rnn_cell_impl.py

# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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# ==============================================================================
"""Module implementing RNN Cells.

This module provides a number of basic commonly used RNN cells, such as LSTM
(Long Short Term Memory) or GRU (Gated Recurrent Unit), and a number of
operators that allow adding dropouts, projections, or embeddings for inputs.
Constructing multi-layer cells is supported by the class `MultiRNNCell`, or by
calling the `rnn` ops several times.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import collections
import hashlib
import numbers

from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_shape
from tensorflow.python.framework import tensor_util
from tensorflow.python.layers import base as base_layer
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import clip_ops
from tensorflow.python.ops import init_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import partitioned_variables
from tensorflow.python.ops import random_ops
from tensorflow.python.ops import variable_scope as vs
from tensorflow.python.ops import variables as tf_variables
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.util import nest


_BIAS_VARIABLE_NAME = "bias"
_WEIGHTS_VARIABLE_NAME = "kernel"


def _like_rnncell(cell):
  """Checks that a given object is an RNNCell by using duck typing."""
  conditions = [hasattr(cell, "output_size"), hasattr(cell, "state_size"),
                hasattr(cell, "zero_state"), callable(cell)]
  return all(conditions)


def _concat(prefix, suffix, static=False):
  """Concat that enables int, Tensor, or TensorShape values.

  This function takes a size specification, which can be an integer, a
  TensorShape, or a Tensor, and converts it into a concatenated Tensor
  (if static = False) or a list of integers (if static = True).

  Args:
    prefix: The prefix; usually the batch size (and/or time step size).
      (TensorShape, int, or Tensor.)
    suffix: TensorShape, int, or Tensor.
    static: If `True`, return a python list with possibly unknown dimensions.
      Otherwise return a `Tensor`.

  Returns:
    shape: the concatenation of prefix and suffix.

  Raises:
    ValueError: if `suffix` is not a scalar or vector (or TensorShape).
    ValueError: if prefix or suffix was `None` and asked for dynamic
      Tensors out.
  """
  if isinstance(prefix, ops.Tensor):
    p = prefix
    p_static = tensor_util.constant_value(prefix)
    if p.shape.ndims == 0:
      p = array_ops.expand_dims(p, 0)
    elif p.shape.ndims != 1:
      raise ValueError("prefix tensor must be either a scalar or vector, "
                       "but saw tensor: %s" % p)
  else:
    p = tensor_shape.as_shape(prefix)
    p_static = p.as_list() if p.ndims is not None else None
    p = (constant_op.constant(p.as_list(), dtype=dtypes.int32)
         if p.is_fully_defined() else None)
  if isinstance(suffix, ops.Tensor):
    s = suffix
    s_static = tensor_util.constant_value(suffix)
    if s.shape.ndims == 0:
      s = array_ops.expand_dims(s, 0)
    elif s.shape.ndims != 1:
      raise ValueError("suffix tensor must be either a scalar or vector, "
                       "but saw tensor: %s" % s)
  else:
    s = tensor_shape.as_shape(suffix)
    s_static = s.as_list() if s.ndims is not None else None
    s = (constant_op.constant(s.as_list(), dtype=dtypes.int32)
         if s.is_fully_defined() else None)

  if static:
    shape = tensor_shape.as_shape(p_static).concatenate(s_static)
    shape = shape.as_list() if shape.ndims is not None else None
  else:
    if p is None or s is None:
      raise ValueError("Provided a prefix or suffix of None: %s and %s"
                       % (prefix, suffix))
    shape = array_ops.concat((p, s), 0)
  return shape


def _zero_state_tensors(state_size, batch_size, dtype):
  """Create tensors of zeros based on state_size, batch_size, and dtype."""
  def get_state_shape(s):
    """Combine s with batch_size to get a proper tensor shape."""
    c = _concat(batch_size, s)
    c_static = _concat(batch_size, s, static=True)
    size = array_ops.zeros(c, dtype=dtype)
    size.set_shape(c_static)
    return size
  return nest.map_structure(get_state_shape, state_size)


class RNNCell(base_layer.Layer):
  """Abstract object representing an RNN cell.

  Every `RNNCell` must have the properties below and implement `call` with
  the signature `(output, next_state) = call(input, state)`.  The optional
  third input argument, `scope`, is allowed for backwards compatibility
  purposes; but should be left off for new subclasses.

