losses.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
# limitations under the License.
# ==============================================================================
"""Built-in loss functions.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import abc

import six

from tensorflow.python.distribute import distribution_strategy_context
from tensorflow.python.framework import ops
from tensorflow.python.framework import smart_cond
from tensorflow.python.framework import tensor_util
from tensorflow.python.keras import backend as K
from tensorflow.python.keras.utils import losses_utils
from tensorflow.python.keras.utils import tf_utils
from tensorflow.python.keras.utils.generic_utils import deserialize_keras_object
from tensorflow.python.keras.utils.generic_utils import serialize_keras_object
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn
from tensorflow.python.ops.losses import losses_impl
from tensorflow.python.ops.losses import util as tf_losses_util
from tensorflow.python.util.tf_export import keras_export
from tensorflow.tools.docs import doc_controls


@keras_export('keras.losses.Loss')
class Loss(object):
  """Loss base class.

  To be implemented by subclasses:
  * `call()`: Contains the logic for loss calculation using `y_true`, `y_pred`.

  Example subclass implementation:
  ```python
  class MeanSquaredError(Loss):
    def call(self, y_true, y_pred):
      y_pred = ops.convert_to_tensor(y_pred)
      y_true = math_ops.cast(y_true, y_pred.dtype)
      return K.mean(math_ops.square(y_pred - y_true), axis=-1)
  ```

  When used with `tf.distribute.Strategy`, outside of built-in training loops
  such as `tf.keras` `compile` and `fit`, please use 'SUM' or 'NONE' reduction
  types, and reduce losses explicitly in your training loop. Using 'AUTO' or
  'SUM_OVER_BATCH_SIZE' will raise an error.

  Please see
  https://www.tensorflow.org/tutorials/distribute/custom_training for more
  details on this.

  You can implement 'SUM_OVER_BATCH_SIZE' using global batch size like:
  ```python
  with strategy.scope():
    loss_obj = tf.keras.losses.CategoricalCrossentropy(
        reduction=tf.keras.losses.Reduction.NONE)
    ....
    loss = (tf.reduce_sum(loss_obj(labels, predictions)) *
            (1. / global_batch_size))
  ```

  Args:
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: Optional name for the op.
  """

  def __init__(self, reduction=losses_utils.ReductionV2.AUTO, name=None):
    losses_utils.ReductionV2.validate(reduction)
    self.reduction = reduction
    self.name = name
    # SUM_OVER_BATCH is only allowed in losses managed by `fit` or
    # CannedEstimators.
    self._allow_sum_over_batch_size = False

  def __call__(self, y_true, y_pred, sample_weight=None):
    """Invokes the `Loss` instance.

    Args:
      y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`
      y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`
      sample_weight: Optional `sample_weight` acts as a
        coefficient for the loss. If a scalar is provided, then the loss is
        simply scaled by the given value. If `sample_weight` is a tensor of size
        `[batch_size]`, then the total loss for each sample of the batch is
        rescaled by the corresponding element in the `sample_weight` vector. If
        the shape of `sample_weight` is `[batch_size, d0, .. dN-1]` (or can be
        broadcasted to this shape), then each loss element of `y_pred` is scaled
        by the corresponding value of `sample_weight`. (Note on`dN-1`: all loss
        functions reduce by 1 dimension, usually axis=-1.)

    Returns:
      Weighted loss float `Tensor`. If `reduction` is `NONE`, this has
        shape `[batch_size, d0, .. dN-1]`; otherwise, it is scalar. (Note `dN-1`
        because all loss functions reduce by 1 dimension, usually axis=-1.)

    Raises:
      ValueError: If the shape of `sample_weight` is invalid.
    """
    # If we are wrapping a lambda function strip '<>' from the name as it is not
    # accepted in scope name.
    scope_name = 'lambda' if self.name == '<lambda>' else self.name
    graph_ctx = tf_utils.graph_context_for_symbolic_tensors(
        y_true, y_pred, sample_weight)
    with K.name_scope(scope_name or self.__class__.__name__), graph_ctx:
      losses = self.call(y_true, y_pred)
      return losses_utils.compute_weighted_loss(
          losses, sample_weight, reduction=self._get_reduction())

  @classmethod
  def from_config(cls, config):
    """Instantiates a `Loss` from its config (output of `get_config()`).

    Args:
        config: Output of `get_config()`.

    Returns:
        A `Loss` instance.
    """
    return cls(**config)

  def get_config(self):
    return {'reduction': self.reduction, 'name': self.name}

  @abc.abstractmethod
  @doc_controls.for_subclass_implementers
  def call(self, y_true, y_pred):
    """Invokes the `Loss` instance.

