代数求导

张一风2025/3/7小于 1 分钟

结论

y对w的转置进行求导等于y对w求导后的转置

若 y 是标量, w 是向量或矩阵, 且采用分母布局, 则有

\frac{\partial y}{\partial w^{T}} = {(\frac{\partial y}{\partial w})}^{T}

示例

设 $w = [w_{1}, w_{2}]^{T}$ , 则有:

\frac{\partial y}{\partial w^{T}} = [\frac{\partial y}{\partial w_{1}}, \frac{\partial y}{\partial w_{2}}] = {[\begin{matrix} \frac{\partial y}{\partial w_{1}} \\ \frac{\partial y}{\partial w_{2}} \end{matrix}]}^{T} = {(\frac{\partial y}{\partial w})}^{T}