Apply a sequence of functions to the input or output of a layer.

  The sequence is specified as a string which may contain the following
  characters:
    a: add previous_value
    n: apply normalization
    d: apply dropout
    z: zero add

  For example, if sequence=="dna", then the output is
    previous_value + normalize(dropout(x))

  Args:
    previous_value: A Tensor, to be added as a residual connection ('a')
    x: A Tensor to be transformed.
    sequence: a string.
    dropout_rate: a float
    norm_type: a string (see apply_norm())
    depth: an integer (size of last dimension of x).
    epsilon: a float (parameter for normalization)
    default_name: a string
    name: a string
    dropout_broadcast_dims:  an optional list of integers less than 3
      specifying in which dimensions to broadcast the dropout decisions.
      saves memory.
    layer_collection: A tensorflow_kfac.LayerCollection. Only used by the
      KFAC optimizer. Default is None.

  Returns:
    a Tensor

def layer_prepostprocess(previous_value,
                         x,
                         sequence,
                         dropout_rate,
                         norm_type,
                         depth,
                         epsilon,
                         default_name,
                         name=None,
                         dropout_broadcast_dims=None,
                         layer_collection=None):
  """Apply a sequence of functions to the input or output of a layer.

  The sequence is specified as a string which may contain the following
  characters:
    a: add previous_value
    n: apply normalization
    d: apply dropout
    z: zero add

  For example, if sequence=="dna", then the output is
    previous_value + normalize(dropout(x))

  Args:
    previous_value: A Tensor, to be added as a residual connection ('a')
    x: A Tensor to be transformed.
    sequence: a string.
    dropout_rate: a float
    norm_type: a string (see apply_norm())
    depth: an integer (size of last dimension of x).
    epsilon: a float (parameter for normalization)
    default_name: a string
    name: a string
    dropout_broadcast_dims:  an optional list of integers less than 3
      specifying in which dimensions to broadcast the dropout decisions.
      saves memory.
    layer_collection: A tensorflow_kfac.LayerCollection. Only used by the
      KFAC optimizer. Default is None.

  Returns:
    a Tensor
  """
  with tf.variable_scope(name, default_name=default_name):
    if sequence == "none":
      return x
    for c in sequence:
      if c == "a":
        x += previous_value
      elif c == "z":
        x = zero_add(previous_value, x)
      elif c == "n":
        x = apply_norm(
            x, norm_type, depth, epsilon, layer_collection=layer_collection)
      else:
        assert c == "d", ("Unknown sequence step %s" % c)
        x = dropout_with_broadcast_dims(
            x, 1.0 - dropout_rate, broadcast_dims=dropout_broadcast_dims)
    return x