    Args:
      y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`
      y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`

    Returns:
      Loss values with the shape `[batch_size, d0, .. dN-1]`.
    """
    NotImplementedError('Must be implemented in subclasses.')

  def _get_reduction(self):
    """Handles `AUTO` reduction cases and returns the reduction value."""
    if (not self._allow_sum_over_batch_size and
        distribution_strategy_context.has_strategy() and
        (self.reduction == losses_utils.ReductionV2.AUTO or
         self.reduction == losses_utils.ReductionV2.SUM_OVER_BATCH_SIZE)):
      raise ValueError(
          'Please use `tf.keras.losses.Reduction.SUM` or '
          '`tf.keras.losses.Reduction.NONE` for loss reduction when losses are '
          'used with `tf.distribute.Strategy` outside of the built-in training '
          'loops. You can implement '
          '`tf.keras.losses.Reduction.SUM_OVER_BATCH_SIZE` using global batch '
          'size like:\n```\nwith strategy.scope():\n'
          '    loss_obj = tf.keras.losses.CategoricalCrossentropy('
          'reduction=tf.keras.losses.Reduction.NONE)\n....\n'
          '    loss = tf.reduce_sum(loss_obj(labels, predictions)) * '
          '(1. / global_batch_size)\n```\nPlease see '
          'https://www.tensorflow.org/tutorials/distribute/custom_training'
          ' for more details.')

    if self.reduction == losses_utils.ReductionV2.AUTO:
      return losses_utils.ReductionV2.SUM_OVER_BATCH_SIZE
    return self.reduction


class LossFunctionWrapper(Loss):
  """Wraps a loss function in the `Loss` class.

  Args:
    fn: The loss function to wrap, with signature `fn(y_true, y_pred,
      **kwargs)`.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: (Optional) name for the loss.
    **kwargs: The keyword arguments that are passed on to `fn`.
  """

  def __init__(self,
               fn,
               reduction=losses_utils.ReductionV2.AUTO,
               name=None,
               **kwargs):
    super(LossFunctionWrapper, self).__init__(reduction=reduction, name=name)
    self.fn = fn
    self._fn_kwargs = kwargs

  def call(self, y_true, y_pred):
    """Invokes the `LossFunctionWrapper` instance.

    Args:
      y_true: Ground truth values.
      y_pred: The predicted values.

    Returns:
      Loss values per sample.
    """
    if tensor_util.is_tensor(y_pred) and tensor_util.is_tensor(y_true):
      y_pred, y_true = tf_losses_util.squeeze_or_expand_dimensions(
          y_pred, y_true)
    return self.fn(y_true, y_pred, **self._fn_kwargs)

  def get_config(self):
    config = {}
    for k, v in six.iteritems(self._fn_kwargs):
      config[k] = K.eval(v) if tf_utils.is_tensor_or_variable(v) else v
    base_config = super(LossFunctionWrapper, self).get_config()
    return dict(list(base_config.items()) + list(config.items()))


@keras_export('keras.losses.MeanSquaredError')
class MeanSquaredError(LossFunctionWrapper):
  """Computes the mean of squares of errors between labels and predictions.

  `loss = square(y_true - y_pred)`

  Usage:

  >>> mse = tf.keras.losses.MeanSquaredError()
  >>> loss = mse([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]])
  >>> loss.numpy()
  0.5

  >>> loss = mse([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]],
  ...            sample_weight=[0.7, 0.3])
  >>> loss.numpy()
  0.25

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.MeanSquaredError())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='mean_squared_error'):
    super(MeanSquaredError, self).__init__(
        mean_squared_error, name=name, reduction=reduction)


@keras_export('keras.losses.MeanAbsoluteError')
class MeanAbsoluteError(LossFunctionWrapper):
  """Computes the mean of absolute difference between labels and predictions.

  `loss = abs(y_true - y_pred)`

  Usage:

  >>> mae = tf.keras.losses.MeanAbsoluteError()
  >>> loss = mae([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]])
  >>> loss.numpy()
  0.5

  >>> loss = mae([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]],
  ...            sample_weight=[0.7, 0.3])
  >>> loss.numpy()
  0.25

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.MeanAbsoluteError())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='mean_absolute_error'):
    super(MeanAbsoluteError, self).__init__(
        mean_absolute_error, name=name, reduction=reduction)


@keras_export('keras.losses.MeanAbsolutePercentageError')
class MeanAbsolutePercentageError(LossFunctionWrapper):
  """Computes the mean absolute percentage error between `y_true` and `y_pred`.

  `loss = 100 * abs(y_true - y_pred) / y_true`

  Usage:

  >>> mape = tf.keras.losses.MeanAbsolutePercentageError()
  >>> loss = mape([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]])
  >>> loss.numpy()
  500000000.0

  >>> loss = mape([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]],
  ...             sample_weight=[0.7, 0.3])
  >>> loss.numpy()
  250000000.0

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.MeanAbsolutePercentageError())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='mean_absolute_percentage_error'):
    super(MeanAbsolutePercentageError, self).__init__(
        mean_absolute_percentage_error, name=name, reduction=reduction)


@keras_export('keras.losses.MeanSquaredLogarithmicError')
class MeanSquaredLogarithmicError(LossFunctionWrapper):
  """Computes the mean squared logarithmic error between `y_true` and `y_pred`.

