Python tensorflow.python.ops.array_ops.gather() Examples

def vector_space_dimension(self, name="vector_space_dimension"):
    """Dimension of vector space on which this acts.  The `k` in `R^k`.

    If this operator represents the batch matrix `A` with
    `A.shape = [N1,...,Nn, k, k]`, the `vector_space_dimension` is `k`.

    Args:
      name:  A name scope to use for ops added by this method.

    Returns:
      `int32` `Tensor`
    """
    # Derived classes get this "for free" once .shape() is implemented.
    with ops.name_scope(self.name):
      with ops.name_scope(name, values=self.inputs):
        return array_ops.gather(self.shape(), self.rank() - 1) 

def _SegmentMinOrMaxGrad(op, grad, is_sorted):
  """Gradient for SegmentMin and (unsorted) SegmentMax. They share similar code."""
  zeros = array_ops.zeros(array_ops.shape(op.inputs[0]),
                          dtype=op.inputs[0].dtype)

  # Get the number of selected (minimum or maximum) elements in each segment.
  gathered_outputs = array_ops.gather(op.outputs[0], op.inputs[1])
  is_selected = math_ops.equal(op.inputs[0], gathered_outputs)
  if is_sorted:
    num_selected = math_ops.segment_sum(math_ops.cast(is_selected, grad.dtype),
                                        op.inputs[1])
  else:
    num_selected = math_ops.unsorted_segment_sum(math_ops.cast(is_selected, grad.dtype),
                                                 op.inputs[1], op.inputs[2])

  # Compute the gradient for each segment. The gradient for the ith segment is
  # divided evenly among the selected elements in that segment.
  weighted_grads = math_ops.div(grad, num_selected)
  gathered_grads = array_ops.gather(weighted_grads, op.inputs[1])

  if is_sorted:
    return array_ops.where(is_selected, gathered_grads, zeros), None
  else:
    return array_ops.where(is_selected, gathered_grads, zeros), None, None 

def _MultiDeviceAddN(tensor_list):
  """Adds tensors from potentially multiple devices."""
  # Basic function structure comes from control_flow_ops.group().
  # Sort tensors according to their devices.
  tensors_on_device = collections.defaultdict(lambda: [])
  for tensor in tensor_list:
    tensors_on_device[tensor.device].append(tensor)

  # For each device, add the tensors on that device first.
  # Then gather the partial sums from multiple devices.
  # TODO(sjhwang): Create hierarchical aggregation tree as pbar's suggestion.
  # E.g., aggregate per GPU, then per task, and so on.
  summands = []

  def DeviceKey(dev):
    return "" if dev is None else dev

  for dev in sorted(six.iterkeys(tensors_on_device), key=DeviceKey):
    tensors = tensors_on_device[dev]
    with ops.colocate_with(tensors[0].op, ignore_existing=True):
      summands.append(math_ops.add_n(tensors))

  return math_ops.add_n(summands) 

def _DynamicStitchGrads(op, grad):
  """Gradients for DynamicStitch."""

  num_values = len(op.inputs) // 2
  indices_grad = [None] * num_values

  def AsInt32(x):
    return (x if op.inputs[0].dtype == dtypes.int32 else
            math_ops.cast(x, dtypes.int32))
  inputs = [AsInt32(op.inputs[i]) for i in xrange(num_values)]
  if isinstance(grad, ops.IndexedSlices):
    output_shape = array_ops.shape(op.outputs[0])
    output_rows = output_shape[0]
    grad = math_ops.unsorted_segment_sum(grad.values, grad.indices, output_rows)
  values_grad = [array_ops.gather(grad, inp) for inp in inputs]
  return indices_grad + values_grad 

def _apply_sparse(self, grad, var):
        lr_t = math_ops.cast(self._lr_t, var.dtype.base_dtype)
        alpha_t = math_ops.cast(self._alpha_t, var.dtype.base_dtype)
        beta_t = math_ops.cast(self._beta_t, var.dtype.base_dtype)

        eps = 1e-7  # cap for moving average

        m = self.get_slot(var, "m")
        m_slice = tf.gather(m, grad.indices)
        m_t = state_ops.scatter_update(m, grad.indices,
                                       tf.maximum(beta_t * m_slice + eps, tf.abs(grad.values)))
        m_t_slice = tf.gather(m_t, grad.indices)

        var_update = state_ops.scatter_sub(var, grad.indices, lr_t * grad.values * tf.exp(
            tf.log(alpha_t) * tf.sign(grad.values) * tf.sign(m_t_slice)))  # Update 'ref' by subtracting 'value
        # Create an op that groups multiple operations.
        # When this op finishes, all ops in input have finished
        return control_flow_ops.group(*[var_update, m_t]) 

def _gini(self, class_counts):
    """Calculate the Gini impurity.

