tensorflow 笔记8：RNN、Lstm源码，训练代码输入输出，维度分析

tensorflow 官网信息：https://www.tensorflow.org/api_docs/python/tf/contrib/rnn/BasicLSTMCell

tensorflow 版本：1.10

如有错误还望指正，一起探讨；

当前层各个参数含义：

Tensorflow 中RNN单个时刻计算流程：

Tensorflow 中 lstm 单个时刻计算流程：

注：上面计算[H，X] * W后和B维度不同， 如何相加，解释如下；

1. tensorflow代码中，用的这个 nn_ops.bias_add（gate_inputs, self._bias）,这个函数的计算方法是，让每个 batch 的输出值，都加上这个 B；
2. 所以维度不同可以相加：【batch_size，Hidden_size】，【Hidden_size】，见函数演示：nn_ops.bias_add

tensorflow 代码分析：见如下

tensorflow version：1.9

注：以下是一个batch，一个时刻的计算，若计算所有时刻，则循环执行以下代码，num_step(句长)次; tensorflow 已经封装好了，不需要我们写；

 RNN 关键代码:
 @tf_export("nn.rnn_cell.BasicRNNCell")
 class BasicRNNCell(LayerRNNCell):
   """The most basic RNN cell.
   Args:
     num_units: int, The number of units in the RNN cell.
     activation: Nonlinearity to use.  Default: `tanh`.
     reuse: (optional) Python boolean describing whether to reuse variables
      in an existing scope.  If not `True`, and the existing scope already has
      the given variables, an error is raised.
     name: String, the name of the layer. Layers with the same name will
       share weights, but to avoid mistakes we require reuse=True in such
       cases.
     dtype: Default dtype of the layer (default of `None` means use the type
       of the first input). Required when `build` is called before `call`.
   """

   def __init__(self,
                num_units,
                activation=None,
                reuse=None,
                name=None,
                dtype=None):
     super(BasicRNNCell, self).__init__(_reuse=reuse, name=name, dtype=dtype)

     # Inputs must be 2-dimensional.
     self.input_spec = base_layer.InputSpec(ndim=2)

     self._num_units = num_units
     self._activation = activation or math_ops.tanh

   @property
   def state_size(self):
     return self._num_units

   @property
   def output_size(self):
     return self._num_units

   def build(self, inputs_shape):
     if inputs_shape[1].value is None:
       raise ValueError("Expected inputs.shape[-1] to be known, saw shape: %s"
                        % inputs_shape)

     input_depth = inputs_shape[1].value

     # 初始化生成 W 和 B，shape 大小为
     # W: [input_size + Hidden_size, Hidden_size)
     # B: [Hidden_size]
     self._kernel = self.add_variable(
         _WEIGHTS_VARIABLE_NAME,
         shape=[input_depth + self._num_units, self._num_units])
     self._bias = self.add_variable(
         _BIAS_VARIABLE_NAME,
         shape=[self._num_units],
         initializer=init_ops.zeros_initializer(dtype=self.dtype))

     self.built = True
   # 循环该函数 num_step(句子长度) 次，则该层计算完；
   def call(self, inputs, state):
     """Most basic RNN: output = new_state = act(W * input + U * state + B)."""
     # output = Ht = tanh([x,Ht-1]*W + B)
     # 如果是第 0 时刻，那么当前的 state(即上一时刻的输出H0)的值全部为0；
     # input 的 shape为: [batch_size,emb_size]
     # state 的 shape为：[batch_zize,Hidden_size]
     # matmul : 矩阵相乘
     # array_ops.concat: 两个矩阵连接,连接后的 shape 为 [batch_size,input_size + Hidden_size],实际就是[Xt,Ht-1]

     # 此时计算: [input,state] * [W,U] == [Xt,Ht-1] * W，得到的shape为:[batch_size,Hidden_size]
     gate_inputs = math_ops.matmul(
         array_ops.concat([inputs, state], 1), self._kernel)
     # B 的shape 为:【Hidden_size】，[Xt,Ht-1] * W 计算后的shape为：[batch_size,Hidden_size]
     # nn_ops.bias_add,这个函数的计算方法是，让每个 batch 得到的值，都加上这个 B；
     # 这一步，加上B后：Ht = tanh([Xt,Ht-1] * W + B),得到的 shape 还是: [batch_size,Hidden_size]
     # 那么这个 Ht 将作为下一时刻的输入和下一层的输入；
     gate_inputs = nn_ops.bias_add(gate_inputs, self._bias)
     output = self._activation(gate_inputs)
     #此时return的维度为:[batch_size,Hidden_size]
     # 一个output作为下一时刻的输入Ht，另一个作为下一层的输入 Ht
     return output, output