  `loss = square(log(y_true) - log(y_pred))`

  Usage:

  >>> msle = tf.keras.losses.MeanSquaredLogarithmicError()
  >>> loss = msle([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]])
  >>> loss.numpy()
  0.24022643

  >>> loss = msle([[0., 1.], [0., 0.]], [[1., 1.], [1., 0.]],
  ...             sample_weight=[0.7, 0.3])
  >>> loss.numpy()
  0.12011322

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.MeanSquaredLogarithmicError())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='mean_squared_logarithmic_error'):
    super(MeanSquaredLogarithmicError, self).__init__(
        mean_squared_logarithmic_error, name=name, reduction=reduction)


@keras_export('keras.losses.BinaryCrossentropy')
class BinaryCrossentropy(LossFunctionWrapper):
  """Computes the cross-entropy loss between true labels and predicted labels.

  Use this cross-entropy loss when there are only two label classes (assumed to
  be 0 and 1). For each example, there should be a single floating-point value
  per prediction.

  In the snippet below, each of the four examples has only a single
  floating-pointing value, and both `y_pred` and `y_true` have the shape
  `[batch_size]`.

  Usage:
  >>> bce = tf.keras.losses.BinaryCrossentropy()
  >>> loss = bce([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  0.81492424

  >>> loss = bce([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...            sample_weight=[1, 0])
  >>> loss.numpy()
  0.45814526

  Usage with the `tf.keras` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.BinaryCrossentropy())
  ```

  Args:
    from_logits: Whether to interpret `y_pred` as a tensor of
      [logit](https://en.wikipedia.org/wiki/Logit) values. By default, we assume
        that `y_pred` contains probabilities (i.e., values in [0, 1]).
      Note: Using from_logits=True may be more numerically stable.
    label_smoothing: Float in [0, 1]. When 0, no smoothing occurs. When > 0, we
      compute the loss between the predicted labels and a smoothed version of
      the true labels, where the smoothing squeezes the labels towards 0.5.
      Larger values of `label_smoothing` correspond to heavier smoothing.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: (Optional) Name for the op.
  """

  def __init__(self,
               from_logits=False,
               label_smoothing=0,
               reduction=losses_utils.ReductionV2.AUTO,
               name='binary_crossentropy'):
    super(BinaryCrossentropy, self).__init__(
        binary_crossentropy,
        name=name,
        reduction=reduction,
        from_logits=from_logits,
        label_smoothing=label_smoothing)
    self.from_logits = from_logits


@keras_export('keras.losses.CategoricalCrossentropy')
class CategoricalCrossentropy(LossFunctionWrapper):
  """Computes the crossentropy loss between the labels and predictions.

  Use this crossentropy loss function when there are two or more label classes.
  We expect labels to be provided in a `one_hot` representation. If you want to
  provide labels as integers, please use `SparseCategoricalCrossentropy` loss.
  There should be `# classes` floating point values per feature.

  In the snippet below, there is `# classes` floating pointing values per
  example. The shape of both `y_pred` and `y_true` are
  `[batch_size, num_classes]`.

  Usage:

  >>> cce = tf.keras.losses.CategoricalCrossentropy()
  >>> loss = cce([[0, 1, 0], [0, 0, 1]],
  ...            [[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
  >>> loss.numpy()
  1.1769392

  >>> loss = cce([[0, 1, 0], [0, 0, 1]],
  ...            [[0.05, 0.95, 0], [0.1, 0.8, 0.1]],
  ...            sample_weight=tf.constant([0.3, 0.7]))
  >>> loss.numpy()
  0.8135988

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.CategoricalCrossentropy())
  ```

  Args:
    from_logits: Whether `y_pred` is expected to be a logits tensor. By default,
      we assume that `y_pred` encodes a probability distribution.
      **Note: Using from_logits=True is more numerically stable.**
    label_smoothing: Float in [0, 1]. When > 0, label values are smoothed,
      meaning the confidence on label values are relaxed. e.g.
      `label_smoothing=0.2` means that we will use a value of `0.1` for label
      `0` and `0.9` for label `1`"
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: Optional name for the op.
  """

  def __init__(self,
               from_logits=False,
               label_smoothing=0,
               reduction=losses_utils.ReductionV2.AUTO,
               name='categorical_crossentropy'):
    super(CategoricalCrossentropy, self).__init__(
        categorical_crossentropy,
        name=name,
        reduction=reduction,
        from_logits=from_logits,
        label_smoothing=label_smoothing)


@keras_export('keras.losses.SparseCategoricalCrossentropy')
class SparseCategoricalCrossentropy(LossFunctionWrapper):
  """Computes the crossentropy loss between the labels and predictions.