    If c(i) denotes the i-th class count and c = sum_i c(i) then
      score = 1 - sum_i ( c(i) / c )^2

    Args:
      class_counts: A 2-D tensor of per-class counts, usually a slice or
        gather from variables.node_sums.

    Returns:
      A 1-D tensor of the Gini impurities for each row in the input.
    """
    smoothed = 1.0 + array_ops.slice(class_counts, [0, 1], [-1, -1])
    sums = math_ops.reduce_sum(smoothed, 1)
    sum_squares = math_ops.reduce_sum(math_ops.square(smoothed), 1)

    return 1.0 - sum_squares / (sums * sums) 

def _weighted_gini(self, class_counts):
    """Our split score is the Gini impurity times the number of examples.

    If c(i) denotes the i-th class count and c = sum_i c(i) then
      score = c * (1 - sum_i ( c(i) / c )^2 )
            = c - sum_i c(i)^2 / c
    Args:
      class_counts: A 2-D tensor of per-class counts, usually a slice or
        gather from variables.node_sums.

    Returns:
      A 1-D tensor of the Gini impurities for each row in the input.
    """
    smoothed = 1.0 + array_ops.slice(class_counts, [0, 1], [-1, -1])
    sums = math_ops.reduce_sum(smoothed, 1)
    sum_squares = math_ops.reduce_sum(math_ops.square(smoothed), 1)

    return sums - sum_squares / sums 

def average_impurity(self):
    """Constructs a TF graph for evaluating the average leaf impurity of a tree.

    If in regression mode, this is the leaf variance. If in classification mode,
    this is the gini impurity.

    Returns:
      The last op in the graph.
    """
    children = array_ops.squeeze(array_ops.slice(
        self.variables.tree, [0, 0], [-1, 1]), squeeze_dims=[1])
    is_leaf = math_ops.equal(constants.LEAF_NODE, children)
    leaves = math_ops.to_int32(array_ops.squeeze(array_ops.where(is_leaf),
                                                 squeeze_dims=[1]))
    counts = array_ops.gather(self.variables.node_sums, leaves)
    gini = self._weighted_gini(counts)
    # Guard against step 1, when there often are no leaves yet.
    def impurity():
      return gini
    # Since average impurity can be used for loss, when there's no data just
    # return a big number so that loss always decreases.
    def big():
      return array_ops.ones_like(gini, dtype=dtypes.float32) * 10000000.
    return control_flow_ops.cond(math_ops.greater(
        array_ops.shape(leaves)[0], 0), impurity, big) 

def _linear_predictions(self, examples):
    """Returns predictions of the form w*x."""
    with name_scope('sdca/prediction'):
      sparse_variables = self._convert_n_to_tensor(self._variables[
          'sparse_features_weights'])
      result = 0.0
      for sfc, sv in zip(examples['sparse_features'], sparse_variables):
        # TODO(sibyl-Aix6ihai): following does not take care of missing features.
        result += math_ops.segment_sum(
            math_ops.multiply(
                array_ops.gather(sv, sfc.feature_indices), sfc.feature_values),
            sfc.example_indices)
      dense_features = self._convert_n_to_tensor(examples['dense_features'])
      dense_variables = self._convert_n_to_tensor(self._variables[
          'dense_features_weights'])

      for i in range(len(dense_variables)):
        result += math_ops.matmul(dense_features[i],
                                  array_ops.expand_dims(dense_variables[i], -1))

    # Reshaping to allow shape inference at graph construction time.
    return array_ops.reshape(result, [-1]) 

def _check_shape(self, shape):
    """Check that the init arg `shape` defines a valid operator."""
    shape = ops.convert_to_tensor(shape, name="shape")
    if not self._verify_pd:
      return shape

    # Further checks are equivalent to verification that this is positive
    # definite.  Why?  Because the further checks simply check that this is a
    # square matrix, and combining the fact that this is square (and thus maps
    # a vector space R^k onto itself), with the behavior of .matmul(), this must
    # be the identity operator.
    rank = array_ops.size(shape)
    assert_matrix = check_ops.assert_less_equal(2, rank)
    with ops.control_dependencies([assert_matrix]):
      last_dim = array_ops.gather(shape, rank - 1)
      second_to_last_dim = array_ops.gather(shape, rank - 2)
      assert_square = check_ops.assert_equal(last_dim, second_to_last_dim)
      return control_flow_ops.with_dependencies([assert_matrix, assert_square],
                                                shape) 

def vector_space_dimension(self, name="vector_space_dimension"):
    """Dimension of vector space on which this acts.  The `k` in `R^k`.

