def loss(self, y_true, y_pred):
        """ categorical crossentropy loss """

        if self.crop_indices is not None:
            y_true = utils.batch_gather(y_true, self.crop_indices)
            y_pred = utils.batch_gather(y_pred, self.crop_indices)

        if self.use_float16:
            y_true = K.cast(y_true, 'float16')
            y_pred = K.cast(y_pred, 'float16')

        # scale and clip probabilities
        # this should not be necessary for softmax output.
        y_pred /= K.sum(y_pred, axis=-1, keepdims=True)
        y_pred = K.clip(y_pred, K.epsilon(), 1)

        # compute log probability
        log_post = K.log(y_pred)  # likelihood

        # loss
        loss = - y_true * log_post

        # weighted loss
        if self.weights is not None:
            loss *= self.weights

        if self.vox_weights is not None:
            loss *= self.vox_weights

        # take the total loss
        # loss = K.batch_flatten(loss)
        mloss = K.mean(K.sum(K.cast(loss, 'float32'), -1))
        tf.verify_tensor_all_finite(mloss, 'Loss not finite')
        return mloss

def kl_multivariate_normal(loc_one, scale_one, loc_two=0.0, scale_two=1.0):
    """Calculate the KL of multivariate normal distributions with
    diagonal covariances.

    Parameters
    ----------
    loc_one : tf.Tensor
        A 0-D tensor, 1-D tensor of length n, or 2-D tensor of shape M
        x n where each row represents the mean of a n-dimensional
        Gaussian.
    scale_one : tf.Tensor
        A tensor of same shape as ``loc_one``, representing the
        standard deviation.
    loc_two : tf.Tensor, optional
        A tensor of same shape as ``loc_one``, representing the
        mean of another Gaussian.
    scale_two : tf.Tensor, optional
        A tensor of same shape as ``loc_one``, representing the
        standard deviation of another Gaussian.

    Returns
    -------
    tf.Tensor
        For 0-D or 1-D tensor inputs, outputs the 0-D tensor
        ``KL( N(z; loc_one, scale_one) || N(z; loc_two, scale_two) )``
        For 2-D tensor inputs, outputs the 1-D tensor
        ``[KL( N(z; loc_one[m,:], scale_one[m,:]) || N(z; loc_two[m,:], scale_two[m,:]) )]_{m=1}^M``

    Raises
    ------
    InvalidArgumentError
        If the location variables have Inf or NaN values, or if the scale
        variables are not positive.
    """
    dependencies = [tf.verify_tensor_all_finite(loc_one, msg=''),
                    tf.verify_tensor_all_finite(loc_two, msg=''),
                    tf.assert_positive(scale_one),
                    tf.assert_positive(scale_two)]
    loc_one = control_flow_ops.with_dependencies(dependencies, loc_one)
    scale_one = control_flow_ops.with_dependencies(dependencies, scale_one)
    loc_one = tf.cast(loc_one, tf.float32)
    scale_one = tf.cast(scale_one, tf.float32)

    if loc_two == 0.0 and scale_two == 1.0:
        # With default arguments, we can avoid some intermediate computation.
        out = tf.square(scale_one) + tf.square(loc_one) - \
              1.0 - 2.0 * tf.log(scale_one)
    else:
        loc_two = control_flow_ops.with_dependencies(dependencies, loc_two)
        scale_two = control_flow_ops.with_dependencies(dependencies, scale_two)
        loc_two = tf.cast(loc_two, tf.float32)
        scale_two = tf.cast(scale_two, tf.float32)
        out = tf.square(scale_one/scale_two) + \
              tf.square((loc_two - loc_one)/scale_two) - \
              1.0 + 2.0 * tf.log(scale_two) - 2.0 * tf.log(scale_one)

    if len(out.get_shape()) <= 1: # scalar or vector
        return 0.5 * tf.reduce_sum(out)
    else: # matrix
        return 0.5 * tf.reduce_sum(out, 1)

def create_generative(parameters):
    print('Creating the neural network model.')
    
