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