    If this operator represents the batch matrix `A` with
    `A.shape = [N1,...,Nn, k, k]`, the `vector_space_dimension` is `k`.

    Args:
      name:  A name scope to use for ops added by this method.

    Returns:
      `int32` `Tensor`
    """
    # Derived classes get this "for free" once .shape() is implemented.
    with ops.name_scope(self.name):
      with ops.name_scope(name, values=self.inputs):
        return array_ops.gather(self.shape(), self.rank() - 1) 

def _get_identity_operator(self, v):
    """Get an `OperatorPDIdentity` to play the role of `D` in `VDV^T`."""
    with ops.name_scope("get_identity_operator", values=[v]):
      if v.get_shape().is_fully_defined():
        v_shape = v.get_shape().as_list()
        v_batch_shape = v_shape[:-2]
        r = v_shape[-1]
        id_shape = v_batch_shape + [r, r]
      else:
        v_shape = array_ops.shape(v)
        v_rank = array_ops.rank(v)
        v_batch_shape = array_ops.strided_slice(v_shape, [0], [v_rank - 2])
        r = array_ops.gather(v_shape, v_rank - 1)  # Last dim of v
        id_shape = array_ops.concat((v_batch_shape, [r, r]), 0)
      return operator_pd_identity.OperatorPDIdentity(
          id_shape, v.dtype, verify_pd=self._verify_pd) 

def _apply_sparse(self, grad, var):
        lr_t = math_ops.cast(self._lr_t, var.dtype.base_dtype)
        beta_t = math_ops.cast(self._beta_t, var.dtype.base_dtype)
        alpha_t = math_ops.cast(self._alpha_t, var.dtype.base_dtype)

        eps = 1e-7  # cap for moving average

        m = self.get_slot(var, "m")
        m_slice = tf.gather(m, grad.indices)
        m_t = state_ops.scatter_update(m, grad.indices,
                                       tf.maximum(beta_t * m_slice + eps, tf.abs(grad.values)))
        m_t_slice = tf.gather(m_t, grad.indices)

        var_update = state_ops.scatter_sub(var, grad.indices,
                                           lr_t * grad.values * (
                                                   1.0 + alpha_t * tf.sign(grad.values) * tf.sign(m_t_slice)))

        # Create an op that groups multiple operations
        # When this op finishes, all ops in input have finished
        return control_flow_ops.group(*[var_update, m_t]) 

def _linear_predictions(self, examples):
    """Returns predictions of the form w*x."""
    with name_scope('sdca/prediction'):
      sparse_variables = self._convert_n_to_tensor(self._variables[
          'sparse_features_weights'])
      result = 0.0
      for sfc, sv in zip(examples['sparse_features'], sparse_variables):
        # TODO(sibyl-Aix6ihai): following does not take care of missing features.
        result += math_ops.segment_sum(
            math_ops.multiply(
                array_ops.gather(sv, sfc.feature_indices), sfc.feature_values),
            sfc.example_indices)
      dense_features = self._convert_n_to_tensor(examples['dense_features'])
      dense_variables = self._convert_n_to_tensor(self._variables[
          'dense_features_weights'])

      for i in range(len(dense_variables)):
        result += math_ops.matmul(dense_features[i],
                                  array_ops.expand_dims(dense_variables[i], -1))

    # Reshaping to allow shape inference at graph construction time.
    return array_ops.reshape(result, [-1]) 

def average_impurity(self):
    """Constructs a TF graph for evaluating the average leaf impurity of a tree.

    If in regression mode, this is the leaf variance. If in classification mode,
    this is the gini impurity.

