反向传播算法

目录

• Chain rule
• Multi-output Perceptron
• Multi-Layer Perceptron

Chain rule

Multi-output Perceptron

Multi-Layer Perceptron

• 对于多隐藏层结构的神经网络能够把隐藏层的节点当作输出层的节点

• For an output layer node \(k\in{K}\)

\[ \frac{\partial{E}}{\partial{W_{jk}}}=O_j\delta_k,\,\delta_k=O_k(1-O_k)(O_k-t_k) \]

• For a hidden layer node \(j\in{J}\)

\[ \frac{\partial{E}}{\partial{W_{ij}}}=O_i\delta_j,\,\delta_j=O_j(1-O_j)\sum_{k\in{K}}\delta_kW_{jk} \]

• 其中\(\delta_k\)能够看作是\(O_j\)的信息；\(\delta_j\)能够看作是\(O_i\)的信息
• 而且下一层的隐藏层偏微分的更新都基于上一隐藏层的偏微分