    tf.reset_default_graph()
    # tf Graph input
    x = tf.placeholder(tf.float32, shape=(1, parameters['n_input']), name='input')
    x = tf.verify_tensor_all_finite(x, "X not finite!")
    y = tf.placeholder(tf.float32, shape=(1, parameters['n_output']), name='expected_output')
    y = tf.verify_tensor_all_finite(y, "Y not finite!")
    x = tf.Print(x, [x], "X: ")
    y = tf.Print(y, [y], "Y: ")
    lstm_state_size = np.sum(parameters['lstm_layers']) * 2
    # Note: Batch size is the first dimension in istate.
    istate = tf.placeholder(tf.float32, shape=(None, lstm_state_size), name='internal_state')
    lr = tf.placeholder(tf.float32, name='learning_rate')

    # The target to track itself and its peers, each with x, y ## and velocity x and y.
    input_size = (parameters['n_peers'] + 1) * 2
    inputToRnn = parameters['input_layer']
    if (parameters['input_layer'] == None):
        inputToRnn = parameters['n_input']

    cells = [rnn_cell.LSTMCell(l, parameters['lstm_layers'][i-1] if (i > 0) else inputToRnn,
                               num_proj=parameters['lstm_layers'][i],
                               cell_clip=parameters['lstm_clip'],
                               use_peepholes=True) for i,l in enumerate(parameters['lstm_layers'])] 
    # TODO: GRUCell support here.
    # cells = [rnn_cell.GRUCell(l, parameters['lstm_layers'][i-1] if (i > 0) else inputToRnn) for i,l in enumerate(parameters['lstm_layers'])]
    model = {
        'input_weights': tf.Variable(tf.random_normal(
            [input_size, parameters['input_layer']]), name='input_weights'),
        'input_bias': tf.Variable(tf.random_normal([parameters['input_layer']]), name='input_bias'),
        'output_weights': tf.Variable(tf.random_normal([parameters['lstm_layers'][-1],
                                                        # 6 = 2 sigma, 2 mean, weight, rho
                                                        parameters['n_mixtures'] * 6]),
                                      name='output_weights'),
        # We need to put at least the standard deviation output biases to about 5 to prevent zeros and infinities.
        # , mean = 5.0, stddev = 3.0
        'output_bias': tf.Variable(tf.random_normal([parameters['n_mixtures'] * 6]),
                                   name='output_bias'),
        'rnn_cell': rnn_cell.MultiRNNCell(cells),
        'lr': lr,
        'x': x,
        'y': y,
        'keep_prob': tf.placeholder(tf.float32),
        'istate': istate
    }

    # The next variables need to be remapped, because we don't have RNN context anymore:
    # RNN/MultiRNNCell/Cell0/LSTMCell/ -> MultiRNNCell/Cell0/LSTMCell/
    # B, W_F_diag, W_O_diag, W_I_diag, W_0
    with tf.variable_scope("RNN"):
        pred = RNN_generative(parameters, x, model, istate)
    
    model['pred'] = pred[0]
    model['last_state'] = pred[1]

    return model

def hessian(y, xs):
    """Calculate Hessian of y with respect to each x in xs.

    Parameters
    ----------
    y : tf.Tensor
        Tensor to calculate Hessian of.
    xs : list of tf.Variable
        List of TensorFlow variables to calculate with respect to.
        The variables can have different shapes.

    Returns
    -------
    tf.Tensor
        A 2-D tensor where each row is
        .. math:: \partial_{xs} ( [ \partial_{xs} y ]_j ).

    Raises
    ------
    InvalidArgumentError
        If the inputs have Inf or NaN values.
    """
    dependencies = [tf.verify_tensor_all_finite(y, msg='')]
    dependencies.extend([tf.verify_tensor_all_finite(x, msg='') for x in xs])

    with tf.control_dependencies(dependencies):
        # Calculate flattened vector grad_{xs} y.
        grads = tf.gradients(y, xs)
        grads = [tf.reshape(grad, [-1]) for grad in grads]
        grads = tf.concat(0, grads)
        # Loop over each element in the vector.
        mat = []
        d = grads.get_shape()[0]
        if not isinstance(d, int):
            d = grads.eval().shape[0]

