Using 'auto'/'sum_over_batch_size' reduction type.

Usage in framework

All in tf.keras.losses available loss functions can be used in our framework. Just use the class name as configuration key and the arguments as as dict.

YAML Configuration

E.g. for tf.losses.MeanAbsoluteError without no arguments

loss:
    MeanSquaredError:

or for tf.losses.Huber with arguments:

loss:
    Huber:
        delta: 0.3

Keras loss functions

BinaryCrossentropy class

tensorflow.keras.losses.BinaryCrossentropy(
    from_logits=False, label_smoothing=0, reduction="auto", name="binary_crossentropy"
)

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].

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

bce = tf.keras.losses.BinaryCrossentropy() bce(y_true, y_pred).numpy() 0.815

Calling with 'sample_weight'.

bce(y_true, y_pred, sample_weight=[1, 0]).numpy() 0.458

Using 'sum' reduction type.

bce = tf.keras.losses.BinaryCrossentropy( ... reduction=tf.keras.losses.Reduction.SUM) bce(y_true, y_pred).numpy() 1.630

Using 'none' reduction type.

bce = tf.keras.losses.BinaryCrossentropy( ... reduction=tf.keras.losses.Reduction.NONE) bce(y_true, y_pred).numpy() array([0.916 , 0.714], dtype=float32)

Usage with the tf.keras API:

model.compile(optimizer='sgd', loss=tf.keras.losses.BinaryCrossentropy())

CategoricalCrossentropy class

tensorflow.keras.losses.CategoricalCrossentropy(
    from_logits=False, label_smoothing=0, reduction="auto", name="categorical_crossentropy"
)

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].

Standalone usage:

y_true = [[0, 1, 0], [0, 0, 1]] y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]]

Using 'auto'/'sum_over_batch_size' reduction type.

cce = tf.keras.losses.CategoricalCrossentropy() cce(y_true, y_pred).numpy() 1.177

Calling with 'sample_weight'.

cce(y_true, y_pred, sample_weight=tf.constant([0.3, 0.7])).numpy() 0.814

Using 'sum' reduction type.

cce = tf.keras.losses.CategoricalCrossentropy( ... reduction=tf.keras.losses.Reduction.SUM) cce(y_true, y_pred).numpy() 2.354

Using 'none' reduction type.

cce = tf.keras.losses.CategoricalCrossentropy( ... reduction=tf.keras.losses.Reduction.NONE) cce(y_true, y_pred).numpy() array([0.0513, 2.303], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.CategoricalCrossentropy())

CategoricalHinge class

tensorflow.keras.losses.CategoricalHinge(reduction="auto", name="categorical_hinge")

Computes the categorical hinge loss between y_true and y_pred.

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

Standalone usage:

y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

h = tf.keras.losses.CategoricalHinge() h(y_true, y_pred).numpy() 1.4

Calling with 'sample_weight'.

h(y_true, y_pred, sample_weight=[1, 0]).numpy() 0.6

Using 'sum' reduction type.

h = tf.keras.losses.CategoricalHinge( ... reduction=tf.keras.losses.Reduction.SUM) h(y_true, y_pred).numpy() 2.8

Using 'none' reduction type.

h = tf.keras.losses.CategoricalHinge( ... reduction=tf.keras.losses.Reduction.NONE) h(y_true, y_pred).numpy() array([1.2, 1.6], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.CategoricalHinge())

CosineSimilarity class

tensorflow.keras.losses.CosineSimilarity(axis=-1, reduction="auto", name="cosine_similarity")

Computes the cosine similarity between labels and predictions.

Note that it is a number between -1 and 1. When it is a negative number between -1 and 0, 0 indicates orthogonality and values closer to -1 indicate greater similarity. The values closer to 1 indicate greater dissimilarity. This makes it usable as a loss function in a setting where you try to maximize the proximity between predictions and targets. If either y_true or y_pred is a zero vector, cosine similarity will be 0 regardless of the proximity between predictions and targets.

loss = -sum(l2_norm(y_true) * l2_norm(y_pred))

Standalone usage:

y_true = [[0., 1.], [1., 1.]] y_pred = [[1., 0.], [1., 1.]]