  This definition of cell differs from the definition used in the literature.
  In the literature, 'cell' refers to an object with a single scalar output.
  This definition refers to a horizontal array of such units.

  An RNN cell, in the most abstract setting, is anything that has
  a state and performs some operation that takes a matrix of inputs.
  This operation results in an output matrix with `self.output_size` columns.
  If `self.state_size` is an integer, this operation also results in a new
  state matrix with `self.state_size` columns.  If `self.state_size` is a
  (possibly nested tuple of) TensorShape object(s), then it should return a
  matching structure of Tensors having shape `[batch_size].concatenate(s)`
  for each `s` in `self.batch_size`.
  """

  def __call__(self, inputs, state, scope=None):
    """Run this RNN cell on inputs, starting from the given state.

    Args:
      inputs: `2-D` tensor with shape `[batch_size x input_size]`.
      state: if `self.state_size` is an integer, this should be a `2-D Tensor`
        with shape `[batch_size x self.state_size]`.  Otherwise, if
        `self.state_size` is a tuple of integers, this should be a tuple
        with shapes `[batch_size x s] for s in self.state_size`.
      scope: VariableScope for the created subgraph; defaults to class name.

    Returns:
      A pair containing:

      - Output: A `2-D` tensor with shape `[batch_size x self.output_size]`.
      - New state: Either a single `2-D` tensor, or a tuple of tensors matching
        the arity and shapes of `state`.
    """
    if scope is not None:
      with vs.variable_scope(scope,
                             custom_getter=self._rnn_get_variable) as scope:
        return super(RNNCell, self).__call__(inputs, state, scope=scope)
    else:
      with vs.variable_scope(vs.get_variable_scope(),
                             custom_getter=self._rnn_get_variable):
        return super(RNNCell, self).__call__(inputs, state)

  def _rnn_get_variable(self, getter, *args, **kwargs):
    variable = getter(*args, **kwargs)
    trainable = (variable in tf_variables.trainable_variables() or
                 (isinstance(variable, tf_variables.PartitionedVariable) and
                  list(variable)[0] in tf_variables.trainable_variables()))
    if trainable and variable not in self._trainable_weights:
      self._trainable_weights.append(variable)
    elif not trainable and variable not in self._non_trainable_weights:
      self._non_trainable_weights.append(variable)
    return variable

  @property
  def state_size(self):
    """size(s) of state(s) used by this cell.

    It can be represented by an Integer, a TensorShape or a tuple of Integers
    or TensorShapes.
    """
    raise NotImplementedError("Abstract method")

  @property
  def output_size(self):
    """Integer or TensorShape: size of outputs produced by this cell."""
    raise NotImplementedError("Abstract method")

  def build(self, _):
    # This tells the parent Layer object that it's OK to call
    # self.add_variable() inside the call() method.
    pass

  def zero_state(self, batch_size, dtype):
    """Return zero-filled state tensor(s).

    Args:
      batch_size: int, float, or unit Tensor representing the batch size.
      dtype: the data type to use for the state.

    Returns:
      If `state_size` is an int or TensorShape, then the return value is a
      `N-D` tensor of shape `[batch_size x state_size]` filled with zeros.

      If `state_size` is a nested list or tuple, then the return value is
      a nested list or tuple (of the same structure) of `2-D` tensors with
      the shapes `[batch_size x s]` for each s in `state_size`.
    """
    with ops.name_scope(type(self).__name__ + "ZeroState", values=[batch_size]):
      state_size = self.state_size
      return _zero_state_tensors(state_size, batch_size, dtype)


class BasicRNNCell(RNNCell):
  """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.
  """

  def __init__(self, num_units, activation=None, reuse=None):
    super(BasicRNNCell, self).__init__(_reuse=reuse)
    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 call(self, inputs, state):
    """Most basic RNN: output = new_state = act(W * input + U * state + B)."""
    output = self._activation(_linear([inputs, state], self._num_units, True))
    return output, output


class GRUCell(RNNCell):
  """Gated Recurrent Unit cell (cf. http://arxiv.org/abs/1406.1078)."""

  def __init__(self,
               num_units,
               activation=None,
               reuse=None,
               kernel_initializer=None,
               bias_initializer=None):
    super(GRUCell, self).__init__(_reuse=reuse)
    self._num_units = num_units
    self._activation = activation or math_ops.tanh
    self._kernel_initializer = kernel_initializer
    self._bias_initializer = bias_initializer

