反向传导算法
From Ufldl
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&= \sum_{j=1}^{S_{n_l}}-(y_j-f(z_j^{(n_l)})) \cdot \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)})) \cdot \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)})) \cdot f'(z_j^{(n_l)}) \cdot \frac{\partial z_j^{(n_l)}}{\partial z_i^{(n_l-1)}} \\ | = \sum_{j=1}^{S_{n_l}}-(y_j-f(z_j^{(n_l)})) \cdot f'(z_j^{(n_l)}) \cdot \frac{\partial z_j^{(n_l)}}{\partial z_i^{(n_l-1)}} \\ | ||
- | &= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)} \cdot \frac{\partial z_j^{(n_l)}}{z_i^{n_l-1}} | + | &= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)} \cdot \frac{\partial z_j^{(n_l)}}{\partial z_i^{n_l-1}} |
= \sum_{j=1}^{S_{n_l}} \left(\delta_j^{(n_l)} \cdot \frac{\partial}{\partial z_i^{n_l-1}}\sum_{k=1}^{S_{n_l-1}}f(z_k^{n_l-1}) \cdot W_{jk}^{n_l-1}\right) \\ | = \sum_{j=1}^{S_{n_l}} \left(\delta_j^{(n_l)} \cdot \frac{\partial}{\partial z_i^{n_l-1}}\sum_{k=1}^{S_{n_l-1}}f(z_k^{n_l-1}) \cdot W_{jk}^{n_l-1}\right) \\ | ||
&= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)} \cdot W_{ji}^{n_l-1} \cdot f'(z_i^{n_l-1}) | &= \sum_{j=1}^{S_{n_l}} \delta_j^{(n_l)} \cdot W_{ji}^{n_l-1} \cdot f'(z_i^{n_l-1}) |