Using 'auto'/'sum_over_batch_size' reduction type.

cosine_loss = tf.keras.losses.CosineSimilarity(axis=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

cosine_loss(y_true, y_pred).numpy() -0.5

Calling with 'sample_weight'.

cosine_loss(y_true, y_pred, sample_weight=[0.8, 0.2]).numpy() -0.0999

Using 'sum' reduction type.

cosine_loss = tf.keras.losses.CosineSimilarity(axis=1, ... reduction=tf.keras.losses.Reduction.SUM) cosine_loss(y_true, y_pred).numpy() -0.999

Using 'none' reduction type.

cosine_loss = tf.keras.losses.CosineSimilarity(axis=1, ... reduction=tf.keras.losses.Reduction.NONE) cosine_loss(y_true, y_pred).numpy() array([-0., -0.999], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='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 this custom training [tutorial] (https://www.tensorflow.org/tutorials/distribute/custom_training) for more details. name: Optional name for the op.

Hinge class

tensorflow.keras.losses.Hinge(reduction="auto", name="hinge")

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.

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

h = tf.keras.losses.Hinge() h(y_true, y_pred).numpy() 1.3

Calling with 'sample_weight'.

h(y_true, y_pred, sample_weight=[1, 0]).numpy() 0.55

Using 'sum' reduction type.

h = tf.keras.losses.Hinge( ... reduction=tf.keras.losses.Reduction.SUM) h(y_true, y_pred).numpy() 2.6

Using 'none' reduction type.

h = tf.keras.losses.Hinge( ... reduction=tf.keras.losses.Reduction.NONE) h(y_true, y_pred).numpy() array([1.1, 1.5], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.Hinge())

Huber class

tensorflow.keras.losses.Huber(delta=1.0, reduction="auto", name="huber_loss")

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

Standalone usage:

y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

h = tf.keras.losses.Huber() h(y_true, y_pred).numpy() 0.155

Calling with 'sample_weight'.

h(y_true, y_pred, sample_weight=[1, 0]).numpy() 0.09

Using 'sum' reduction type.

h = tf.keras.losses.Huber( ... reduction=tf.keras.losses.Reduction.SUM) h(y_true, y_pred).numpy() 0.31

Using 'none' reduction type.

h = tf.keras.losses.Huber( ... reduction=tf.keras.losses.Reduction.NONE) h(y_true, y_pred).numpy() array([0.18, 0.13], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.Huber())

kl_divergence function

tensorflow.keras.losses.KLD(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

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)).astype(np.float64) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.kullback_leibler_divergence(y_true, y_pred) assert loss.shape == (2,) y_true = tf.keras.backend.clip(y_true, 1e-7, 1) y_pred = tf.keras.backend.clip(y_pred, 1e-7, 1) assert np.array_equal( ... loss.numpy(), np.sum(y_true * np.log(y_true / y_pred), axis=-1))

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.

KLDivergence class

tensorflow.keras.losses.KLDivergence(reduction="auto", name="kl_divergence")

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

Standalone usage:

y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

kl = tf.keras.losses.KLDivergence() kl(y_true, y_pred).numpy() 0.458

Calling with 'sample_weight'.

kl(y_true, y_pred, sample_weight=[0.8, 0.2]).numpy() 0.366

Using 'sum' reduction type.

kl = tf.keras.losses.KLDivergence( ... reduction=tf.keras.losses.Reduction.SUM) kl(y_true, y_pred).numpy() 0.916

Using 'none' reduction type.

kl = tf.keras.losses.KLDivergence( ... reduction=tf.keras.losses.Reduction.NONE) kl(y_true, y_pred).numpy() array([0.916, -3.08e-06], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.KLDivergence())

LogCosh class

tensorflow.keras.losses.LogCosh(reduction="auto", name="log_cosh")

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.

