RNN(Recurrent Neural Network)循环神经网络。

对于CNN来说,比如图像处理,它逐渐从局部空间抽象到全局空间,有一种空间层次感,通道可以与空间一起卷积,也可以分开卷积。同时由于卷积权重共享,它可以减少参数。

对RNN来说,它擅长处理序列问题,也就是输入中存在依赖的情况,比如预测下一个词语(N对N),情感分类(N对1),encoder-decoder(如seq2seq,N对M)等。

本文力求简洁,仅做概要总结。

1,简单RNN分析

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uryu+fv1+qX8bH/AAAeV3z9+v1S/jY/4AWKgArq8rvn79fql/Gx/wAAHld8/fr9Uv42P+AFioAK6vK75+/X6pfxsf8AACH3CFW4v/QLKhTXur6LrZN0o98iix3Z5riXkOW1/M6W9qS626L1hBrhIcp1c5sZW1kVR6LNFvGqSJpGUkXHJJNSqc1wJs7x9Wg+6XHdAUeCX+SLL7mQqWp2lR2nXkaKizGJipUT45m7BYvY80hi8Tovc6DlFiuXPgtrV2WxaylStvlh1Qlt84lUvmJI38U13fH1+CJnIIEbplSSLgmkUukpS9EBAXJU1lI+o7+NZt8hKzSVfvyPnrdDm6S7jSXWcqWo2kpz9ESgEcsp/okZkvbKlPiiRo8/yPskhkhhwqFyPkWsCxpdBXk3VUSJEjl6zdDtp/dc38YerkxtWepKCoWo5xmZOmqcYlSpSIcF2DODbbiVOTrKqnPyXULtdMaczSx2GZbP3QtsTGOtCQSCXkgUuHRMTnTjxkipFFhr95H0lTjhyYqbOMi2plTEIXQRJJIn6hBLLOlUYMq+c1nHmOz5W8tYlhzmHp/QpIl6G380OP8ApESJ3wsWFZeRKrk6gutcu7Umh5MVbOPsY+Hg26xecKnXPyq2PcJJEIl23dKXUJeUHmJnKtzLztrpGjj023iYPyU5w7clVcONSqRSedHOUpdCpumbcGL4yz7cfqxJvgAAUcfLVXfl+tNmhrGUu24tJdCEpSFQr6WbyKD3DSZd+UxOVVIXm6uyYhkul0Btvyu+fv1+qX8bH/ADanBv/QS/XtrzfvG4mCPT49IrCuryu+fv1+qX8bH/AAAeV3z9+v1S/jY/4AWKgNxXV5XfP36/VL+Nj/gBCfhBqAvhQdQ0aleytoytHrhquaMVjvUEinLrKb5nS7PZLj0hfaIE8Ifk1rrNjc+3SdLYMmURFs3RZCYkVtKTfUolpIUhds59k2PF5ndFAUmibmRDL1mYkqga1NbV7IW+pxY5FF5iVMdJg7J97m+evExL3RRYbly4Mq0tiObSUkx+Tyqk8NWMnNpFMgkf+Kb7hfC1m7oS7wIUpNJd0BATg/0XaVvbipPVk3b0tfSxF3CSfJEVV7VrOQvQ7wSfEasiX0oXQ9sOZ9+kJDz8w2puDkJV8ryLJggq6XP1CFJrOPPXetskMlZWbS5OFY5+qajEGCtQp0pi0bsohttc9ffPBUu5wMqZIhzdEpTfYE87aUG2s/Ss3VFUPk39Vv0jytSTxy7xik16CdRBIuyUnVIIbcGzRPy07p3GvZON+VdmkVUmJzbXJLr61XBi94UyRe8Ocb34R65p7d5Ypts2V0PajXShUu8NrOr/ANIhyeGLFmfdCmLLS3BwxDq7N57r3slUjYGeOjsmmrHdOuflTl8AhUieGLCxEDKPU0DY/LXEMmzReZ5rE+Tk07jNKvze5MQzdkTT56uYhiE0dDQTVvEH511mlvtaRsnV1ZWaj21AcoXnRI+VIvIM0zH2DK6T6fcae6KI7Yyts9omGOFN3ZHl0pU0fWlMRVQRK3OI2TbJPWyvWSVLqKPVFPGOkujRXDlPtDmuq+3kq+tXdeBpmmPJ5+iZk82DGdFP21XTzVXZN343T5XfP36/VL+Nj/gBtbgv/S7zfswlv0pRL8eox8LCuryu+fv1+qX8bH/AD83WXrPqVsqZW/FMHS0m1F1dH8QFjI6j9MyzJwUm0cyZilGR/LEMloiiKluDUTaGpWGfzkypj2lpGoGVV77Z98LEMufA5TUzzWZvBMeQjPHDXhTsMoVV0bs7qq+4T7hNffFFmVprHULYuALDUJTDKAaae2Gbpcay/wBgyqpttQ3fGxAVmTNr8wVtaRsCleSrUpOKPc2DJHwTpbnj5mbjV89c4Y7unUXRqP3xeLSLFBpzhFd3Lv7a0J/ejcY5HN+YtJPg5yolOYx9BSbZjnFT1hKvnr15wLh1BSmr5Ip87hrHyhyaiw7AxsCned8RBIqRC9ZYon5nHuP8qzLbW8ykryL1ViaPa9flV+1E095r1eANV8GbZ9vQFgG9UOGxSTVVKmdKqnLtkakMYiRe97Bj/wBKIqvZVKbVnV9pGEyqZTanwptLmJWzEzJmYxtayr1fY5UxumrrPypjdwMK4Mq13yCZc0JxylgSQqh4eSNq3ubl7Ul705/DGsOFGq1xU9R2xtMzdJtTyrwj5ydU2khdZ+btzG7nbW/qEkGFyJCKoiNp61NHGqQjUpI2Fdu3XN49VqgQhDujq/atWwTRtK7ZibG0HTOKv/Q3sAjZaHMpWzy9i9qLqUgypyqFWJpGNew65lGrxMu9vY9wbxT7okmKs4ZgIh5/Yer56fsYyoqYbQlRL1YRvHunBdhB4YvzOqY2g+yTa6Bt4fv5XfP