    Returns:
      The last op in the graph.
    """
    children = array_ops.squeeze(array_ops.slice(
        self.variables.tree, [0, 0], [-1, 1]), squeeze_dims=[1])
    is_leaf = math_ops.equal(constants.LEAF_NODE, children)
    leaves = math_ops.to_int32(array_ops.squeeze(array_ops.where(is_leaf),
                                                 squeeze_dims=[1]))
    counts = array_ops.gather(self.variables.node_sums, leaves)
    gini = self._weighted_gini(counts)
    # Guard against step 1, when there often are no leaves yet.
    def impurity():
      return gini
    # Since average impurity can be used for loss, when there's no data just
    # return a big number so that loss always decreases.
    def big():
      return array_ops.ones_like(gini, dtype=dtypes.float32) * 10000000.
    return control_flow_ops.cond(math_ops.greater(
        array_ops.shape(leaves)[0], 0), impurity, big) 

def _weighted_gini(self, class_counts):
    """Our split score is the Gini impurity times the number of examples.

    If c(i) denotes the i-th class count and c = sum_i c(i) then
      score = c * (1 - sum_i ( c(i) / c )^2 )
            = c - sum_i c(i)^2 / c
    Args:
      class_counts: A 2-D tensor of per-class counts, usually a slice or
        gather from variables.node_sums.

    Returns:
      A 1-D tensor of the Gini impurities for each row in the input.
    """
    smoothed = 1.0 + array_ops.slice(class_counts, [0, 1], [-1, -1])
    sums = math_ops.reduce_sum(smoothed, 1)
    sum_squares = math_ops.reduce_sum(math_ops.square(smoothed), 1)

    return sums - sum_squares / sums 

def _gini(self, class_counts):
    """Calculate the Gini impurity.

    If c(i) denotes the i-th class count and c = sum_i c(i) then
      score = 1 - sum_i ( c(i) / c )^2

    Args:
      class_counts: A 2-D tensor of per-class counts, usually a slice or
        gather from variables.node_sums.

    Returns:
      A 1-D tensor of the Gini impurities for each row in the input.
    """
    smoothed = 1.0 + array_ops.slice(class_counts, [0, 1], [-1, -1])
    sums = math_ops.reduce_sum(smoothed, 1)
    sum_squares = math_ops.reduce_sum(math_ops.square(smoothed), 1)

    return 1.0 - sum_squares / (sums * sums) 

def _SegmentMinOrMaxGrad(op, grad):
  """Gradient for SegmentMin and SegmentMax. Both share the same code."""
  zeros = array_ops.zeros(
      array_ops.shape(op.inputs[0]), dtype=op.inputs[0].dtype)

  # Get the number of selected (minimum or maximum) elements in each segment.
  gathered_outputs = array_ops.gather(op.outputs[0], op.inputs[1])
  is_selected = math_ops.equal(op.inputs[0], gathered_outputs)
  num_selected = math_ops.segment_sum(
      math_ops.cast(is_selected, grad.dtype), op.inputs[1])

  # Compute the gradient for each segment. The gradient for the ith segment is
  # divided evenly among the selected elements in that segment.
  weighted_grads = math_ops.div(grad, num_selected)
  gathered_grads = array_ops.gather(weighted_grads, op.inputs[1])

  return array_ops.where(is_selected, gathered_grads, zeros), None 

def _DynamicStitchGrads(op, grad):
  """Gradients for DynamicStitch."""

  num_values = len(op.inputs) // 2
  indices_grad = [None] * num_values

  def AsInt32(x):
    return (x if op.inputs[0].dtype == dtypes.int32 else
            math_ops.cast(x, dtypes.int32))
  inputs = [AsInt32(op.inputs[i]) for i in xrange(num_values)]
  if isinstance(grad, ops.IndexedSlices):
    output_shape = array_ops.shape(op.outputs[0])
    output_rows = output_shape[0]
    grad = math_ops.unsorted_segment_sum(grad.values, grad.indices, output_rows)
  values_grad = [array_ops.gather(grad, inp) for inp in inputs]
  return indices_grad + values_grad 

def _MultiDeviceAddN(tensor_list):
  """Adds tensors from potentially multiple devices."""
  # Basic function structure comes from control_flow_ops.group().
  # Sort tensors according to their devices.
  tensors_on_device = collections.defaultdict(lambda: [])
  for tensor in tensor_list:
    tensors_on_device[tensor.device].append(tensor)