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

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

  def call(self, inputs, state):
    """Gated recurrent unit (GRU) with nunits cells."""
    with vs.variable_scope("gates"):  # Reset gate and update gate.
      # We start with bias of 1.0 to not reset and not update.
      bias_ones = self._bias_initializer
      if self._bias_initializer is None:
        dtype = [a.dtype for a in [inputs, state]][0]
        bias_ones = init_ops.constant_initializer(1.0, dtype=dtype)
      value = math_ops.sigmoid(
          _linear([inputs, state], 2 * self._num_units, True, bias_ones,
                  self._kernel_initializer))
      r, u = array_ops.split(value=value, num_or_size_splits=2, axis=1)
    with vs.variable_scope("candidate"):
      c = self._activation(
          _linear([inputs, r * state], self._num_units, True,
                  self._bias_initializer, self._kernel_initializer))
    new_h = u * state + (1 - u) * c
    return new_h, new_h


_LSTMStateTuple = collections.namedtuple("LSTMStateTuple", ("c", "h"))


class LSTMStateTuple(_LSTMStateTuple):
  """Tuple used by LSTM Cells for `state_size`, `zero_state`, and output state.

  Stores two elements: `(c, h)`, in that order.

  Only used when `state_is_tuple=True`.
  """
  __slots__ = ()

  @property
  def dtype(self):
    (c, h) = self
    if c.dtype != h.dtype:
      raise TypeError("Inconsistent internal state: %s vs %s" %
                      (str(c.dtype), str(h.dtype)))
    return c.dtype


class BasicLSTMCell(RNNCell):
  """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):
    """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).
      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.
    """
    super(BasicLSTMCell, self).__init__(_reuse=reuse)
    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)
    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):
    return (LSTMStateTuple(self._num_units, self._num_units)
            if self._state_is_tuple else 2 * self._num_units)

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

  def call(self, inputs, state):
    """Long short-term memory cell (LSTM)."""
    sigmoid = math_ops.sigmoid
    # Parameters of gates are concatenated into one multiply for efficiency.
    if self._state_is_tuple:
      c, h = state
    else:
      c, h = array_ops.split(value=state, num_or_size_splits=2, axis=1)

    concat = _linear([inputs, h], 4 * self._num_units, True)

    # i = input_gate, j = new_input, f = forget_gate, o = output_gate
    i, j, f, o = array_ops.split(value=concat, num_or_size_splits=4, axis=1)

    new_c = (
        c * sigmoid(f + self._forget_bias) + sigmoid(i) * self._activation(j))
    new_h = self._activation(new_c) * sigmoid(o)

    if self._state_is_tuple:
      new_state = LSTMStateTuple(new_c, new_h)
    else:
      new_state = array_ops.concat([new_c, new_h], 1)
    return new_h, new_state


class LSTMCell(RNNCell):
  """Long short-term memory unit (LSTM) recurrent network cell.

  The default non-peephole implementation is based on:

    http://deeplearning.cs.cmu.edu/pdfs/Hochreiter97_lstm.pdf

  S. Hochreiter and J. Schmidhuber.
  "Long Short-Term Memory". Neural Computation, 9(8):1735-1780, 1997.

  The peephole implementation is based on:

    https://research.google.com/pubs/archive/43905.pdf

  Hasim Sak, Andrew Senior, and Francoise Beaufays.
  "Long short-term memory recurrent neural network architectures for
   large scale acoustic modeling." INTERSPEECH, 2014.

  The class uses optional peep-hole connections, optional cell clipping, and
  an optional projection layer.
  """

  def __init__(self, num_units,
               use_peepholes=False, cell_clip=None,
               initializer=None, num_proj=None, proj_clip=None,
               num_unit_shards=None, num_proj_shards=None,
               forget_bias=1.0, state_is_tuple=True,
               activation=None, reuse=None):
    """Initialize the parameters for an LSTM cell.