 LSTM 关键代码：

 @tf_export("nn.rnn_cell.BasicLSTMCell")
 class BasicLSTMCell(LayerRNNCell):
   """Basic LSTM recurrent network cell.
   The implementation is based on: http://arxiv.org/abs/1409.2329.
   We add forget_bias (default: 1) to the biases of the forget gate in order to
   reduce the scale of forgetting in the beginning of the training.
   It does not allow cell clipping, a projection layer, and does not
   use peep-hole connections: it is the basic baseline.
   For advanced models, please use the full @{tf.nn.rnn_cell.LSTMCell}
   that follows.
   """

   def __init__(self,
                num_units,
                forget_bias=1.0,
                state_is_tuple=True,
                activation=None,
                reuse=None,
                name=None,
                dtype=None):
     """Initialize the basic LSTM cell.
     Args:
       num_units: int, The number of units in the LSTM cell.
       forget_bias: float, The bias added to forget gates (see above).
         Must set to `0.0` manually when restoring from CudnnLSTM-trained
         checkpoints.
       state_is_tuple: If True, accepted and returned states are 2-tuples of
         the `c_state` and `m_state`.  If False, they are concatenated
         along the column axis.  The latter behavior will soon be deprecated.
       activation: Activation function of the inner states.  Default: `tanh`.
       reuse: (optional) Python boolean describing whether to reuse variables
         in an existing scope.  If not `True`, and the existing scope already has
         the given variables, an error is raised.
       name: String, the name of the layer. Layers with the same name will
         share weights, but to avoid mistakes we require reuse=True in such
         cases.
       dtype: Default dtype of the layer (default of `None` means use the type
         of the first input). Required when `build` is called before `call`.
       When restoring from CudnnLSTM-trained checkpoints, must use
       `CudnnCompatibleLSTMCell` instead.
     """
     super(BasicLSTMCell, self).__init__(_reuse=reuse, name=name, dtype=dtype)
     if not state_is_tuple:
       logging.warn("%s: Using a concatenated state is slower and will soon be "
                    "deprecated.  Use state_is_tuple=True.", self)

     # Inputs must be 2-dimensional.
     self.input_spec = base_layer.InputSpec(ndim=2)

     self._num_units = num_units
     self._forget_bias = forget_bias
     self._state_is_tuple = state_is_tuple
     self._activation = activation or math_ops.tanh

   @property
   def state_size(self):
     # 隐藏层的 size：
     return (LSTMStateTuple(self._num_units, self._num_units)
             if self._state_is_tuple else 2 * self._num_units)

   @property
   def output_size(self):
     # 输出层的size：Hidden_size
     return self._num_units

   def build(self, inputs_shape):
     if inputs_shape[1].value is None:
       raise ValueError("Expected inputs.shape[-1] to be known, saw shape: %s"
                        % inputs_shape)

     #inputs的维度为:[batch_size,input_size]
     #如果是第一层每个时刻词语的输入，则这个input_size 就是 embedding_size,就等于词向量的维度；
     # 所以 此时 input_depth，就是input_size
     input_depth = inputs_shape[1].value
     # h_depth 就是 Hidden_size,隐藏层的维度
     h_depth = self._num_units

