# 反向传导算法

 Revision as of 05:33, 8 April 2013 (view source)Wikiroot (Talk | contribs)← Older edit Revision as of 03:54, 9 April 2013 (view source)Kandeng (Talk | contribs) Newer edit → Line 80: Line 80: \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) [/itex] [/itex] - - - [译者注：完整推导过程如下： - - :$- \delta^{(n_{l-1})}_i = \frac{\partial}{\partial z^{n_l-1}_i}J(W,b;x,y) = \frac{\partial}{\partial z^{n_l}_i}J(W,b;x,y)\cdot\frac{\partial z^{n_l}_i}{\partial z^{n_{l-1}}_i} -$ - - :$- = \delta^{(n_l)}_i\cdot\frac{\partial z^{n_l}_i}{\partial z^{n_{l-1}}_i} = \delta^{(n_l)}_i\cdot\frac{\partial}{\partial z^{n_{l-1}}_i}\sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} f(z^{n_l-1}_i) - = \left( \sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} \delta^{(n_l)}_i \right) f'(z^{n_l-1}_i) -$ - - 根据递推过程，将 $\textstyle n_l-1$ 与 $\textstyle n_l$ 的关系替换为 $\textstyle l$ 与 $\textstyle l+1$ 的关系，可以得到上面的结果： - - :$- \delta^{(l)}_i = \left( \sum_{j=1}^{s_{l+1}} W^{(l)}_{ji} \delta^{(l+1)}_j \right) f'(z^{(l)}_i) -$ - 以上的逐步反向递推求导的过程就是“反向传播”算法的本意所在。]