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [0., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

l = tf.keras.losses.LogCosh() l(y_true, y_pred).numpy() 0.108

Calling with 'sample_weight'.

l(y_true, y_pred, sample_weight=[0.8, 0.2]).numpy() 0.087

Using 'sum' reduction type.

l = tf.keras.losses.LogCosh( ... reduction=tf.keras.losses.Reduction.SUM) l(y_true, y_pred).numpy() 0.217

Using 'none' reduction type.

l = tf.keras.losses.LogCosh( ... reduction=tf.keras.losses.Reduction.NONE) l(y_true, y_pred).numpy() array([0.217, 0.], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.LogCosh())

Loss class

tensorflow.keras.losses.Loss(reduction="auto", name=None)

Loss base class.

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

Example subclass implementation:

class MeanSquaredError(Loss):

  def call(self, y_true, y_pred):
    y_pred = tf.convert_to_tensor_v2(y_pred)
    y_true = tf.cast(y_true, y_pred.dtype)
    return tf.reduce_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 this custom training tutorial for more details on this.

You can implement 'SUM_OVER_BATCH_SIZE' using global batch size like:

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))

mean_absolute_error function

tensorflow.keras.losses.MAE(y_true, y_pred)

Computes the mean absolute error between labels and predictions.

loss = mean(abs(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.abs(y_true - y_pred), axis=-1))

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].

mean_absolute_percentage_error function

tensorflow.keras.losses.MAPE(y_true, y_pred)

Computes the mean absolute percentage error between y_true and y_pred.

loss = 100 * mean(abs((y_true - y_pred) / y_true), axis=-1)

Standalone usage:

y_true = np.random.random(size=(2, 3)) y_true = np.maximum(y_true, 1e-7) # Prevent division by zero y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_percentage_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), ... 100. * np.mean(np.abs((y_true - y_pred) / y_true), axis=-1))

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].

mean_squared_error function

tensorflow.keras.losses.MSE(y_true, y_pred)

Computes the mean squared error between labels and predictions.

After computing the squared distance between the inputs, the mean value over the last dimension is returned.

loss = mean(square(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.square(y_true - y_pred), axis=-1))

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].

mean_squared_logarithmic_error function

tensorflow.keras.losses.MSLE(y_true, y_pred)

Computes the mean squared logarithmic error between y_true and y_pred.

loss = mean(square(log(y_true + 1) - log(y_pred + 1)), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_logarithmic_error(y_true, y_pred) assert loss.shape == (2,) y_true = np.maximum(y_true, 1e-7) y_pred = np.maximum(y_pred, 1e-7) assert np.allclose( ... loss.numpy(), ... np.mean( ... np.square(np.log(y_true + 1.) - np.log(y_pred + 1.)), axis=-1))

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].

MeanAbsoluteError class

tensorflow.keras.losses.MeanAbsoluteError(reduction="auto", name="mean_absolute_error")

Computes the mean of absolute difference between labels and predictions.

loss = abs(y_true - y_pred)

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

mae = tf.keras.losses.MeanAbsoluteError() mae(y_true, y_pred).numpy() 0.5

Calling with 'sample_weight'.

mae(y_true, y_pred, sample_weight=[0.7, 0.3]).numpy() 0.25

Using 'sum' reduction type.

mae = tf.keras.losses.MeanAbsoluteError( ... reduction=tf.keras.losses.Reduction.SUM) mae(y_true, y_pred).numpy() 1.0

Using 'none' reduction type.

mae = tf.keras.losses.MeanAbsoluteError( ... reduction=tf.keras.losses.Reduction.NONE) mae(y_true, y_pred).numpy() array([0.5, 0.5], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.MeanAbsoluteError())

MeanAbsolutePercentageError class

tensorflow.keras.losses.MeanAbsolutePercentageError(
    reduction="auto", name="mean_absolute_percentage_error"
)

Computes the mean absolute percentage error between y_true and y_pred.

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

Standalone usage:

y_true = [[2., 1.], [2., 3.]] y_pred = [[1., 1.], [1., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

mape = tf.keras.losses.MeanAbsolutePercentageError() mape(y_true, y_pred).numpy() 50.