        for j in range(d):
            # Calculate grad_{xs} ( [ grad_{xs} y ]_j ).
            gradjgrads = tf.gradients(grads[j], xs)
            # Flatten into vector.
            hi = []
            for l in range(len(xs)):
                hij = gradjgrads[l]
                # return 0 if gradient doesn't exist; TensorFlow returns None
                if hij is None:
                    hij = tf.zeros(xs[l].get_shape(), dtype=tf.float32)

                hij = tf.reshape(hij, [-1])
                hi.append(hij)

            hi = tf.concat(0, hi)
            mat.append(hi)

        # Form matrix where each row is grad_{xs} ( [ grad_{xs} y ]_j ).
        return tf.pack(mat)

 def _validate(self):
   vops = [tf.assert_positive(self._scale),
           tf.assert_positive(self._high - self._low),
           tf.verify_tensor_all_finite(self._high,
                                       "Upper bound not finite"),
           tf.verify_tensor_all_finite(self._low,
                                       "Lower bound not finite"),
           tf.verify_tensor_all_finite(self._loc,
                                       "Loc not finite"),
           tf.verify_tensor_all_finite(self._scale,
                                       "Scale not finite"),
          ]
   return tf.group(*vops, name="ValidationOps")

def kl_multivariate_normal(loc_one, scale_one, loc_two=0.0, scale_two=1.0):
    """Calculate the KL of multivariate normal distributions with
    diagonal covariances.

    Parameters
    ----------
    loc_one : tf.Tensor
        n-dimensional vector, or M x n-dimensional matrix where each
        row represents the mean of a n-dimensional Gaussian
    scale_one : tf.Tensor
        n-dimensional vector, or M x n-dimensional matrix where each
        row represents the standard deviation of a n-dimensional Gaussian
    loc_two : tf.Tensor, optional
        n-dimensional vector, or M x n-dimensional matrix where each
        row represents the mean of a n-dimensional Gaussian
    scale_two : tf.Tensor, optional
        n-dimensional vector, or M x n-dimensional matrix where each
        row represents the standard deviation of a n-dimensional Gaussian

    Returns
    -------
    tf.Tensor
        for scalar or vector inputs, outputs the scalar
        ``KL( N(z; loc_one, scale_one) || N(z; loc_two, scale_two) )``
        for matrix inputs, outputs the vector
        ``[KL( N(z; loc_one[m,:], scale_one[m,:]) || N(z; loc_two[m,:], scale_two[m,:]) )]_{m=1}^M``

    Raises
    ------
    InvalidArgumentError
        If the location variables have Inf or NaN values, or if the scale
        variables are not positive.
    """
    dependencies = [tf.verify_tensor_all_finite(loc_one, msg=''),
                  tf.verify_tensor_all_finite(loc_two, msg=''),
                  tf.assert_positive(scale_one),
                  tf.assert_positive(scale_two)]
    loc_one = control_flow_ops.with_dependencies(dependencies, loc_one)
    loc_two = control_flow_ops.with_dependencies(dependencies, loc_two)
    scale_one = control_flow_ops.with_dependencies(dependencies, scale_one)
    scale_two = control_flow_ops.with_dependencies(dependencies, scale_two)

    if loc_two == 0.0 and scale_two == 1.0:
        return 0.5 * tf.reduce_sum(
            tf.square(scale_one) + tf.square(loc_one) - \
            1.0 - 2.0 * tf.log(scale_one))
    else:
        return 0.5 * tf.reduce_sum(
            tf.square(scale_one/scale_two) + \
            tf.square((loc_two - loc_one)/scale_two) - \
            1.0 + 2.0 * tf.log(scale_two) - 2.0 * tf.log(scale_one), 1)

    def mean_dice(self, y_true, y_pred):
        """ weighted mean dice across all patches and labels """

        # compute dice, which will now be [batch_size, nb_labels]
        dice_metric = self.dice(y_true, y_pred)

        # weigh the entries in the dice matrix:
        if self.weights is not None:
            dice_metric *= self.weights
        if self.vox_weights is not None:
            dice_metric *= self.vox_weights

