LaTeX 测试

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BP算法

训练集

设

$$\begin{array}{l}{\text { Set } a^{(1)}=x^{(i)}} \\ {\text { Perform forward propagation to compute } a^{(l)} \text { for } l=2,3, \ldots, L} \\ {\text { Using } y^{(i)}, \text { compute } \delta^{(L)}=a^{(L)}-y^{(i)}} \\ {\text { Compute } \delta^{(L-1)}, \delta^{(l+1)}, \ldots, \delta^{(2)}} \\ {\Delta_{i j}^{(l)} :=\Delta_{i j}^{(l)}+a_{j}^{(l)} \delta_{i}^{(l+1)}}\end{array}$$

$\begin{array}{l}{D{i j}^{(l)} :=\frac{1}{m} \Delta{i j}^{(l)}+\lambda \Theta{i j}^{(l)}} & {\text { if } j \neq 0} \ {D{i j}^{(l)} :=\frac{1}{m} \Delta_{i j}^{(l)}} & {\text { if } j=0}\end{array}$

其中 $\frac{\partial}{\partial \Theta{i j}^{(l)}} J(\Theta)=D{i j}^{(l)}$

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