  # For each device, add the tensors on that device first.
  # Then gather the partial sums from multiple devices.
  # TODO(sjhwang): Create hierarchical aggregation tree as pbar's suggestion.
  # E.g., aggregate per GPU, then per task, and so on.
  summands = []

  def DeviceKey(dev):
    return "" if dev is None else dev

  for dev in sorted(six.iterkeys(tensors_on_device), key=DeviceKey):
    tensors = tensors_on_device[dev]
    with ops.colocate_with(tensors[0].op, ignore_existing=True):
      summands.append(math_ops.add_n(tensors))

  return math_ops.add_n(summands) 

def _clip_sparse(self, grad, var):
    assert isinstance(grad, ops.IndexedSlices)
    clip_dims = self._vars_to_clip_dims[var]
    if 0 in clip_dims:
      logging.warning("Clipping norm across dims %s for %s is inefficient "
                      "when including sparse dimension 0.", clip_dims,
                      var.op.name)
      return self._clip_dense(var)

    with ops.colocate_with(var):
      var_subset = array_ops.gather(var, grad.indices)
    with self._maybe_colocate_with(var):
      normalized_var_subset = clip_ops.clip_by_norm(
          var_subset, self._max_norm, clip_dims)
      delta = ops.IndexedSlices(
          var_subset - normalized_var_subset, grad.indices, grad.dense_shape)
    with ops.colocate_with(var):
      return var.scatter_sub(delta, use_locking=self._use_locking) 

def _check_chol(self, chol):
    """Verify that `chol` is proper."""
    chol = ops.convert_to_tensor(chol, name="chol")
    if not self.verify_pd:
      return chol

    shape = array_ops.shape(chol)
    rank = array_ops.rank(chol)

    is_matrix = check_ops.assert_rank_at_least(chol, 2)
    is_square = check_ops.assert_equal(
        array_ops.gather(shape, rank - 2), array_ops.gather(shape, rank - 1))

    deps = [is_matrix, is_square]
    diag = array_ops.matrix_diag_part(chol)
    deps.append(check_ops.assert_positive(diag))

    return control_flow_ops.with_dependencies(deps, chol) 

def sparse_retain(sp_input, to_retain):
  """Retains specified non-empty values within a `SparseTensor`.

  For example, if `sp_input` has shape `[4, 5]` and 4 non-empty string values:

      [0, 1]: a
      [0, 3]: b
      [2, 0]: c
      [3, 1]: d

  and `to_retain = [True, False, False, True]`, then the output will
  be a `SparseTensor` of shape `[4, 5]` with 2 non-empty values:

      [0, 1]: a
      [3, 1]: d

  Args:
    sp_input: The input `SparseTensor` with `N` non-empty elements.
    to_retain: A bool vector of length `N` with `M` true values.

  Returns:
    A `SparseTensor` with the same shape as the input and `M` non-empty
    elements corresponding to the true positions in `to_retain`.

  Raises:
    TypeError: If `sp_input` is not a `SparseTensor`.
  """
  sp_input = _convert_to_sparse_tensor(sp_input)

  to_retain = ops.convert_to_tensor(to_retain)

  # Shape checking, if shape is known at graph construction time
  retain_shape = to_retain.get_shape()
  retain_shape.assert_has_rank(1)
  sp_input.values.get_shape()[0].merge_with(retain_shape[0])

  where_true = array_ops.reshape(array_ops.where(to_retain), [-1])
  new_indices = array_ops.gather(sp_input.indices, where_true)
  new_values = array_ops.gather(sp_input.values, where_true)
  return sparse_tensor.SparseTensor(new_indices, new_values,
                                    array_ops.identity(sp_input.dense_shape)) 

def _UnsortedSegmentSumGrad(op, grad):
  """Gradient for SegmentSum."""
  return array_ops.gather(grad, op.inputs[1]), None, None 

def _do_gather(params, ids, name=None):
  """Deals with doing gather differently for resource variables."""
  if isinstance(params, resource_variable_ops.ResourceVariable):
    return params.sparse_read(ids, name=name)
  return array_ops.gather(params, ids, name=name) 

def _SegmentMeanGrad(op, grad):
  """Gradient for SegmentMean."""
  input_rank = array_ops.rank(op.inputs[0])
  ones_shape = array_ops.concat([
      array_ops.shape(op.inputs[1]),
      array_ops.fill(array_ops.expand_dims(input_rank - 1, 0), 1)
  ], 0)
  ones = array_ops.fill(ones_shape,
                        constant_op.constant(1, dtype=grad.dtype))
  scaled_grad = math_ops.div(grad, math_ops.segment_sum(ones, op.inputs[1]))
  return array_ops.gather(scaled_grad, op.inputs[1]), None 

def _SegmentSumGrad(op, grad):
  """Gradient for SegmentSum."""
  return array_ops.gather(grad, op.inputs[1]), None 

def _ProdGrad(op, grad):
  """Gradient for Prod."""
  # The gradient can be expressed by dividing the product by each entry of the
  # input tensor, but this approach can't deal with zeros in the input.
  # Here, we avoid this problem by composing the output as a product of two
  # cumprod operations.