36/VLeNj/AIAZPmo9FrLR7YbMTs6I7XF+rDMe1XZ5XfP36/VL+Nj/AIAPK75+/X6pfxsf8ALFQFxIrq8rvn79fql/Gx/wAjVn6tdmXoe0cO+vRcqGrGmlJpJFqyjeydN3yCulXH5lS6BVel0hdUIhcI9l9rHMtaSlqSotm3cyBakSeLrPFipItm5W7gplTG83TqMTdwMba8wBQoJJ5Q7GX8r+sGs3Z5vKwOKB9ClTprnZsk8OkQ6vqvdJE149yLHsuXBJW4tidrL3BW+WDUBNvmipOSjEjfyW8r4ez3AnRGRrOIYIMmDZFkzbl5NJu3SKQiReqUpd0BX/AJYIqq4XNbmAZV1NtKiq1BCnySMkybcgkurzI26XvdP6pdwSvEd7Y+nxzQd7T/wISIHn+V9kkMkSOE1uP8hWWxzDoKYEe1M/SjS6d7kidtV94UvhjHLC2+fV1aGmrRRDxeHo2EZkNWUsxPpcP36/b1Y1I/Q0croVP3hOuNXZ/wDCSv8A5sLeWggleJVo3Lgqfe5uqvtqnN3iCRDiwOgKGg7RUHH09FE5tFRaG0sqbbP01VVT9Ixz6zGOJ5fx1RwyrizU2io1zm3tLay3lOMIE6RW3kgeMS0HxKZXViZU++c5EkzH1H2toWiiufJCYt8M190L2SxykjWap20co42dBnBuSSL4Lcmj+kFirlykzbqrrqlRRSLrMqc2ghCdcacr9YsSfYDwqGrmBuPTTSoaakk5iEdGMRB2lr0G0nOU+93RTj3RR/y1aRyW+mjzUfhOE+CqgGS300eaj8JwnwVUB6evswsPGvQjhl3zrQ9bK44NqMum0Sg5Fx6khLIfO5z9+TZ8cSHHr32sxA5gLYTdFVCU5Wb8nanaWHGqzcF2kl0+PpFN2f4d0RbsbeWeoiq/lLXjMVhXscXkomZVx0t6ja9BVI5t9XrF3vD1jncqnr/JFpKLsVflGQrzNDB3el6nM5bwhUiM6e5hsF5Ip9HbeV+2n5XdEhQAc2U5y6NURbEZBCWormpJmbrNxUUNKucHBoYiHIJOsSKGUSxdH1n5XSc3Ho3DdLVuDjKzMLXEzaZhanf48qtDO0KeY4n9QQSOqQ5Cd8ZIhhLsRLy7QZ7TZv73UvIl5ElWGQqaHMfcXS1q8ro7062nwBPi2U4y2H5KTClCcJQSKZ46GdaUkVV+mTdOuhyuhXvtLfT4YynOlUkhO0zBWephTlKyuQ8LFJEJ+5WevW7XP3JSbPeGP1Bpu511KcpLO/UFyJdzitD0RAFg2zdptuJGUV1G5q3J0jaXB9fU6Qk9lEsRUq1VS18LqtOb1/UCODaMhjYbNPxvRQw4/VDdP/8Akxhbrp2lGbbVJeiqRYUJSMJTUUlyMZDsUmDUnVSSIUhf/Qo98AHUbgAAAAAAAAAAAAAAAAgllP8ARIzJe2VKfFEjRHLKf6JGZL2ypT4okaOByPtkhkwWBsXQtMXFk68jKfRbVbKFOV5K8qqcypTade8fQXdLuDL5WNbTcc7j3yBXLJ0kduukfcVIYmg5B2wFXfLVrKzuW63VhivPkLpxCLcPOwu7Oqdw4MTqajHObT3A0/S2H/6lFZY//sRD4Q3ErREOlplP/wCoHU9RHYyhKee0knFN5U8auVqq65VE+nlNOnomFmvMp7dW6XgAAq4+WjT3Bv8A0Ev17a837xuJgiH3Bv8A0Ev17a837xuJgj0+O1YAABuAAAAAAAgVkS+lC6HthzPv0hIKp6bj6wp6Qg5dtzyKkUDtXTfUYnKpG2Tk2RH3Il9KF0PbDmffpCSo89d6WyQyYvbi19LWkp3yBpKJRhYflDL83SOc/bTbxts+oebd+yVG32pxvCVpF+Skeg5K6SIRcyRyql2NWopyG3DnGdAK2Jy33asfpW3tOUTS8fTkHCtI2FYaDoMUktgpyn1kP32vb17+sa0zZuV5i00hQsQgV5VFaf7FjmnfeeuDdRJJLWYx+86w2BdG4Ta11FyFQOYySmOQL2qPiWZnDhdXoEIUvv8AdET6Hzfpxkg6qao7Q3PkqtkC8kos2p/5nZt94jVDUfc6x99U22bolJaqjOXvbpcW7o1tbihKdpZkYyzWHYoMElj75+SKQusZGMStTV8lX1CRtRSsItTjiRKdwlFO/nhBLWfkuV7rRoObq69Iy0V89/q0ag4L/wBLvN+zCW/SlEvxEDgv/S7zfswlv0pRL8enx8LAAAMgAAAh5wiu7l39taE/vRuMac4RXdy7+2tCf3o3GORzvmLSTErlWppO8VPkg6wiE5qKKuV0VoqqqQnKl1kKfYOTrnHvwMCxpiDj4iKbFZxrBArVq3R3Ekik0EIO8A5u+fhE1bc3LLbW81XxFS1jTSc3KxiXJIHVVVKQ5NeshFSlNpMXUY+91xsdYhoqLOWPYlW5uloQaImKkTZ3CE6JR2xrW6V+6ftDNxEfUEbPHbyBDHLJxkUq6aIaegqZLUcp/AG/Wc/a3R+o27j5tnU5tdWhFqSqaXjPIqknhHhXTQjUpjqmLrKTbVVP0+8LoLvGmWI71HCJ5irv21noyMetqXotyvKnmZFiqyO6XMQhUm7cipCGMXXtHPo07BCCRA3tz11Ecc1Ho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alt="" width="300" />