        # return one minus mean dice as loss
        mean_dice_metric = K.mean(dice_metric)
        tf.verify_tensor_all_finite(mean_dice_metric, 'metric not finite')
        return mean_dice_metric

 def testVerifyTensorAllFiniteSucceeds(self):
     x_shape = [5, 4]
     x = np.random.random_sample(x_shape).astype(np.float32)
     with self.test_session():
         t = tf.constant(x, shape=x_shape, dtype=tf.float32)
         t_verified = tf.verify_tensor_all_finite(t, "Input is not a number.")
         self.assertAllClose(x, t_verified.eval())

def log_sum_exp(x):
    """Compute the ``log_sum_exp`` of the elements in x.

    Parameters
    ----------
    x : tf.Tensor
        vector or matrix with second dimension 1
        shape=TensorShape([Dimension(N)])
        shape=TensorShape([Dimension(N), Dimension(1)])

    Returns
    -------
    tf.Tensor
        scalar if vector input, vector if matrix tensor input
    
    Raises
    ------
    InvalidArgumentError
        If the input has Inf or NaN values.
    """
    dependencies = [tf.verify_tensor_all_finite(x, msg='')]
    x = control_flow_ops.with_dependencies(dependencies, x);

    x_max = tf.reduce_max(x)
    return tf.add(x_max, tf.log(tf.reduce_sum(tf.exp(tf.sub(x, x_max)))))

    def __init__(self, rnn_states, type_embedder, name='DelexicalizedDynamicPredicateEmbedder'):
        """Construct DelexicalizedDynamicPredicateEmbedder.

        Args:
            rnn_states (SequenceBatch): of shape (num_contexts, seq_length, rnn_state_dim)
            type_embedder (TokenEmbedder)
            name (str)
        """
        self._type_embedder = type_embedder

        with tf.name_scope(name):
            # column indices of rnn_states (indexes time)
            self._col_indices = FeedSequenceBatch()  # (num_predicates, max_predicate_mentions)

            # row indices of rnn_states (indexes utterance)
            self._row_indices = tf.placeholder(dtype=tf.int32, shape=[None])  # (num_predicates,)
            row_indices_expanded = expand_dims_for_broadcast(self._row_indices, self._col_indices.values)

            # (num_predicates, max_predicate_mentions, rnn_state_dim)
            rnn_states_selected = SequenceBatch(
                gather_2d(rnn_states.values, row_indices_expanded, self._col_indices.values),
                self._col_indices.mask)

            # (num_predicates, rnn_state_dim)
            rnn_embeds = reduce_mean(rnn_states_selected, allow_empty=True)
            rnn_embeds = tf.verify_tensor_all_finite(rnn_embeds, "RNN-state-based embeddings")

            self._type_seq_embedder = MeanSequenceEmbedder(type_embedder.embeds, name='TypeEmbedder')
            self._embeds = tf.concat(1, [rnn_embeds, self._type_seq_embedder.embeds])

def log_sum_exp(input_tensor, reduction_indices=None, keep_dims=False):
    """Compute the ``log_sum_exp`` of elements in a tensor, taking
    the sum across axes given by ``reduction_indices``.

    Parameters
    ----------
    input_tensor : tf.Tensor
        The tensor to reduce. Should have numeric type.
    reduction_indices : int or list of int, optional
        The dimensions to reduce. If `None` (the default), reduces all
        dimensions.
    keep_dims : bool, optional
        If true, retains reduced dimensions with length 1.

    Returns
    -------
    tf.Tensor
        The reduced tensor.

    Raises
    ------
    InvalidArgumentError
        If the input has Inf or NaN values.
    """
    dependencies = [tf.verify_tensor_all_finite(input_tensor, msg='')]
    input_tensor = control_flow_ops.with_dependencies(dependencies, input_tensor);
    input_tensor = tf.cast(input_tensor, dtype=tf.float32)

    x_max = tf.reduce_max(input_tensor, reduction_indices, keep_dims=True)
    return tf.squeeze(x_max) + tf.log(tf.reduce_sum(
        tf.exp(input_tensor - x_max), reduction_indices, keep_dims))

def cumprod(xs):
    """Cumulative product of a tensor along its outer dimension.

    https://github.com/tensorflow/tensorflow/issues/813

    Parameters
    ----------
    xs : tf.Tensor
        A 1-D or higher tensor.