  input_shape = array_ops.shape(op.inputs[0])
  # Reshape reduction indices for the case where the parameter is a scalar
  reduction_indices = array_ops.reshape(op.inputs[1], [-1])

  # Expand grad to full input shape
  output_shape_kept_dims = math_ops.reduced_shape(input_shape, op.inputs[1])
  tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
  grad = array_ops.reshape(grad, output_shape_kept_dims)
  grad = array_ops.tile(grad, tile_scaling)

  # Pack all reduced dimensions into a single one, so we can perform the
  # cumprod ops. If the reduction dims list is empty, it defaults to float32,
  # so we need to cast here.  We put all the shape-related ops on CPU to avoid
  # copying back and forth, and since listdiff is CPU only.
  with ops.device("/cpu:0"):
    reduced = math_ops.cast(reduction_indices, dtypes.int32)
    idx = math_ops.range(0, array_ops.rank(op.inputs[0]))
    other, _ = array_ops.setdiff1d(idx, reduced)
    perm = array_ops.concat([reduced, other], 0)
    reduced_num = math_ops.reduce_prod(array_ops.gather(input_shape, reduced))
    other_num = math_ops.reduce_prod(array_ops.gather(input_shape, other))
  permuted = array_ops.transpose(op.inputs[0], perm)
  permuted_shape = array_ops.shape(permuted)
  reshaped = array_ops.reshape(permuted, (reduced_num, other_num))

  # Calculate product, leaving out the current entry
  left = math_ops.cumprod(reshaped, axis=0, exclusive=True)
  right = math_ops.cumprod(reshaped, axis=0, exclusive=True, reverse=True)
  y = array_ops.reshape(left * right, permuted_shape)

  # Invert the transpose and reshape operations.
  # Make sure to set the statically known shape information through a reshape.
  out = grad * array_ops.transpose(y, array_ops.invert_permutation(perm))
  return array_ops.reshape(out, input_shape), None 

def _HandleNestedIndexedSlices(grad):
  assert isinstance(grad, ops.IndexedSlices)
  if isinstance(grad.values, ops.Tensor):
    return grad
  else:
    assert isinstance(grad.values, ops.IndexedSlices)
    g = _HandleNestedIndexedSlices(grad.values)
    return ops.IndexedSlices(g.values,
                             array_ops.gather(grad.indices, g.indices),
                             g.dense_shape) 

def _apply_sparse(self, grad, var):
    beta1_power = math_ops.cast(self._beta1_power, var.dtype.base_dtype)
    beta2_power = math_ops.cast(self._beta2_power, var.dtype.base_dtype)
    lr_t = math_ops.cast(self._lr_t, var.dtype.base_dtype)
    beta1_t = math_ops.cast(self._beta1_t, var.dtype.base_dtype)
    beta2_t = math_ops.cast(self._beta2_t, var.dtype.base_dtype)
    epsilon_t = math_ops.cast(self._epsilon_t, var.dtype.base_dtype)
    lr = (lr_t * math_ops.sqrt(1 - beta2_power) / (1 - beta1_power))

    # m := beta1 * m + (1 - beta1) * g_t
    m = self.get_slot(var, "m")
    m_t = state_ops.scatter_update(m, grad.indices,
                                   beta1_t * array_ops.gather(m, grad.indices) +
                                   (1 - beta1_t) * grad.values,
                                   use_locking=self._use_locking)

    # v := beta2 * v + (1 - beta2) * (g_t * g_t)
    v = self.get_slot(var, "v")
    v_t = state_ops.scatter_update(v, grad.indices,
                                   beta2_t * array_ops.gather(v, grad.indices) +
                                   (1 - beta2_t) * math_ops.square(grad.values),
                                   use_locking=self._use_locking)

    # variable -= learning_rate * m_t / (epsilon_t + sqrt(v_t))
    m_t_slice = array_ops.gather(m_t, grad.indices)
    v_t_slice = array_ops.gather(v_t, grad.indices)
    denominator_slice = math_ops.sqrt(v_t_slice) + epsilon_t
    var_update = state_ops.scatter_sub(var, grad.indices,
                                       lr * m_t_slice / denominator_slice,
                                       use_locking=self._use_locking)
    return control_flow_ops.group(var_update, m_t, v_t)