     # self._kernel == W；则此时 W的维度 为【input_size + Hidden_size，4* Hidden_size】
     # 此处定义四个 W 和 B，是为了，一次就把 i，j，f，o 计算出来；相当于图中的 ft，it，ct‘，ot
     self._kernel = self.add_variable(
         _WEIGHTS_VARIABLE_NAME,
         shape=[input_depth + h_depth, 4 * self._num_units])
     # 此时的B的维度为【4 * Hidden_size】
     self._bias = self.add_variable(
         _BIAS_VARIABLE_NAME,
         shape=[4 * self._num_units],
         initializer=init_ops.zeros_initializer(dtype=self.dtype))

     self.built = True

   def call(self, inputs, state):
     """Long short-term memory cell (LSTM).
     Args:
       inputs: `2-D` tensor with shape `[batch_size, input_size]`.
       state: An `LSTMStateTuple` of state tensors, each shaped
         `[batch_size, num_units]`, if `state_is_tuple` has been set to
         `True`.  Otherwise, a `Tensor` shaped
         `[batch_size, 2 * num_units]`.
     Returns:
       A pair containing the new hidden state, and the new state (either a
         `LSTMStateTuple` or a concatenated state, depending on
         `state_is_tuple`).
     """
     sigmoid = math_ops.sigmoid
     one = constant_op.constant(1, dtype=dtypes.int32)
     # Parameters of gates are concatenated into one multiply for efficiency.
     # 每一层的第0时刻的 c 和 h，元素全部初始化为0；
     if self._state_is_tuple:
       c, h = state
     else:
       c, h = array_ops.split(value=state, num_or_size_splits=2, axis=one)

     # 此时刻的 input：Xt 和 上一时刻的输出：Ht-1，进行结合；
     # inputs shape : [batch_size,input_size],第一层的时候，input_size，就相当于 embedding_size
     # 结合后的维度为【batch_size，input_size + Hidden_size】，W的维度为【input_size + Hidden_size，4*hidden_size】
     # 两者进行矩阵相乘后的维度为：【batch_size,4*hidden_size】
     gate_inputs = math_ops.matmul(
         array_ops.concat([inputs, h], 1), self._kernel)
     # B 的shape 为:【4 * Hidden_size】，[Xt,Ht-1] * W 计算后的shape为：[batch_size, 4 * Hidden_size]
     # nn_ops.bias_add,这个函数的计算方法是，让每个 batch 得到的值，都加上这个 B；
     # 这一步，加上B后，得到的是，i，j，f，o 的结合， [Xt,Ht-1] * W + B,得到的 shape 还是: [batch_size, 4 * Hidden_size]
     #  加上偏置B后的维度为：【batch_size，4 * Hidden_size】
     gate_inputs = nn_ops.bias_add(gate_inputs, self._bias)

     # i = input_gate, j = new_input, f = forget_gate, o = output_gate
     # 从以上的矩阵相乘后，分割出来四部分，就是 i，j，f，o的值；
     # 每个的维度为【batch_size，Hidden_size】
     i, j, f, o = array_ops.split(
         value=gate_inputs, num_or_size_splits=4, axis=one)

     forget_bias_tensor = constant_op.constant(self._forget_bias, dtype=f.dtype)

     # Note that using `add` and `multiply` instead of `+` and `*` gives a
     # performance improvement. So using those at the cost of readability.
     add = math_ops.add
     # 此处加上遗忘的 bias，选择遗忘元素；
     # 以下计算是：对应元素相乘：因为四个参数的维度都是【batch_size，hidden_size】，计算后维度不变；
     # new_c = c*sigmoid（f+bias) + sigmoid(i)*tanh(o)

     # 计算后的维度为【batch_size,hidden_size】
     multiply = math_ops.multiply
     new_c = add(multiply(c, sigmoid(add(f, forget_bias_tensor))),
                 multiply(sigmoid(i), self._activation(j)))
     # 以下计算是：对应元素相乘：因为2个参数的维度都是【batch_size，hidden_size】，计算后维度不变；
     #new_h = sigmoid(o) * tanh(new_c)

     new_h = multiply(self._activation(new_c), sigmoid(o))

     # 计算后的维度是(值不相等)：new_c == new_h == 【batch_size,hidden_size】

     if self._state_is_tuple:
       new_state = LSTMStateTuple(new_c, new_h)
     else:
       new_state = array_ops.concat([new_c, new_h], 1)
     # new_h:最后一个时刻的H，new_state：最后一个时刻的 H和C；循环执行该函数，执行 num_step次(即 最大的步长),则该层计算完全;
     # 此时的 new_c 和 new_h,作为下一时刻的输入，new_h 和下一时刻的，Xt+1 进行连接，连接后的维度为，【batch_size，input_size + Hidden_size】
     # 如果还有下一层的话，那么此刻的 new_h,变身为下一时刻的 Xt
     return new_h, new_state