| @@ -74,17 +74,17 @@ This work is licensed under a [Creative Commons Attribution-NonCommercial 4.0 In | |||||
| [知乎文章][zhihu] | |||||
| Copyright © Scruel. All Rights Reserved. | |||||
| By: Scruel | |||||
| [知乎文章][zhihu] | |||||
| [zhihu]: https://zhuanlan.zhihu.com/p/32781741 | [zhihu]: https://zhuanlan.zhihu.com/p/32781741 | ||||
| [baidupan]: https://pan.baidu.com/s/1mkmnRIC | [baidupan]: https://pan.baidu.com/s/1mkmnRIC | ||||
| [bilibili_zh]: http://www.bilibili.com/video/av9912938?bbid=F8173D95-FF96-47EF-B7F4-0779D698B8051978infoc | |||||
| [bilibili_en1]: https://www.bilibili.com/video/av17624209/?from=search&seid=15848135050308500663 | |||||
| [bilibili_en2]: https://www.bilibili.com/video/av17624412/?from=search&seid=15848135050308500663 | |||||
| [bilibili_zh]: http://www.bilibili.com/video/av9912938 | |||||
| [bilibili_en1]: https://www.bilibili.com/video/av17624209 | |||||
| [bilibili_en2]: https://www.bilibili.com/video/av17624412/ | |||||
| [GitHub with MathJax]: https://chrome.google.com/webstore/detail/ioemnmodlmafdkllaclgeombjnmnbima | [GitHub with MathJax]: https://chrome.google.com/webstore/detail/ioemnmodlmafdkllaclgeombjnmnbima | ||||
| [Typora]: https://typora.io/ | [Typora]: https://typora.io/ | ||||
| [honor code]: https://www.coursera.org/learn/machine-learning/supplement/nh65Z/machine-learning-honor-code | [honor code]: https://www.coursera.org/learn/machine-learning/supplement/nh65Z/machine-learning-honor-code | ||||
| @@ -84,11 +84,11 @@ $Size(\Theta^{(2)})=s_3 \times (s_2 + 1) = 1 \times 4$ | |||||
|  |  | ||||
| 对第 $1$ 层的所有激活单元应用激活函数,从而得到第 $2$ 层激活单元的值: | |||||
| 对输入层(Layer 1)的所有激活单元应用激活函数,从而得到隐藏层(Layer 2)中激活单元的值: | |||||
| $\begin{align*} a_1^{(2)} = g(\Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 + \Theta_{12}^{(1)}x_2 + \Theta_{13}^{(1)}x_3) \newline a_2^{(2)} = g(\Theta_{20}^{(1)}x_0 + \Theta_{21}^{(1)}x_1 + \Theta_{22}^{(1)}x_2 + \Theta_{23}^{(1)}x_3) \newline a_3^{(2)} = g(\Theta_{30}^{(1)}x_0 + \Theta_{31}^{(1)}x_1 + \Theta_{32}^{(1)}x_2 + \Theta_{33}^{(1)}x_3) \newline \end{align*}$ | $\begin{align*} a_1^{(2)} = g(\Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 + \Theta_{12}^{(1)}x_2 + \Theta_{13}^{(1)}x_3) \newline a_2^{(2)} = g(\Theta_{20}^{(1)}x_0 + \Theta_{21}^{(1)}x_1 + \Theta_{22}^{(1)}x_2 + \Theta_{23}^{(1)}x_3) \newline a_3^{(2)} = g(\Theta_{30}^{(1)}x_0 + \Theta_{31}^{(1)}x_1 + \Theta_{32}^{(1)}x_2 + \Theta_{33}^{(1)}x_3) \newline \end{align*}$ | ||||
| 对第 $2$ 层的所有激活单元应用激活函数,从而得到输出: | |||||
| 对 Layer 2 中的所有激活单元应用激活函数,从而得到输出: | |||||
| $h_\Theta(x) = a_1^{(3)} = g(\Theta_{10}^{(2)}a_0^{(2)} + \Theta_{11}^{(2)}a_1^{(2)} + \Theta_{12}^{(2)}a_2^{(2)} + \Theta_{13}^{(2)}a_3^{(2)})$ | $h_\Theta(x) = a_1^{(3)} = g(\Theta_{10}^{(2)}a_0^{(2)} + \Theta_{11}^{(2)}a_1^{(2)} + \Theta_{12}^{(2)}a_2^{(2)} + \Theta_{13}^{(2)}a_3^{(2)})$ | ||||
| @@ -130,10 +130,12 @@ ${{z}^{\left( 2 \right)}}={{\Theta }^{\left( 1 \right)}} {{X}^{T}}$,这时 $z^ | |||||
| 当然,神经网络不仅限于三层,每层的激活单元数量也并不固定: | |||||
| 当然,神经网络可有多层,每层的激活单元数量也并不固定: | |||||
|  |  | ||||
| > 我们习惯于将输入层称为神经网络的第 0 层,如上图的神经网络被称为三层网络。 | |||||
| ## 8.5 例子和直观理解1(Examples and Intuitions I) | ## 8.5 例子和直观理解1(Examples and Intuitions I) | ||||
| 为了更好的理解神经网络,举例单层神经网络进行逻辑运算的例子。 | 为了更好的理解神经网络,举例单层神经网络进行逻辑运算的例子。 | ||||
| @@ -159,7 +159,7 @@ $J(\Theta) ={y}\log \left( 1+{{e}^{-z^{(L)}}} \right)+\left( 1-{y} \right)\log \ | |||||
|  |  | ||||
| 再次为了便于计算,我们用到如上图这个四层神经网络。 | |||||
| 再次为了便于计算,我们用到如上图这个三层(输入层一般不计数)神经网络。 | |||||
| 忆及 $z^{(l)} = \Theta^{(l-1)}a^{(l-1)}$,我们有 $h_\Theta(x)=a^{(4)}= g(z^{(4)})=g(\Theta^{(3)}a^{(3)})$ | 忆及 $z^{(l)} = \Theta^{(l-1)}a^{(l-1)}$,我们有 $h_\Theta(x)=a^{(4)}= g(z^{(4)})=g(\Theta^{(3)}a^{(3)})$ | ||||