    Returns
    -------
    tf.Tensor
        A tensor with `cumprod` applied along its outer dimension.

    Raises
    ------
    InvalidArgumentError
        If the input has Inf or NaN values.
    """
    dependencies = [tf.verify_tensor_all_finite(xs, msg='')]
    xs = control_flow_ops.with_dependencies(dependencies, xs)
    xs = tf.cast(xs, dtype=tf.float32)

    values = tf.unpack(xs)
    out = []
    prev = tf.ones_like(values[0])
    for val in values:
        s = prev * val
        out.append(s)
        prev = s

    result = tf.pack(out)
    return result

 def init_target(self):
     with tf.name_scope('target') as scope:
         self.target = self.reduced_loss + self.reg * self.regularization
         self.checked_target = tf.verify_tensor_all_finite(
             self.target,
             msg='NaN or Inf in target value', 
             name='target')
         tf.summary.scalar('target', self.checked_target)

def multivariate_rbf(x, y=0.0, sigma=1.0, l=1.0):
    """Squared-exponential kernel

    .. math:: k(x, y) = \sigma^2 \exp{ -1/(2l^2) \sum_i (x_i - y_i)^2 }

    Parameters
    ----------
    x : tf.Tensor
        A n-D tensor.
    y : tf.Tensor, optional
        A tensor of same shape as ``x``.
    sigma : tf.Tensor, optional
        A 0-D tensor, representing the standard deviation of radial
        basis function.
    l : tf.Tensor, optional
        A 0-D tensor, representing the lengthscale of radial basis
        function.

    Returns
    -------
    tf.Tensor
        A tensor of one less dimension than the input.

    Raises
    ------
    InvalidArgumentError
        If the mean variables have Inf or NaN values, or if the scale
        and length variables are not positive.
    """
    dependencies = [tf.verify_tensor_all_finite(x, msg=''),
                    tf.verify_tensor_all_finite(y, msg=''),
                    tf.assert_positive(sigma),
                    tf.assert_positive(l)]
    x = control_flow_ops.with_dependencies(dependencies, x)
    y = control_flow_ops.with_dependencies(dependencies, y)
    sigma = control_flow_ops.with_dependencies(dependencies, sigma)
    l = control_flow_ops.with_dependencies(dependencies, l)
    x = tf.cast(x, dtype=tf.float32)
    y = tf.cast(y, dtype=tf.float32)
    sigma = tf.cast(sigma, dtype=tf.float32)
    l = tf.cast(l, dtype=tf.float32)

    return tf.pow(sigma, 2.0) * \
           tf.exp(-1.0/(2.0*tf.pow(l, 2.0)) * \
           tf.reduce_sum(tf.pow(x - y , 2.0)))

def l1_normalize(x, dim, name=None):
  """l1 normalizes x.

  Args:
    x: The tensor to normalize.
    dim: The dimension to normalize along.
    name: Optional name for this op.
  Returns:
    x normalized along dim.
  """
  with tf.op_scope([x], name, 'l1_normalize') as scope:
    x = tf.convert_to_tensor(x, name='x')
    x = tf.verify_tensor_all_finite(x, 'Error at input %s' % scope)
    x_norm = tf.reduce_sum(tf.abs(x), [dim], keep_dims=True)
    return tf.verify_tensor_all_finite(tf.div(x,
                                              x_norm,
                                              name=scope),
                                       'Error at %s' % scope)

def l2_normalize(x, dim, name=None):
  """l2 normalizes x and caps the gradient of the Square Root.