    Args:
      num_units: int, The number of units in the LSTM cell
      use_peepholes: bool, set True to enable diagonal/peephole connections.
      cell_clip: (optional) A float value, if provided the cell state is clipped
        by this value prior to the cell output activation.
      initializer: (optional) The initializer to use for the weight and
        projection matrices.
      num_proj: (optional) int, The output dimensionality for the projection
        matrices.  If None, no projection is performed.
      proj_clip: (optional) A float value.  If `num_proj > 0` and `proj_clip` is
        provided, then the projected values are clipped elementwise to within
        `[-proj_clip, proj_clip]`.
      num_unit_shards: Deprecated, will be removed by Jan. 2017.
        Use a variable_scope partitioner instead.
      num_proj_shards: Deprecated, will be removed by Jan. 2017.
        Use a variable_scope partitioner instead.
      forget_bias: Biases of the forget gate are initialized by default to 1
        in order to reduce the scale of forgetting at the beginning of
        the training.
      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.  This 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.
    """
    super(LSTMCell, self).__init__(_reuse=reuse)
    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)
    if num_unit_shards is not None or num_proj_shards is not None:
      logging.warn(
          "%s: The num_unit_shards and proj_unit_shards parameters are "
          "deprecated and will be removed in Jan 2017.  "
          "Use a variable scope with a partitioner instead.", self)

    self._num_units = num_units
    self._use_peepholes = use_peepholes
    self._cell_clip = cell_clip
    self._initializer = initializer
    self._num_proj = num_proj
    self._proj_clip = proj_clip
    self._num_unit_shards = num_unit_shards
    self._num_proj_shards = num_proj_shards
    self._forget_bias = forget_bias
    self._state_is_tuple = state_is_tuple
    self._activation = activation or math_ops.tanh

    if num_proj:
      self._state_size = (
          LSTMStateTuple(num_units, num_proj)
          if state_is_tuple else num_units + num_proj)
      self._output_size = num_proj
    else:
      self._state_size = (
          LSTMStateTuple(num_units, num_units)
          if state_is_tuple else 2 * num_units)
      self._output_size = num_units

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

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

  def call(self, inputs, state):
    """Run one step of LSTM.

    Args:
      inputs: input Tensor, 2D, batch x num_units.
      state: if `state_is_tuple` is False, this must be a state Tensor,
        `2-D, batch x state_size`.  If `state_is_tuple` is True, this must be a
        tuple of state Tensors, both `2-D`, with column sizes `c_state` and
        `m_state`.

    Returns:
      A tuple containing:

      - A `2-D, [batch x output_dim]`, Tensor representing the output of the
        LSTM after reading `inputs` when previous state was `state`.
        Here output_dim is:
           num_proj if num_proj was set,
           num_units otherwise.
      - Tensor(s) representing the new state of LSTM after reading `inputs` when
        the previous state was `state`.  Same type and shape(s) as `state`.

    Raises:
      ValueError: If input size cannot be inferred from inputs via
        static shape inference.
    """
    num_proj = self._num_units if self._num_proj is None else self._num_proj
    sigmoid = math_ops.sigmoid

    if self._state_is_tuple:
      (c_prev, m_prev) = state
    else:
      c_prev = array_ops.slice(state, [0, 0], [-1, self._num_units])
      m_prev = array_ops.slice(state, [0, self._num_units], [-1, num_proj])

    dtype = inputs.dtype
    input_size = inputs.get_shape().with_rank(2)[1]
    if input_size.value is None:
      raise ValueError("Could not infer input size from inputs.get_shape()[-1]")
    scope = vs.get_variable_scope()
    with vs.variable_scope(scope, initializer=self._initializer) as unit_scope:
      if self._num_unit_shards is not None:
        unit_scope.set_partitioner(
            partitioned_variables.fixed_size_partitioner(
                self._num_unit_shards))
      # i = input_gate, j = new_input, f = forget_gate, o = output_gate
      lstm_matrix = _linear([inputs, m_prev], 4 * self._num_units, bias=True)
      i, j, f, o = array_ops.split(
          value=lstm_matrix, num_or_size_splits=4, axis=1)
      # Diagonal connections
      if self._use_peepholes:
        with vs.variable_scope(unit_scope) as projection_scope:
          if self._num_unit_shards is not None:
            projection_scope.set_partitioner(None)
          w_f_diag = vs.get_variable(
              "w_f_diag", shape=[self._num_units], dtype=dtype)
          w_i_diag = vs.get_variable(
              "w_i_diag", shape=[self._num_units], dtype=dtype)
          w_o_diag = vs.get_variable(
              "w_o_diag", shape=[self._num_units], dtype=dtype)