  Use this crossentropy loss function when there are two or more label classes.
  We expect labels to be provided as integers. If you want to provide labels
  using `one-hot` representation, please use `CategoricalCrossentropy` loss.
  There should be `# classes` floating point values per feature for `y_pred`
  and a single floating point value per feature for `y_true`.

  In the snippet below, there is a single floating point value per example for
  `y_true` and `# classes` floating pointing values per example for `y_pred`.
  The shape of `y_true` is `[batch_size]` and the shape of `y_pred` is
  `[batch_size, num_classes]`.

  Usage:

  >>> scce = tf.keras.losses.SparseCategoricalCrossentropy()
  >>> loss = scce([1, 2], [[0.05, 0.95, 0], [0.1, 0.8, 0.1]])
  >>> loss.numpy()
  1.1769392

  >>> loss = scce([1, 2], [[0.05, 0.95, 0], [0.1, 0.8, 0.1]],
  ...             sample_weight=tf.constant([0.3, 0.7]))
  >>> loss.numpy()
  0.8135988

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.SparseCategoricalCrossentropy())
  ```

  Args:
    from_logits: Whether `y_pred` is expected to be a logits tensor. By default,
      we assume that `y_pred` encodes a probability distribution.
      Note: Using from_logits=True may be more numerically stable.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: Optional name for the op.
  """

  def __init__(self,
               from_logits=False,
               reduction=losses_utils.ReductionV2.AUTO,
               name='sparse_categorical_crossentropy'):
    super(SparseCategoricalCrossentropy, self).__init__(
        sparse_categorical_crossentropy,
        name=name,
        reduction=reduction,
        from_logits=from_logits)


@keras_export('keras.losses.Hinge')
class Hinge(LossFunctionWrapper):
  """Computes the hinge loss between `y_true` and `y_pred`.

  `loss = maximum(1 - y_true * y_pred, 0)`

  `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are
  provided we will convert them to -1 or 1.

  Usage:

  >>> h = tf.keras.losses.Hinge()
  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  1.3

  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]], sample_weight=[1, 0])
  >>> loss.numpy()
  0.55

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.Hinge())
  ```
  """

  def __init__(self, reduction=losses_utils.ReductionV2.AUTO, name='hinge'):
    super(Hinge, self).__init__(hinge, name=name, reduction=reduction)


@keras_export('keras.losses.SquaredHinge')
class SquaredHinge(LossFunctionWrapper):
  """Computes the squared hinge loss between `y_true` and `y_pred`.

  `loss = square(maximum(1 - y_true * y_pred, 0))`

  `y_true` values are expected to be -1 or 1. If binary (0 or 1) labels are
  provided we will convert them to -1 or 1.

  Usage:

  >>> h = tf.keras.losses.SquaredHinge()
  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  1.86

  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]], sample_weight=[1, 0])
  >>> loss.numpy()
  0.73

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.SquaredHinge())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='squared_hinge'):
    super(SquaredHinge, self).__init__(
        squared_hinge, name=name, reduction=reduction)


@keras_export('keras.losses.CategoricalHinge')
class CategoricalHinge(LossFunctionWrapper):
  """Computes the categorical hinge loss between `y_true` and `y_pred`.

  `loss = maximum(neg - pos + 1, 0)`
  where `neg = sum(y_true * y_pred)` and `pos = maximum(1 - y_true)`

  Usage:

  >>> h = tf.keras.losses.CategoricalHinge()
  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  1.4000001

  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]], sample_weight=[1, 0])
  >>> loss.numpy()
  0.6

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.CategoricalHinge())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='categorical_hinge'):
    super(CategoricalHinge, self).__init__(
        categorical_hinge, name=name, reduction=reduction)


@keras_export('keras.losses.Poisson')
class Poisson(LossFunctionWrapper):
  """Computes the Poisson loss between `y_true` and `y_pred`.

  `loss = y_pred - y_true * log(y_pred)`

  Usage:

  >>> p = tf.keras.losses.Poisson()
  >>> loss = p([[0., 1.], [0., 0.]], [[1., 1.], [0., 0.]])
  >>> loss.numpy()
  0.49999997

  >>> loss = p([[0., 1.], [0., 0.]], [[1., 1.], [0., 0.]],
  ...          sample_weight=[1., 0.])
  >>> loss.numpy()
  0.49999997