  Args:
    x: The tensor to normalize.
    dim: The dimension to normalize along.
    name: Optional name for this op.
  Returns:
    x normalized along dim.
  """
  with tf.op_scope([x], name, 'l2_normalize') as scope:
    x = tf.convert_to_tensor(x, name='x')
    x = tf.verify_tensor_all_finite(x, 'Error at input %s' % scope)
    x_norm = capped_sqrt(tf.reduce_sum(tf.square(x), [dim], keep_dims=True))
    return tf.verify_tensor_all_finite(tf.div(x,
                                              x_norm,
                                              name=scope),
                                       'Error at %s' % scope)

def embed(sequence_batch, embeds):
    mask = sequence_batch.mask
    embedded_values = tf.gather(embeds, sequence_batch.values)
    embedded_values = tf.verify_tensor_all_finite(embedded_values, 'embedded_values')

    # set all pad embeddings to zero
    broadcasted_mask = expand_dims_for_broadcast(mask, embedded_values)
    embedded_values *= broadcasted_mask

    return SequenceBatch(embedded_values, mask)

def to_simplex(x):
    """Transform real vector of length ``(K-1)`` to a simplex of dimension ``K``
    using a backward stick breaking construction.

    Parameters
    ----------
    x : tf.Tensor
        A 1-D or 2-D tensor.

    Returns
    -------
    tf.Tensor
        A tensor of same shape as input but with last dimension of
        size ``K``.

    Raises
    ------
    InvalidArgumentError
        If the input has Inf or NaN values.

    Notes
    -----
    x as a 3-D or higher tensor is not guaranteed to be supported.
    """
    dependencies = [tf.verify_tensor_all_finite(x, msg='')]
    x = control_flow_ops.with_dependencies(dependencies, x)
    x = tf.cast(x, dtype=tf.float32)

    if isinstance(x, tf.Tensor) or isinstance(x, tf.Variable):
        shape = get_dims(x)
    else:
        shape = x.shape

    if len(shape) == 1:
        n_rows = ()
        K_minus_one = shape[0]
        eq = -tf.log(tf.cast(K_minus_one - tf.range(K_minus_one),
                             dtype=tf.float32))
        z = tf.sigmoid(eq + x)
        pil = tf.concat(0, [z, tf.constant([1.0])])
        piu = tf.concat(0, [tf.constant([1.0]), 1.0 - z])
        S = cumprod(piu)
        return S * pil
    else:
        n_rows = shape[0]
        K_minus_one = shape[1]
        eq = -tf.log(tf.cast(K_minus_one - tf.range(K_minus_one),
                             dtype=tf.float32))
        z = tf.sigmoid(eq + x)
        pil = tf.concat(1, [z, tf.ones([n_rows, 1])])
        piu = tf.concat(1, [tf.ones([n_rows, 1]), 1.0 - z])
        # cumulative product along 1st axis
        S = tf.pack([cumprod(piu_x) for piu_x in tf.unpack(piu)])
        return S * pil

    def testVerifyTensorAllFiniteFails(self):
        x_shape = [5, 4]
        x = np.random.random_sample(x_shape).astype(np.float32)
        my_msg = "Input is not a number."

        # Test NaN.
        x[0] = np.nan
        with self.test_session():
            with self.assertRaisesOpError(my_msg):
                t = tf.constant(x, shape=x_shape, dtype=tf.float32)
                t_verified = tf.verify_tensor_all_finite(t, my_msg)
                t_verified.eval()

        # Test Inf.
        x[0] = np.inf
        with self.test_session():
            with self.assertRaisesOpError(my_msg):
                t = tf.constant(x, shape=x_shape, dtype=tf.float32)
                t_verified = tf.verify_tensor_all_finite(t, my_msg)
                t_verified.eval()

 def init_learnable_params(self):
     self.w = [None] * self.order
     for i in range(1, self.order + 1):
         r = self.rank
         if i == 1:
             r = 1
         rnd_weights = tf.random_uniform([self.n_features, r], -self.init_std, self.init_std)
         self.w[i - 1] = tf.verify_tensor_all_finite(
             tf.Variable(rnd_weights, trainable=True, name='embedding_' + str(i)),
             msg='NaN or Inf in w[{}].'.format(i-1))
     self.b = tf.Variable(self.init_std, trainable=True, name='bias')
     tf.summary.scalar('bias', self.b)