      if self._use_peepholes:
        c = (sigmoid(f + self._forget_bias + w_f_diag * c_prev) * c_prev +
             sigmoid(i + w_i_diag * c_prev) * self._activation(j))
      else:
        c = (sigmoid(f + self._forget_bias) * c_prev + sigmoid(i) *
             self._activation(j))

      if self._cell_clip is not None:
        # pylint: disable=invalid-unary-operand-type
        c = clip_ops.clip_by_value(c, -self._cell_clip, self._cell_clip)
        # pylint: enable=invalid-unary-operand-type
      if self._use_peepholes:
        m = sigmoid(o + w_o_diag * c) * self._activation(c)
      else:
        m = sigmoid(o) * self._activation(c)

      if self._num_proj is not None:
        with vs.variable_scope("projection") as proj_scope:
          if self._num_proj_shards is not None:
            proj_scope.set_partitioner(
                partitioned_variables.fixed_size_partitioner(
                    self._num_proj_shards))
          m = _linear(m, self._num_proj, bias=False)

        if self._proj_clip is not None:
          # pylint: disable=invalid-unary-operand-type
          m = clip_ops.clip_by_value(m, -self._proj_clip, self._proj_clip)
          # pylint: enable=invalid-unary-operand-type

    new_state = (LSTMStateTuple(c, m) if self._state_is_tuple else
                 array_ops.concat([c, m], 1))
    return m, new_state


def _enumerated_map_structure(map_fn, *args, **kwargs):
  ix = [0]
  def enumerated_fn(*inner_args, **inner_kwargs):
    r = map_fn(ix[0], *inner_args, **inner_kwargs)
    ix[0] += 1
    return r
  return nest.map_structure(enumerated_fn, *args, **kwargs)


class DropoutWrapper(RNNCell):
  """Operator adding dropout to inputs and outputs of the given cell."""

  def __init__(self, cell, input_keep_prob=1.0, output_keep_prob=1.0,
               state_keep_prob=1.0, variational_recurrent=False,
               input_size=None, dtype=None, seed=None):
    """Create a cell with added input, state, and/or output dropout.

    If `variational_recurrent` is set to `True` (**NOT** the default behavior),
    then the the same dropout mask is applied at every step, as described in:

    Y. Gal, Z Ghahramani.  "A Theoretically Grounded Application of Dropout in
    Recurrent Neural Networks".  https://arxiv.org/abs/1512.05287

    Otherwise a different dropout mask is applied at every time step.

    Args:
      cell: an RNNCell, a projection to output_size is added to it.
      input_keep_prob: unit Tensor or float between 0 and 1, input keep
        probability; if it is constant and 1, no input dropout will be added.
      output_keep_prob: unit Tensor or float between 0 and 1, output keep
        probability; if it is constant and 1, no output dropout will be added.
      state_keep_prob: unit Tensor or float between 0 and 1, output keep
        probability; if it is constant and 1, no output dropout will be added.
        State dropout is performed on the *output* states of the cell.
      variational_recurrent: Python bool.  If `True`, then the same
        dropout pattern is applied across all time steps per run call.
        If this parameter is set, `input_size` **must** be provided.
      input_size: (optional) (possibly nested tuple of) `TensorShape` objects
        containing the depth(s) of the input tensors expected to be passed in to
        the `DropoutWrapper`.  Required and used **iff**
         `variational_recurrent = True` and `input_keep_prob < 1`.
      dtype: (optional) The `dtype` of the input, state, and output tensors.
        Required and used **iff** `variational_recurrent = True`.
      seed: (optional) integer, the randomness seed.

    Raises:
      TypeError: if cell is not an RNNCell.
      ValueError: if any of the keep_probs are not between 0 and 1.
    """
    if not _like_rnncell(cell):
      raise TypeError("The parameter cell is not a RNNCell.")
    with ops.name_scope("DropoutWrapperInit"):
      def tensor_and_const_value(v):
        tensor_value = ops.convert_to_tensor(v)
        const_value = tensor_util.constant_value(tensor_value)
        return (tensor_value, const_value)
      for prob, attr in [(input_keep_prob, "input_keep_prob"),
                         (state_keep_prob, "state_keep_prob"),
                         (output_keep_prob, "output_keep_prob")]:
        tensor_prob, const_prob = tensor_and_const_value(prob)
        if const_prob is not None:
          if const_prob < 0 or const_prob > 1:
            raise ValueError("Parameter %s must be between 0 and 1: %d"
                             % (attr, const_prob))
          setattr(self, "_%s" % attr, float(const_prob))
        else:
          setattr(self, "_%s" % attr, tensor_prob)