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.Poisson())
  ```
  """

  def __init__(self, reduction=losses_utils.ReductionV2.AUTO, name='poisson'):
    super(Poisson, self).__init__(poisson, name=name, reduction=reduction)


@keras_export('keras.losses.LogCosh')
class LogCosh(LossFunctionWrapper):
  """Computes the logarithm of the hyperbolic cosine of the prediction error.

  `logcosh = log((exp(x) + exp(-x))/2)`,
  where x is the error `y_pred - y_true`.

  Usage:

  >>> l = tf.keras.losses.LogCosh()
  >>> loss = l([[0., 1.], [0., 0.]], [[1., 1.], [0., 0.]])
  >>> loss.numpy()
  0.10844523

  >>> loss = l([[0., 1.], [0., 0.]], [[1., 1.], [0., 0.]],
  ...          sample_weight=[1., 0.])
  >>> loss.numpy()
  0.10844523

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.LogCosh())
  ```
  """

  def __init__(self, reduction=losses_utils.ReductionV2.AUTO, name='logcosh'):
    super(LogCosh, self).__init__(logcosh, name=name, reduction=reduction)


@keras_export('keras.losses.KLDivergence')
class KLDivergence(LossFunctionWrapper):
  """Computes Kullback-Leibler divergence loss between `y_true` and `y_pred`.

  `loss = y_true * log(y_true / y_pred)`

  See: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence

  Usage:

  >>> kl = tf.keras.losses.KLDivergence()
  >>> loss = kl([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  0.45814306

  >>> loss = kl([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...           sample_weight=[1, 0])
  >>> loss.numpy()
  0.4581446

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.KLDivergence())
  ```
  """

  def __init__(self,
               reduction=losses_utils.ReductionV2.AUTO,
               name='kullback_leibler_divergence'):
    super(KLDivergence, self).__init__(
        kullback_leibler_divergence, name=name, reduction=reduction)


@keras_export('keras.losses.Huber')
class Huber(LossFunctionWrapper):
  """Computes the Huber loss between `y_true` and `y_pred`.

  For each value x in `error = y_true - y_pred`:

  ```
  loss = 0.5 * x^2                  if |x| <= d
  loss = 0.5 * d^2 + d * (|x| - d)  if |x| > d
  ```
  where d is `delta`. See: https://en.wikipedia.org/wiki/Huber_loss

  Usage:

  >>> h = tf.keras.losses.Huber()
  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]])
  >>> loss.numpy()
  0.155

  >>> loss = h([[0, 1], [0, 0]], [[0.6, 0.4], [0.4, 0.6]],
  ...          sample_weight=[1, 0])
  >>> loss.numpy()
  0.09

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.Huber())
  ```

  Args:
    delta: A float, the point where the Huber loss function changes from a
      quadratic to linear.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: Optional name for the op.
  """

  def __init__(self,
               delta=1.0,
               reduction=losses_utils.ReductionV2.AUTO,
               name='huber_loss'):
    super(Huber, self).__init__(
        huber_loss, name=name, reduction=reduction, delta=delta)


@keras_export('keras.metrics.mean_squared_error',
              'keras.metrics.mse',
              'keras.metrics.MSE',
              'keras.losses.mean_squared_error',
              'keras.losses.mse',
              'keras.losses.MSE')
def mean_squared_error(y_true, y_pred):
  """Computes the mean squared error between labels and predictions.

  `loss = square(y_true - y_pred)`

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Mean squared error values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  return K.mean(math_ops.squared_difference(y_pred, y_true), axis=-1)


@keras_export('keras.metrics.mean_absolute_error',
              'keras.metrics.mae',
              'keras.metrics.MAE',
              'keras.losses.mean_absolute_error',
              'keras.losses.mae',
              'keras.losses.MAE')
def mean_absolute_error(y_true, y_pred):
  """Computes the mean absolute error between labels and predictions.

  `loss = abs(y_true - y_pred)`

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Mean absolute error values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  return K.mean(math_ops.abs(y_pred - y_true), axis=-1)


@keras_export('keras.metrics.mean_absolute_percentage_error',
              'keras.metrics.mape',
              'keras.metrics.MAPE',
              'keras.losses.mean_absolute_percentage_error',
              'keras.losses.mape',
              'keras.losses.MAPE')
def mean_absolute_percentage_error(y_true, y_pred):
  """Computes the mean absolute percentage error between `y_true` and `y_pred`.

  `loss = 100 * abs(y_true - y_pred) / y_true`

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Mean absolute percentage error values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  diff = math_ops.abs(
      (y_true - y_pred) / K.maximum(math_ops.abs(y_true), K.epsilon()))
  return 100. * K.mean(diff, axis=-1)


@keras_export('keras.metrics.mean_squared_logarithmic_error',
              'keras.metrics.msle',
              'keras.metrics.MSLE',
              'keras.losses.mean_squared_logarithmic_error',
              'keras.losses.msle',
              'keras.losses.MSLE')
def mean_squared_logarithmic_error(y_true, y_pred):
  """Computes the mean squared logarithmic error between `y_true` and `y_pred`.

