Sonyfe25cp的玩具

###Neuron Network Fp

在前一节的model部分已经知道下面的式子：

$$a_1^{(2)} = g(\Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 +\Theta_{12}^{(1)}x_2 +\Theta_{13}^{(1)}x_3)$$ $$a_2^{(2)} = g(\Theta_{20}^{(1)}x_0 + \Theta_{21}^{(1)}x_1 +\Theta_{22}^{(1)}x_2 +\Theta_{23}^{(1)}x_3)$$ $$a_3^{(2)} = g(\Theta_{30}^{(1)}x_0 + \Theta_{31}^{(1)}x_1 +\Theta_{32}^{(1)}x_2 +\Theta_{33}^{(1)}x_3)$$ $$h_{\Theta}(x) = a_1^{(3)} = g(\Theta_{10}^{(2)}a_0^{(2)} + \Theta_{11}^{(2)}a_1^{(2)} +\Theta_{12}^{(2)}a_2^{(2)} +\Theta_{13}^{(2)}a_3^{(2)})$$

定义: $z_1^{(2)} = \Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 +\Theta_{12}^{(1)}x_2 +\Theta_{13}^{(1)}x_3$

于是$a_1^{(2)}=g(z_1^{(2)})$

而 $x = \left[ \begin{array}{c} x_0\\ x_1\\ x_2\\ x_3\end{array}\right]$ $z^{(2)} = \left[ \begin{array}{c} z_1^{(2)}\\ z_2^{(2)}\\ z_3^{(2)}\end{array}\right]$

可以得到： $h_\Theta(x) = g(\Theta_{10}^{(2)}a_0^{(2)} + \Theta_{11}^{2}a_1^{(2)} + \Theta_{12}^{(2)}a_2^{(2)} + \Theta_{13}^{(2)}a_3^{(2)})$