From 3c90a3c39099a83bf9a1f3b91881f184b958904a Mon Sep 17 00:00:00 2001 From: daming-lu Date: Thu, 26 Apr 2018 12:10:30 -0700 Subject: [PATCH] fix math formula bug --- 06.understand_sentiment/README.cn.md | 12 +++++------- 06.understand_sentiment/README.md | 12 +++++------- 2 files changed, 10 insertions(+), 14 deletions(-) diff --git a/06.understand_sentiment/README.cn.md b/06.understand_sentiment/README.cn.md index bf8e3ce..4ae294b 100644 --- a/06.understand_sentiment/README.cn.md +++ b/06.understand_sentiment/README.cn.md @@ -58,13 +58,11 @@ $$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{t-1}+b_h)$$ $$ h_t=F(x_t,h_{t-1})$$ $F$由下列公式组合而成\[[7](#参考文献)\]： -\begin{align} -i_t & = \sigma(W_{xi}x_t+W_{hi}h_{t-1}+W_{ci}c_{t-1}+b_i)\\\\ -f_t & = \sigma(W_{xf}x_t+W_{hf}h_{t-1}+W_{cf}c_{t-1}+b_f)\\\\ -c_t & = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{t-1}+b_c)\\\\ -o_t & = \sigma(W_{xo}x_t+W_{ho}h_{t-1}+W_{co}c_{t}+b_o)\\\\ -h_t & = o_t\odot tanh(c_t)\\\\ -\end{align} +$$ i_t = \sigma{(W_{xi}x_t+W_{hi}h_{t-1}+W_{ci}c_{t-1}+b_i)} $$ +$$ f_t = \sigma(W_{xf}x_t+W_{hf}h_{t-1}+W_{cf}c_{t-1}+b_f) $$ +$$ c_t = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{t-1}+b_c) $$ +$$ o_t = \sigma(W_{xo}x_t+W_{ho}h_{t-1}+W_{co}c_{t}+b_o) $$ +$$ h_t = o_t\odot tanh(c_t) $$ 其中，$i_t, f_t, c_t, o_t$分别表示输入门，遗忘门，记忆单元及输出门的向量值，带角标的$W$及$b$为模型参数，$tanh$为双曲正切函数，$\odot$表示逐元素（elementwise）的乘法操作。输入门控制着新输入进入记忆单元$c$的强度，遗忘门控制着记忆单元维持上一时刻值的强度，输出门控制着输出记忆单元的强度。三种门的计算方式类似，但有着完全不同的参数，它们各自以不同的方式控制着记忆单元$c$，如图2所示：

diff --git a/06.understand_sentiment/README.md b/06.understand_sentiment/README.md index cee0d02..f682f30 100644 --- a/06.understand_sentiment/README.md +++ b/06.understand_sentiment/README.md @@ -60,13 +60,11 @@ Compared to the structure of a simple RNN, an LSTM includes memory cell $c$, inp $$ h_t=F(x_t,h_{t-1})$$ $F$ contains following formulations\[[7](#references)\]： -\begin{align} -i_t & = \sigma(W_{xi}x_t+W_{hi}h_{t-1}+W_{ci}c_{t-1}+b_i)\\\\ -f_t & = \sigma(W_{xf}x_t+W_{hf}h_{t-1}+W_{cf}c_{t-1}+b_f)\\\\ -c_t & = f_t\odot c_{t-1}+i_t\odot \tanh(W_{xc}x_t+W_{hc}h_{t-1}+b_c)\\\\ -o_t & = \sigma(W_{xo}x_t+W_{ho}h_{t-1}+W_{co}c_{t}+b_o)\\\\ -h_t & = o_t\odot \tanh(c_t)\\\\ -\end{align} +$$ i_t = \sigma{(W_{xi}x_t+W_{hi}h_{t-1}+W_{ci}c_{t-1}+b_i)} $$ +$$ f_t = \sigma(W_{xf}x_t+W_{hf}h_{t-1}+W_{cf}c_{t-1}+b_f) $$ +$$ c_t = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{t-1}+b_c) $$ +$$ o_t = \sigma(W_{xo}x_t+W_{ho}h_{t-1}+W_{co}c_{t}+b_o) $$ +$$ h_t = o_t\odot tanh(c_t) $$ In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate, respectively. $W$ and $b$ are model parameters, $\tanh$ is a hyperbolic tangent, and $\odot$ denotes an element-wise product operation. The input gate controls the magnitude of the new input into the memory cell $c$; the forget gate controls the memory propagated from the last time step; the output gate controls the magnitutde of the output. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 2: -- GitLab