  `loss = square(log(y_true) - log(y_pred))`

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Mean squared logarithmic error values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  first_log = math_ops.log(K.maximum(y_pred, K.epsilon()) + 1.)
  second_log = math_ops.log(K.maximum(y_true, K.epsilon()) + 1.)
  return K.mean(math_ops.squared_difference(first_log, second_log), axis=-1)


def _maybe_convert_labels(y_true):
  """Converts binary labels into -1/1."""
  are_zeros = math_ops.equal(y_true, 0)
  are_ones = math_ops.equal(y_true, 1)
  is_binary = math_ops.reduce_all(math_ops.logical_or(are_zeros, are_ones))

  def _convert_binary_labels():
    # Convert the binary labels to -1 or 1.
    return 2. * y_true - 1.

  updated_y_true = smart_cond.smart_cond(is_binary,
                                         _convert_binary_labels, lambda: y_true)
  return updated_y_true


@keras_export('keras.metrics.squared_hinge', 'keras.losses.squared_hinge')
def squared_hinge(y_true, y_pred):
  """Computes the squared hinge loss between `y_true` and `y_pred`.

  `loss = square(maximum(1 - y_true * y_pred, 0))`

  Args:
    y_true: The ground truth values. `y_true` values are expected to be -1 or 1.
      If binary (0 or 1) labels are provided we will convert them to -1 or 1.
      shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
     Squared hinge loss values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  y_true = _maybe_convert_labels(y_true)
  return K.mean(
      math_ops.square(math_ops.maximum(1. - y_true * y_pred, 0.)), axis=-1)


@keras_export('keras.metrics.hinge', 'keras.losses.hinge')
def hinge(y_true, y_pred):
  """Computes the hinge loss between `y_true` and `y_pred`.

  `loss = maximum(1 - y_true * y_pred, 0)`

  Args:
    y_true: The ground truth values. `y_true` values are expected to be -1 or 1.
      If binary (0 or 1) labels are provided they will be converted to -1 or 1.
      shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Hinge loss values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  y_true = _maybe_convert_labels(y_true)
  return K.mean(math_ops.maximum(1. - y_true * y_pred, 0.), axis=-1)


@keras_export('keras.losses.categorical_hinge')
def categorical_hinge(y_true, y_pred):
  """Computes the categorical hinge loss between `y_true` and `y_pred`.

  `loss = maximum(neg - pos + 1, 0)`
  where `neg = sum(y_true * y_pred)` and `pos = maximum(1 - y_true)`

  Args:
    y_true: The ground truth values. `y_true` values are expected to be -1 or 1.
      If binary (0 or 1) labels are provided they will be converted to -1 or 1.
    y_pred: The predicted values.

  Returns:
    Categorical hinge loss values.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  pos = math_ops.reduce_sum(y_true * y_pred, axis=-1)
  neg = math_ops.reduce_max((1. - y_true) * y_pred, axis=-1)
  return math_ops.maximum(0., neg - pos + 1.)


def huber_loss(y_true, y_pred, delta=1.0):
  """Computes Huber loss value.

  For each value x in `error = y_true - y_pred`:

  ```
  loss = 0.5 * x^2                  if |x| <= d
  loss = 0.5 * d^2 + d * (|x| - d)  if |x| > d
  ```
  where d is `delta`. See: https://en.wikipedia.org/wiki/Huber_loss

  Args:
    y_true: tensor of true targets.
    y_pred: tensor of predicted targets.
    delta: A float, the point where the Huber loss function changes from a
      quadratic to linear.

  Returns:
    Tensor with one scalar loss entry per sample.
  """
  y_pred = math_ops.cast(y_pred, dtype=K.floatx())
  y_true = math_ops.cast(y_true, dtype=K.floatx())
  error = math_ops.subtract(y_pred, y_true)
  abs_error = math_ops.abs(error)
  quadratic = math_ops.minimum(abs_error, delta)
  linear = math_ops.subtract(abs_error, quadratic)
  return math_ops.add(
      math_ops.multiply(
          ops.convert_to_tensor(0.5, dtype=quadratic.dtype),
          math_ops.multiply(quadratic, quadratic)),
      math_ops.multiply(delta, linear))


@keras_export('keras.losses.logcosh')
def logcosh(y_true, y_pred):
  """Logarithm of the hyperbolic cosine of the prediction error.

  `log(cosh(x))` is approximately equal to `(x ** 2) / 2` for small `x` and
  to `abs(x) - log(2)` for large `x`. This means that 'logcosh' works mostly
  like the mean squared error, but will not be so strongly affected by the
  occasional wildly incorrect prediction.

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
    Logcosh error values. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)

  def _logcosh(x):
    return x + nn.softplus(-2. * x) - math_ops.log(2.)

  return K.mean(_logcosh(y_pred - y_true), axis=-1)


@keras_export('keras.metrics.categorical_crossentropy',
              'keras.losses.categorical_crossentropy')
def categorical_crossentropy(y_true,
                             y_pred,
                             from_logits=False,
                             label_smoothing=0):
  """Computes the categorical crossentropy loss.