    # Set cell, variational_recurrent, seed before running the code below
    self._cell = cell
    self._variational_recurrent = variational_recurrent
    self._seed = seed

    self._recurrent_input_noise = None
    self._recurrent_state_noise = None
    self._recurrent_output_noise = None

    if variational_recurrent:
      if dtype is None:
        raise ValueError(
            "When variational_recurrent=True, dtype must be provided")

      def convert_to_batch_shape(s):
        # Prepend a 1 for the batch dimension; for recurrent
        # variational dropout we use the same dropout mask for all
        # batch elements.
        return array_ops.concat(
            ([1], tensor_shape.TensorShape(s).as_list()), 0)

      def batch_noise(s, inner_seed):
        shape = convert_to_batch_shape(s)
        return random_ops.random_uniform(shape, seed=inner_seed, dtype=dtype)

      if (not isinstance(self._input_keep_prob, numbers.Real) or
          self._input_keep_prob < 1.0):
        if input_size is None:
          raise ValueError(
              "When variational_recurrent=True and input_keep_prob < 1.0 or "
              "is unknown, input_size must be provided")
        self._recurrent_input_noise = _enumerated_map_structure(
            lambda i, s: batch_noise(s, inner_seed=self._gen_seed("input", i)),
            input_size)
      self._recurrent_state_noise = _enumerated_map_structure(
          lambda i, s: batch_noise(s, inner_seed=self._gen_seed("state", i)),
          cell.state_size)
      self._recurrent_output_noise = _enumerated_map_structure(
          lambda i, s: batch_noise(s, inner_seed=self._gen_seed("output", i)),
          cell.output_size)

  def _gen_seed(self, salt_prefix, index):
    if self._seed is None:
      return None
    salt = "%s_%d" % (salt_prefix, index)
    string = (str(self._seed) + salt).encode("utf-8")
    return int(hashlib.md5(string).hexdigest()[:8], 16) & 0x7FFFFFFF

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

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

  def zero_state(self, batch_size, dtype):
    with ops.name_scope(type(self).__name__ + "ZeroState", values=[batch_size]):
      return self._cell.zero_state(batch_size, dtype)

  def _variational_recurrent_dropout_value(
      self, index, value, noise, keep_prob):
    """Performs dropout given the pre-calculated noise tensor."""
    # uniform [keep_prob, 1.0 + keep_prob)
    random_tensor = keep_prob + noise

    # 0. if [keep_prob, 1.0) and 1. if [1.0, 1.0 + keep_prob)
    binary_tensor = math_ops.floor(random_tensor)
    ret = math_ops.div(value, keep_prob) * binary_tensor
    ret.set_shape(value.get_shape())
    return ret

  def _dropout(self, values, salt_prefix, recurrent_noise, keep_prob):
    """Decides whether to perform standard dropout or recurrent dropout."""
    if not self._variational_recurrent:
      def dropout(i, v):
        return nn_ops.dropout(
            v, keep_prob=keep_prob, seed=self._gen_seed(salt_prefix, i))
      return _enumerated_map_structure(dropout, values)
    else:
      def dropout(i, v, n):
        return self._variational_recurrent_dropout_value(i, v, n, keep_prob)
      return _enumerated_map_structure(dropout, values, recurrent_noise)

  def __call__(self, inputs, state, scope=None):
    """Run the cell with the declared dropouts."""
    def _should_dropout(p):
      return (not isinstance(p, float)) or p < 1

    if _should_dropout(self._input_keep_prob):
      inputs = self._dropout(inputs, "input",
                             self._recurrent_input_noise,
                             self._input_keep_prob)
    output, new_state = self._cell(inputs, state, scope)
    if _should_dropout(self._state_keep_prob):
      new_state = self._dropout(new_state, "state",
                                self._recurrent_state_noise,
                                self._state_keep_prob)
    if _should_dropout(self._output_keep_prob):
      output = self._dropout(output, "output",
                             self._recurrent_output_noise,
                             self._output_keep_prob)
    return output, new_state


class ResidualWrapper(RNNCell):
  """RNNCell wrapper that ensures cell inputs are added to the outputs."""

  def __init__(self, cell):
    """Constructs a `ResidualWrapper` for `cell`.

