# 反向传导算法

 Revision as of 13:52, 9 April 2013 (view source)Kandeng (Talk | contribs)← Older edit Revision as of 14:46, 9 April 2013 (view source)Kandeng (Talk | contribs) Newer edit → Line 96: Line 96: [/itex] [/itex] + {译者注： + :+ \begin{align} + \delta^{(n_l-1)}_i &=\frac{\partial}{\partial z^{n_l-1}_i}J(W,b;x,y) + = \frac{\partial}{\partial z^{n_l-1}_i}\frac{1}{2} \left\|y - h_{W,b}(x)\right\|^2 + = \frac{\partial}{\partial z^{n_1-1}_i}\frac{1}{2} \sum_{j=1}^{S_{n_l}}(y_j-a_j^{(n_l)})^2 \\ + &= \frac{1}{2} \sum_{j=1}^{S_{n_l}}\frac{\partial}{\partial z^{n_l-1}_i}(y_i-a_j^{(n_l)})^2 + = \frac{1}{2} \sum_{j=1}^{S_{n_l}}\frac{\partial}{\partial z^{n_l-1}_i}(y_i-f(z_j^{(n_l)})^2 \\ + &= \sum_{j=1}^{S_{n_l}}(y_j-f(z_j^{(n_l)})\frac{\partial}{\partial z_i^{(n_l-1)}}f(z_j^{(n_l)}) + = \sum_{j=1}^{S_{n_l}}(y_j-f(z_j^{(n_l)}) f'(z_j^{(n_l)})\frac{\partial z_j^{(n_l)}}{\partial z_i^{(n_l-1)}} \\ + &= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)}\frac{\partial z_j^{(n_l)}}{z_i^{n_l-1}} + = \sum_{j=1}^{S_{n_l}} \left(\delta_j^{(n_l)}\frac{\partial}{\partial z_i^{n_l-1}}\sum_{k=1}^{S_{n_l-1}}f(z_k^{n_l-1})W_{jk}^{n_l-1}\right) \\ + &= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)} W_{ji}^{n_l-1}f'(z_i^{n_l-1}) + = \left(\sum_{j=1}^{S_{n_l-1}}W_{ji}^{n_l-1}\delta_j^{(n_l)}\right)f'(z_i^{n_l-1}) + \end{align} + + ]