反向传导算法
From Ufldl
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:<math> | :<math> | ||
= \delta^{(n_l)}_i\cdot\frac{\partial z^{n_l}_i}{\partial z^{n_{l-1}}_i} = \delta^{(n_l)}_i\cdot\frac{\partial}{\partial z^{n_{l-1}}_i}\sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} f(z^{n_l-1}_i) | = \delta^{(n_l)}_i\cdot\frac{\partial z^{n_l}_i}{\partial z^{n_{l-1}}_i} = \delta^{(n_l)}_i\cdot\frac{\partial}{\partial z^{n_{l-1}}_i}\sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} f(z^{n_l-1}_i) | ||
| - | = \left( \sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} \delta^{(n_l)}_i \right) f(z^{n_l-1}_i) | + | = \left( \sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} \delta^{(n_l)}_i \right) f'(z^{n_l-1}_i) |
</math> | </math> | ||
| - | + | 根据递推过程，将<math>n_l-1<\math>与<math>n_l<\math>的关系替换为l与l+1的关系，可以得到原作者的结果： | |
::<math> | ::<math> | ||
\delta^{(l)}_i = \left( \sum_{j=1}^{s_{l+1}} W^{(l)}_{ji} \delta^{(l+1)}_j \right) f'(z^{(l)}_i) | \delta^{(l)}_i = \left( \sum_{j=1}^{s_{l+1}} W^{(l)}_{ji} \delta^{(l+1)}_j \right) f'(z^{(l)}_i) | ||
