提交 e6ef0740 编写于 作者: W wanglun

Fix typo of RNN formula

上级 fc8fda74
......@@ -43,7 +43,7 @@
循环神经网络按时间展开后如图1所示:在第$t$时刻,网络读入第$t$个输入$x_t$(向量表示)及前一时刻隐层的状态值$h_{t-1}$(向量表示,$h_0$一般初始化为$0$向量),计算得出本时刻隐层的状态值$h_t$,重复这一步骤直至读完所有输入。如果将循环神经网络所表示的函数记为$f$,则其公式可表示为:
$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{h-1}+b_h)$$
$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{t-1}+b_h)$$
其中$W_{xh}$是输入到隐层的矩阵参数,$W_{hh}$是隐层到隐层的矩阵参数,$b_h$为隐层的偏置向量(bias)参数,$\sigma$为$sigmoid$函数。
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......@@ -45,7 +45,7 @@ Figure 1. An illustration of an unfolded RNN in time.
As shown in Figure 1, we unfold an RNN: at the $t$-th time step, the network takes two inputs: the $t$-th input vector $\vec{x_t}$ and the latent state from the last time-step $\vec{h_{t-1}}$. From those, it computes the latent state of the current step $\vec{h_t}$. This process is repeated until all inputs are consumed. Denoting the RNN as function $f$, it can be formulated as follows:
$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{h-1}}+\vec{b_h})$$
$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{t-1}}+\vec{b_h})$$
where $W_{xh}$ is the weight matrix to feed into the latent layer; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$ function.
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......@@ -85,7 +85,7 @@
循环神经网络按时间展开后如图1所示:在第$t$时刻,网络读入第$t$个输入$x_t$(向量表示)及前一时刻隐层的状态值$h_{t-1}$(向量表示,$h_0$一般初始化为$0$向量),计算得出本时刻隐层的状态值$h_t$,重复这一步骤直至读完所有输入。如果将循环神经网络所表示的函数记为$f$,则其公式可表示为:
$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{h-1}+b_h)$$
$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{t-1}+b_h)$$
其中$W_{xh}$是输入到隐层的矩阵参数,$W_{hh}$是隐层到隐层的矩阵参数,$b_h$为隐层的偏置向量(bias)参数,$\sigma$为$sigmoid$函数。
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......@@ -87,7 +87,7 @@ Figure 1. An illustration of an unfolded RNN in time.
As shown in Figure 1, we unfold an RNN: at the $t$-th time step, the network takes two inputs: the $t$-th input vector $\vec{x_t}$ and the latent state from the last time-step $\vec{h_{t-1}}$. From those, it computes the latent state of the current step $\vec{h_t}$. This process is repeated until all inputs are consumed. Denoting the RNN as function $f$, it can be formulated as follows:
$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{h-1}}+\vec{b_h})$$
$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{t-1}}+\vec{b_h})$$
where $W_{xh}$ is the weight matrix to feed into the latent layer; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$ function.
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