 $z_{\text{ref}}$ 映射到其感知(或者说主观)价值,反应了人类相比起相同大小回报,对损失的敏感性更大
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