如图,这里以N对N为例,X为输入,y为输出,h为隐藏状态。

假设输入X_t对应权重矩阵为U,隐藏状态h_t-1对应的的权重为W,输出y_t对应的权重为V,这里U,W,V一般对各个时刻t来说是共享的。

对于t时刻,有以下公式:

其中第一个激活函数一般为tanh或relu等,第二个一般为softmax。第一式以矩阵方式运行,提高效率。

TensorFlow调用:

tf.nn.rnn_cell.BasicRNNCell(
num_units,
activation=None,# type string
reuse=None,
name=None,
dtype=None,
**kwargs,
)

BPTT(back-propagation through time):反向传播

t时刻的损失为:

求和,求偏导:

如果我们以tanh作为激活函数,则中间项

由于tanh函数偏导小于1,多次连乘导致“梯度消失”,如果采用relu激活,导数为1容易导致“梯度爆炸”。

解决梯度爆炸:通过梯度裁剪,容易处理

解决梯度消失:下面将要介绍的LSTM

2,LSTM(长短期记忆)

LSTM通过门的操作来实现信息的选取,遗忘门通过一个sigmoid激活函数对上一个细胞状态c_t-1进行更新,再加上输入门的新信息。

可以看到,上面水平线中,只有与门的2个交换操作,以及一个CEC(常量误差传播子,权值为1的自连接,一个线性激活,保证误差传递而不会发生梯度消失或爆炸)。

相关公式为:

TensorFlow实现:

tf.nn.rnn_cell.BasicLSTMCell(
num_units,
forget_bias=1.0,#Ger et al等在2000年提出,遗忘门偏置为1使得LSTM更加健壮。
state_is_tuple=True,
activation=None,
reuse=None,
name=None,
dtype=None,
**kwargs,
)

3,LSTM变体

  • 变体1:添加图中深色部分连接。个人理解:输入和遗忘部分加入之前的细胞状态学习可以获得更多context信息,输出门添加基于新的细胞状态信息学习。感觉上比基础LSTM要厉害些,也没增加参数。

  • 变体2:输入i_t直接用1-f_t表示。个人认为这样做不太恰当,需要遗忘的细胞状态信息,以及需要增加的输入信息,它们应该分开学习。共同学习存在一种矛盾:比如遗忘的部分想要降低参数,而增加的部分想要提高参数。好处是参数减少了。

  • 变体3:GRU。使用2个门(重置门和更新门)代替LSTM的3个门,计算效率高,内存占用少,效果差不多,实际中比较流行。将细胞状态c与隐藏状态h合并,这个变体思想类似变体1,参数减少了不少。

TensorFlow GRU实现

tf.nn.rnn_cell.GRUCell(
num_units,
activation=None,
reuse=None,
kernel_initializer=None,
bias_initializer=None,
name=None,
dtype=None,
**kwargs,
)

参考资料

https://blog.csdn.net/zhaojc1995/article/details/80572098

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