    Args:
      cell: An instance of `RNNCell`.
    """
    self._cell = cell

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

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

  def zero_state(self, batch_size, dtype):
    with ops.name_scope(type(self).__name__ + "ZeroState", values=[batch_size]):
      return self._cell.zero_state(batch_size, dtype)

  def __call__(self, inputs, state, scope=None):
    """Run the cell and add its inputs to its outputs.

    Args:
      inputs: cell inputs.
      state: cell state.
      scope: optional cell scope.

    Returns:
      Tuple of cell outputs and new state.

    Raises:
      TypeError: If cell inputs and outputs have different structure (type).
      ValueError: If cell inputs and outputs have different structure (value).
    """
    outputs, new_state = self._cell(inputs, state, scope=scope)
    nest.assert_same_structure(inputs, outputs)
    # Ensure shapes match
    def assert_shape_match(inp, out):
      inp.get_shape().assert_is_compatible_with(out.get_shape())
    nest.map_structure(assert_shape_match, inputs, outputs)
    res_outputs = nest.map_structure(
        lambda inp, out: inp + out, inputs, outputs)
    return (res_outputs, new_state)


class DeviceWrapper(RNNCell):
  """Operator that ensures an RNNCell runs on a particular device."""

  def __init__(self, cell, device):
    """Construct a `DeviceWrapper` for `cell` with device `device`.

    Ensures the wrapped `cell` is called with `tf.device(device)`.

    Args:
      cell: An instance of `RNNCell`.
      device: A device string or function, for passing to `tf.device`.
    """
    self._cell = cell
    self._device = device

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

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

  def zero_state(self, batch_size, dtype):
    with ops.name_scope(type(self).__name__ + "ZeroState", values=[batch_size]):
      with ops.device(self._device):
        return self._cell.zero_state(batch_size, dtype)

  def __call__(self, inputs, state, scope=None):
    """Run the cell on specified device."""
    with ops.device(self._device):
      return self._cell(inputs, state, scope=scope)


class MultiRNNCell(RNNCell):
  """RNN cell composed sequentially of multiple simple cells."""

  def __init__(self, cells, state_is_tuple=True):
    """Create a RNN cell composed sequentially of a number of RNNCells.

    Args:
      cells: list of RNNCells that will be composed in this order.
      state_is_tuple: If True, accepted and returned states are n-tuples, where
        `n = len(cells)`.  If False, the states are all
        concatenated along the column axis.  This latter behavior will soon be
        deprecated.

    Raises:
      ValueError: if cells is empty (not allowed), or at least one of the cells
        returns a state tuple but the flag `state_is_tuple` is `False`.
    """
    super(MultiRNNCell, self).__init__()
    if not cells:
      raise ValueError("Must specify at least one cell for MultiRNNCell.")
    if not nest.is_sequence(cells):
      raise TypeError(
          "cells must be a list or tuple, but saw: %s." % cells)

    self._cells = cells
    self._state_is_tuple = state_is_tuple
    if not state_is_tuple:
      if any(nest.is_sequence(c.state_size) for c in self._cells):
        raise ValueError("Some cells return tuples of states, but the flag "
                         "state_is_tuple is not set.  State sizes are: %s"
                         % str([c.state_size for c in self._cells]))

  @property
  def state_size(self):
    if self._state_is_tuple:
      return tuple(cell.state_size for cell in self._cells)
    else:
      return sum([cell.state_size for cell in self._cells])

  @property
  def output_size(self):
    return self._cells[-1].output_size

  def zero_state(self, batch_size, dtype):
    with ops.name_scope(type(self).__name__ + "ZeroState", values=[batch_size]):
      if self._state_is_tuple:
        return tuple(cell.zero_state(batch_size, dtype) for cell in self._cells)
      else:
        # We know here that state_size of each cell is not a tuple and
        # presumably does not contain TensorArrays or anything else fancy
        return super(MultiRNNCell, self).zero_state(batch_size, dtype)