Calling with 'sample_weight'.

mape(y_true, y_pred, sample_weight=[0.7, 0.3]).numpy() 20.

Using 'sum' reduction type.

mape = tf.keras.losses.MeanAbsolutePercentageError( ... reduction=tf.keras.losses.Reduction.SUM) mape(y_true, y_pred).numpy() 100.

Using 'none' reduction type.

mape = tf.keras.losses.MeanAbsolutePercentageError( ... reduction=tf.keras.losses.Reduction.NONE) mape(y_true, y_pred).numpy() array([25., 75.], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd',
              loss=tf.keras.losses.MeanAbsolutePercentageError())

MeanSquaredError class

tensorflow.keras.losses.MeanSquaredError(reduction="auto", name="mean_squared_error")

Computes the mean of squares of errors between labels and predictions.

loss = square(y_true - y_pred)

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

mse = tf.keras.losses.MeanSquaredError() mse(y_true, y_pred).numpy() 0.5

Calling with 'sample_weight'.

mse(y_true, y_pred, sample_weight=[0.7, 0.3]).numpy() 0.25

Using 'sum' reduction type.

mse = tf.keras.losses.MeanSquaredError( ... reduction=tf.keras.losses.Reduction.SUM) mse(y_true, y_pred).numpy() 1.0

Using 'none' reduction type.

mse = tf.keras.losses.MeanSquaredError( ... reduction=tf.keras.losses.Reduction.NONE) mse(y_true, y_pred).numpy() array([0.5, 0.5], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.MeanSquaredError())

MeanSquaredLogarithmicError class

tensorflow.keras.losses.MeanSquaredLogarithmicError(
    reduction="auto", name="mean_squared_logarithmic_error"
)

Computes the mean squared logarithmic error between y_true and y_pred.

loss = square(log(y_true + 1.) - log(y_pred + 1.))

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [1., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

msle = tf.keras.losses.MeanSquaredLogarithmicError() msle(y_true, y_pred).numpy() 0.240

Calling with 'sample_weight'.

msle(y_true, y_pred, sample_weight=[0.7, 0.3]).numpy() 0.120

Using 'sum' reduction type.

msle = tf.keras.losses.MeanSquaredLogarithmicError( ... reduction=tf.keras.losses.Reduction.SUM) msle(y_true, y_pred).numpy() 0.480

Using 'none' reduction type.

msle = tf.keras.losses.MeanSquaredLogarithmicError( ... reduction=tf.keras.losses.Reduction.NONE) msle(y_true, y_pred).numpy() array([0.240, 0.240], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd',
              loss=tf.keras.losses.MeanSquaredLogarithmicError())

Poisson class

tensorflow.keras.losses.Poisson(reduction="auto", name="poisson")

Computes the Poisson loss between y_true and y_pred.

loss = y_pred - y_true * log(y_pred)

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[1., 1.], [0., 0.]]

Using 'auto'/'sum_over_batch_size' reduction type.

p = tf.keras.losses.Poisson() p(y_true, y_pred).numpy() 0.5

Calling with 'sample_weight'.

p(y_true, y_pred, sample_weight=[0.8, 0.2]).numpy() 0.4

Using 'sum' reduction type.

p = tf.keras.losses.Poisson( ... reduction=tf.keras.losses.Reduction.SUM) p(y_true, y_pred).numpy() 0.999

Using 'none' reduction type.

p = tf.keras.losses.Poisson( ... reduction=tf.keras.losses.Reduction.NONE) p(y_true, y_pred).numpy() array([0.999, 0.], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.Poisson())

ReductionV2 class

tensorflow.keras.losses.Reduction(*args, **kwargs)

Types of loss reduction.

Contains the following values:

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, we expect reduction value to be SUM or NONE. Using AUTO in that case will raise an error.
NONE: Weighted losses with one dimension reduced (axis=-1, or axis specified by loss function). When this reduction type used with built-in Keras training loops like fit/evaluate, the unreduced vector loss is passed to the optimizer but the reported loss will be a scalar value.
SUM: Scalar sum of weighted losses.
SUM_OVER_BATCH_SIZE: Scalar SUM divided by number of elements in losses. This reduction type is not supported when used with tf.distribute.Strategy outside of built-in training loops like tf.keras compile/fit.

