反向传导算法

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\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)
</math>  
</math>  
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[译者注:完整推导过程如下:
 
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:<math>
 
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\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}
 
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</math>
 
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:<math>
 
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= \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)
 
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= \left( \sum_{j=1}^{s_{l-1}} W^{n_l-1}_{ji} \delta^{(n_l)}_i \right) f'(z^{n_l-1}_i)
 
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</math>
 
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根据递推过程,将 <math>\textstyle n_l-1</math> 与 <math>\textstyle n_l</math> 的关系替换为 <math>\textstyle l</math> 与 <math>\textstyle l+1</math> 的关系,可以得到上面的结果:
 
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:<math>
 
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\delta^{(l)}_i = \left( \sum_{j=1}^{s_{l+1}} W^{(l)}_{ji} \delta^{(l+1)}_j \right) f'(z^{(l)}_i)
 
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</math>
 
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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。]
 

Revision as of 03:54, 9 April 2013

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