  def call(self, inputs, state):
    """Run this multi-layer cell on inputs, starting from state."""
    cur_state_pos = 0
    cur_inp = inputs
    new_states = []
    for i, cell in enumerate(self._cells):
      with vs.variable_scope("cell_%d" % i):
        if self._state_is_tuple:
          if not nest.is_sequence(state):
            raise ValueError(
                "Expected state to be a tuple of length %d, but received: %s" %
                (len(self.state_size), state))
          cur_state = state[i]
        else:
          cur_state = array_ops.slice(state, [0, cur_state_pos],
                                      [-1, cell.state_size])
          cur_state_pos += cell.state_size
        cur_inp, new_state = cell(cur_inp, cur_state)
        new_states.append(new_state)

    new_states = (tuple(new_states) if self._state_is_tuple else
                  array_ops.concat(new_states, 1))

    return cur_inp, new_states


class _SlimRNNCell(RNNCell):
  """A simple wrapper for slim.rnn_cells."""

  def __init__(self, cell_fn):
    """Create a SlimRNNCell from a cell_fn.

    Args:
      cell_fn: a function which takes (inputs, state, scope) and produces the
        outputs and the new_state. Additionally when called with inputs=None and
        state=None it should return (initial_outputs, initial_state).

    Raises:
      TypeError: if cell_fn is not callable
      ValueError: if cell_fn cannot produce a valid initial state.
    """
    if not callable(cell_fn):
      raise TypeError("cell_fn %s needs to be callable", cell_fn)
    self._cell_fn = cell_fn
    self._cell_name = cell_fn.func.__name__
    init_output, init_state = self._cell_fn(None, None)
    output_shape = init_output.get_shape()
    state_shape = init_state.get_shape()
    self._output_size = output_shape.with_rank(2)[1].value
    self._state_size = state_shape.with_rank(2)[1].value
    if self._output_size is None:
      raise ValueError("Initial output created by %s has invalid shape %s" %
                       (self._cell_name, output_shape))
    if self._state_size is None:
      raise ValueError("Initial state created by %s has invalid shape %s" %
                       (self._cell_name, state_shape))

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

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

  def __call__(self, inputs, state, scope=None):
    scope = scope or self._cell_name
    output, state = self._cell_fn(inputs, state, scope=scope)
    return output, state


def _linear(args,
            output_size,
            bias,
            bias_initializer=None,
            kernel_initializer=None):
  """Linear map: sum_i(args[i] * W[i]), where W[i] is a variable.

  Args:
    args: a 2D Tensor or a list of 2D, batch x n, Tensors.
    output_size: int, second dimension of W[i].
    bias: boolean, whether to add a bias term or not.
    bias_initializer: starting value to initialize the bias
      (default is all zeros).
    kernel_initializer: starting value to initialize the weight.

  Returns:
    A 2D Tensor with shape [batch x output_size] equal to
    sum_i(args[i] * W[i]), where W[i]s are newly created matrices.

  Raises:
    ValueError: if some of the arguments has unspecified or wrong shape.
  """
  if args is None or (nest.is_sequence(args) and not args):
    raise ValueError("`args` must be specified")
  if not nest.is_sequence(args):
    args = [args]

  # Calculate the total size of arguments on dimension 1.
  total_arg_size = 0
  shapes = [a.get_shape() for a in args]
  for shape in shapes:
    if shape.ndims != 2:
      raise ValueError("linear is expecting 2D arguments: %s" % shapes)
    if shape[1].value is None:
      raise ValueError("linear expects shape[1] to be provided for shape %s, "
                       "but saw %s" % (shape, shape[1]))
    else:
      total_arg_size += shape[1].value

  dtype = [a.dtype for a in args][0]

  # Now the computation.
  scope = vs.get_variable_scope()
  with vs.variable_scope(scope) as outer_scope:
    weights = vs.get_variable(
        _WEIGHTS_VARIABLE_NAME, [total_arg_size, output_size],
        dtype=dtype,
        initializer=kernel_initializer)
    if len(args) == 1:
      res = math_ops.matmul(args[0], weights)
    else:
      res = math_ops.matmul(array_ops.concat(args, 1), weights)
    if not bias:
      return res
    with vs.variable_scope(outer_scope) as inner_scope:
      inner_scope.set_partitioner(None)
      if bias_initializer is None:
        bias_initializer = init_ops.constant_initializer(0.0, dtype=dtype)
      biases = vs.get_variable(
          _BIAS_VARIABLE_NAME, [output_size],
          dtype=dtype,
          initializer=bias_initializer)
    return nn_ops.bias_add(res, biases)