  Args:
    y_true: tensor of true targets.
    y_pred: tensor of predicted targets.
    from_logits: Whether `y_pred` is expected to be a logits tensor. By default,
      we assume that `y_pred` encodes a probability distribution.
    label_smoothing: Float in [0, 1]. If > `0` then smooth the labels.

  Returns:
    Categorical crossentropy loss value.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  label_smoothing = ops.convert_to_tensor(label_smoothing, dtype=K.floatx())

  def _smooth_labels():
    num_classes = math_ops.cast(array_ops.shape(y_true)[1], y_pred.dtype)
    return y_true * (1.0 - label_smoothing) + (label_smoothing / num_classes)

  y_true = smart_cond.smart_cond(label_smoothing,
                                 _smooth_labels, lambda: y_true)
  return K.categorical_crossentropy(y_true, y_pred, from_logits=from_logits)


@keras_export('keras.metrics.sparse_categorical_crossentropy',
              'keras.losses.sparse_categorical_crossentropy')
def sparse_categorical_crossentropy(y_true, y_pred, from_logits=False, axis=-1):
  """Computes the sparse categorical crossentropy loss.

  Args:
    y_true: Ground truth values.
    y_pred: The predicted values.
    from_logits: Whether `y_pred` is expected to be a logits tensor. By default,
      we assume that `y_pred` encodes a probability distribution.
    axis: (Optional) Defaults to -1. The dimension along which the entropy is
      computed.

  Returns:
    Sparse categorical crossentropy loss value.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  return K.sparse_categorical_crossentropy(
      y_true, y_pred, from_logits=from_logits, axis=axis)


@keras_export('keras.metrics.binary_crossentropy',
              'keras.losses.binary_crossentropy')
def binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0):
  """Computes the binary crossentropy loss.

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.
    from_logits: Whether `y_pred` is expected to be a logits tensor. By default,
      we assume that `y_pred` encodes a probability distribution.
    label_smoothing: Float in [0, 1]. If > `0` then smooth the labels.

  Returns:
    Binary crossentropy loss value. shape = `[batch_size, d0, .. dN-1]`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  label_smoothing = ops.convert_to_tensor(label_smoothing, dtype=K.floatx())

  def _smooth_labels():
    return y_true * (1.0 - label_smoothing) + 0.5 * label_smoothing

  y_true = smart_cond.smart_cond(label_smoothing,
                                 _smooth_labels, lambda: y_true)
  return K.mean(
      K.binary_crossentropy(y_true, y_pred, from_logits=from_logits), axis=-1)


@keras_export('keras.metrics.kullback_leibler_divergence',
              'keras.metrics.kld',
              'keras.metrics.KLD',
              'keras.losses.kullback_leibler_divergence',
              'keras.losses.kld',
              'keras.losses.KLD')
def kullback_leibler_divergence(y_true, y_pred):
  """Computes Kullback-Leibler divergence loss between `y_true` and `y_pred`.

  `loss = y_true * log(y_true / y_pred)`

  See: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence

  Usage:

  ```python
  loss = tf.keras.losses.KLD([.4, .9, .2], [.5, .8, .12])
  print('Loss: ', loss.numpy())  # Loss: 0.11891246
  ```

  Args:
    y_true: Tensor of true targets.
    y_pred: Tensor of predicted targets.

  Returns:
    A `Tensor` with loss.

  Raises:
      TypeError: If `y_true` cannot be cast to the `y_pred.dtype`.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  y_true = K.clip(y_true, K.epsilon(), 1)
  y_pred = K.clip(y_pred, K.epsilon(), 1)
  return math_ops.reduce_sum(y_true * math_ops.log(y_true / y_pred), axis=-1)


@keras_export('keras.metrics.poisson', 'keras.losses.poisson')
def poisson(y_true, y_pred):
  """Computes the Poisson loss between y_true and y_pred.

  The Poisson loss is the mean of the elements of the `Tensor`
  `y_pred - y_true * log(y_pred)`.

  Args:
    y_true: Ground truth values. shape = `[batch_size, d0, .. dN]`.
    y_pred: The predicted values. shape = `[batch_size, d0, .. dN]`.

  Returns:
     Poisson loss value. shape = `[batch_size, d0, .. dN-1]`.

  Raises:
      InvalidArgumentError: If `y_true` and `y_pred` have incompatible shapes.
  """
  y_pred = ops.convert_to_tensor(y_pred)
  y_true = math_ops.cast(y_true, y_pred.dtype)
  return K.mean(y_pred - y_true * math_ops.log(y_pred + K.epsilon()), axis=-1)


@keras_export(
    'keras.losses.cosine_similarity',
    v1=[
        'keras.metrics.cosine_proximity',
        'keras.metrics.cosine',
        'keras.losses.cosine_proximity',
        'keras.losses.cosine',
        'keras.losses.cosine_similarity',
    ])
def cosine_similarity(y_true, y_pred, axis=-1):
  """Computes the cosine similarity between labels and predictions.

