反向传导算法
From Ufldl
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[译者注: | [译者注: | ||
- | + | :<math> | |
+ | \begin{align} | ||
+ | \delta^{(n_l)}_i &= \frac{\partial}{\partial z^{n_l}_i}J(W,b;x,y) | ||
+ | = \frac{\partial}{\partial z^{n_l}_i}\frac{1}{2} \left\|y - h_{W,b}(x)\right\|^2 \\ | ||
+ | &= \frac{\partial}{\partial z^{n_l}_i}\frac{1}{2} \sum_{j=1}^{S_{n_l}} (y_j-a_j^{(n_l)})^2 | ||
+ | = \frac{\partial}{\partial z^{n_l}_i}\frac{1}{2} \sum_{j=1}^{S_{n_l}} (y_j-f(z_j^{(n_l)}))^2 \\ | ||
+ | &= - (y_i - f(z_j^{(n_l)})) \cdot f'(z^{(n_l)}_i) | ||
+ | = - (y_i - a^{(n_l)}_i) \cdot f'(z^{(n_l)}_i) | ||
+ | \end{align} | ||
+ | </math> | ||
] | ] | ||