LSTM神经网络走读
0设计概述
RNN梯度爆炸和消失比较严重,RNN隐层只有一个状态h记录短期记忆,增加一个长期记忆状态c似乎就可以解决问题。
如何控制长期状态c,设计:增加三个开关,控制是否记录前一时刻的长期状态,是否把当前输入记录为长期状态单元 ,是否把当长期状态输出。
1前向计算
输入:前一个时刻的状态单元Ct-1,前一时刻的输出Ht-1,当前时刻的输入Xt;
输出:当前时刻的状态单元Ct,当前时刻的最终输出Ht。
1.1遗忘门:上一时刻的状态单元有多少保留到当前时刻![](data:image/png;base64,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)
1.2输入门:当前时刻输入x有多少保留到状态单元 ![](data:image/png;base64,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)
1.3当前输入的状态单元 :![](data:image/png;base64,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)
1.4计算当前时刻状态单元 :![](data:image/png;base64,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)
遗忘门*前一时刻状态单元 +输入门*当前输入状态
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1.5输出门:控制当前时刻状态单元 对当前输出有多少影响![](data:image/png;base64,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)
1.6 最终输出:由状态单元和输出门共同决定![](data:image/png;base64,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)
2训练
原理与bp同,每个神经元多了五个参数f,i,c,o,h:
LSTM需要学习的参数总共有八组:输入门,遗忘门,输出门和状态单元的权重矩阵W和偏置b
像bp一样,借助netj,不过这里是三个门的netj:
梯度为
其中netj为![](data:image/png;base64,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)
2.1沿时间维度:
计算t-1时刻的梯度(第一项是t时刻的梯度),主要计算第二项:![](data:image/png;base64,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)
由LSTM公式:![](data:image/png;base64,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)
由全导数公式:![](data:image/png;base64,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)
可拆开项,求得
和![](data:image/png;base64,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)
带入求得:![](data:image/png;base64,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)
带入求得由t时刻传递任意k时刻的误差:![](data:image/png;base64,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)
2.2沿上一层:
l层与l-1层的梯度关系:![](data:image/png;base64,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)
全导数公式:
具体过程是分开每项计算:
计算W:
计算偏置b
3GRU (Gated Recurrent Unit)
相对于LSTM,有两个改动:
1把遗忘门,输入门和输出门改为两个门:更新门z和重置门r;
2将单元状态和输出改为一个状态:h
备注:
激活函数tanh和sigmoid的导函数都是原函数的函数:
参考:相关网络博客及文献