  Note that it is a negative quantity between -1 and 0, where 0 indicates
  orthogonality and values closer to -1 indicate greater similarity. This makes
  it usable as a loss function in a setting where you try to maximize the
  proximity between predictions and targets.

  `loss = -sum(y_true * y_pred)`

  Args:
    y_true: Tensor of true targets.
    y_pred: Tensor of predicted targets.
    axis: Axis along which to determine similarity.

  Returns:
    Cosine similarity tensor.
  """
  y_true = nn.l2_normalize(y_true, axis=axis)
  y_pred = nn.l2_normalize(y_pred, axis=axis)
  return -math_ops.reduce_sum(y_true * y_pred, axis=axis)


@keras_export('keras.losses.CosineSimilarity')
class CosineSimilarity(LossFunctionWrapper):
  """Computes the cosine similarity between `y_true` and `y_pred`.

  `loss = -sum(y_true * y_pred)`

  Usage:

  >>> cosine_loss = tf.keras.losses.CosineSimilarity(axis=1)
  >>> loss = cosine_loss([[0., 1.], [1., 1.]], [[1., 0.], [1., 1.]])
  >>> # l2_norm(y_true) = [[0., 1.], [1./1.414], 1./1.414]]]
  >>> # l2_norm(y_pred) = [[1., 0.], [1./1.414], 1./1.414]]]
  >>> # l2_norm(y_true) . l2_norm(y_pred) = [[0., 0.], [0.5, 0.5]]
  >>> # loss = mean(sum(l2_norm(y_true) . l2_norm(y_pred), axis=1))
  >>> #       = ((0. + 0.) +  (0.5 + 0.5)) / 2
  >>> loss.numpy()
  -0.49999997

  Usage with the `compile` API:

  ```python
  model = tf.keras.Model(inputs, outputs)
  model.compile('sgd', loss=tf.keras.losses.CosineSimilarity(axis=1))
  ```

  Args:
    axis: (Optional) Defaults to -1. The dimension along which the cosine
      similarity is computed.
    reduction: (Optional) Type of `tf.keras.losses.Reduction` to apply to loss.
      Default value is `AUTO`. `AUTO` indicates that the reduction option will
      be determined by the usage context. For almost all cases this defaults to
      `SUM_OVER_BATCH_SIZE`.
      When used with `tf.distribute.Strategy`, outside of built-in training
      loops such as `tf.keras` `compile` and `fit`, using `AUTO` or
      `SUM_OVER_BATCH_SIZE` will raise an error. Please see
      https://www.tensorflow.org/tutorials/distribute/custom_training
      for more details on this.
    name: Optional name for the op.
  """

  def __init__(self,
               axis=-1,
               reduction=losses_utils.ReductionV2.AUTO,
               name='cosine_similarity'):
    super(CosineSimilarity, self).__init__(
        cosine_similarity, reduction=reduction, name=name, axis=axis)


# Aliases.

bce = BCE = binary_crossentropy
mse = MSE = mean_squared_error
mae = MAE = mean_absolute_error
mape = MAPE = mean_absolute_percentage_error
msle = MSLE = mean_squared_logarithmic_error
kld = KLD = kullback_leibler_divergence


def is_categorical_crossentropy(loss):
  result = ((isinstance(loss, CategoricalCrossentropy) or
             (isinstance(loss, LossFunctionWrapper) and
              loss.fn == categorical_crossentropy) or
             (hasattr(loss, '__name__') and
              loss.__name__ == 'categorical_crossentropy') or
             (loss == 'categorical_crossentropy')))
  return result


@keras_export('keras.losses.serialize')
def serialize(loss):
  return serialize_keras_object(loss)


@keras_export('keras.losses.deserialize')
def deserialize(name, custom_objects=None):
  return deserialize_keras_object(
      name,
      module_objects=globals(),
      custom_objects=custom_objects,
      printable_module_name='loss function')


@keras_export('keras.losses.get')
def get(identifier):
  if identifier is None:
    return None
  if isinstance(identifier, six.string_types):
    identifier = str(identifier)
    return deserialize(identifier)
  if isinstance(identifier, dict):
    return deserialize(identifier)
  elif callable(identifier):
    return identifier
  else:
    raise ValueError('Could not interpret '
                     'loss function identifier:', identifier)


LABEL_DTYPES_FOR_LOSSES = {
    losses_impl.sparse_softmax_cross_entropy: 'int32',
    sparse_categorical_crossentropy: 'int32'
}