You can implement 'SUM_OVER_BATCH_SIZE' using global batch size like:

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)

Please see the custom training guide # pylint: disable=line-too-long for more details on this.

SparseCategoricalCrossentropy class

tensorflow.keras.losses.SparseCategoricalCrossentropy(
    from_logits=False, reduction="auto", name="sparse_categorical_crossentropy"
)

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].

Standalone usage:

y_true = [1, 2] y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]]

Using 'auto'/'sum_over_batch_size' reduction type.

scce = tf.keras.losses.SparseCategoricalCrossentropy() scce(y_true, y_pred).numpy() 1.177

Calling with 'sample_weight'.

scce(y_true, y_pred, sample_weight=tf.constant([0.3, 0.7])).numpy() 0.814

Using 'sum' reduction type.

scce = tf.keras.losses.SparseCategoricalCrossentropy( ... reduction=tf.keras.losses.Reduction.SUM) scce(y_true, y_pred).numpy() 2.354

Using 'none' reduction type.

scce = tf.keras.losses.SparseCategoricalCrossentropy( ... reduction=tf.keras.losses.Reduction.NONE) scce(y_true, y_pred).numpy() array([0.0513, 2.303], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd',
              loss=tf.keras.losses.SparseCategoricalCrossentropy())

SquaredHinge class

tensorflow.keras.losses.SquaredHinge(reduction="auto", name="squared_hinge")

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.

Standalone usage:

y_true = [[0., 1.], [0., 0.]] y_pred = [[0.6, 0.4], [0.4, 0.6]]

Using 'auto'/'sum_over_batch_size' reduction type.

h = tf.keras.losses.SquaredHinge() h(y_true, y_pred).numpy() 1.86

Calling with 'sample_weight'.

h(y_true, y_pred, sample_weight=[1, 0]).numpy() 0.73

Using 'sum' reduction type.

h = tf.keras.losses.SquaredHinge( ... reduction=tf.keras.losses.Reduction.SUM) h(y_true, y_pred).numpy() 3.72

Using 'none' reduction type.

h = tf.keras.losses.SquaredHinge( ... reduction=tf.keras.losses.Reduction.NONE) h(y_true, y_pred).numpy() array([1.46, 2.26], dtype=float32)

Usage with the compile() API:

model.compile(optimizer='sgd', loss=tf.keras.losses.SquaredHinge())

binary_crossentropy function

tensorflow.keras.losses.binary_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)

Computes the binary crossentropy loss.

Standalone usage:

y_true = [[0, 1], [0, 0]] y_pred = [[0.6, 0.4], [0.4, 0.6]] loss = tf.keras.losses.binary_crossentropy(y_true, y_pred) assert loss.shape == (2,) loss.numpy() array([0.916 , 0.714], dtype=float32)

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].

categorical_crossentropy function

tensorflow.keras.losses.categorical_crossentropy(y_true, y_pred, from_logits=False, label_smoothing=0)

Computes the categorical crossentropy loss.

Standalone usage:

y_true = [[0, 1, 0], [0, 0, 1]] y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] loss = tf.keras.losses.categorical_crossentropy(y_true, y_pred) assert loss.shape == (2,) loss.numpy() array([0.0513, 2.303], dtype=float32)

Args: y_true: Tensor of one-hot 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.

categorical_hinge function

tensorflow.keras.losses.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=maximum((1-y_true)*y_pred) and pos=sum(y_true*y_pred)

Standalone usage:

y_true = np.random.randint(0, 3, size=(2,)) y_true = tf.keras.utils.to_categorical(y_true, num_classes=3) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.categorical_hinge(y_true, y_pred) assert loss.shape == (2,) pos = np.sum(y_true * y_pred, axis=-1) neg = np.amax((1. - y_true) * y_pred, axis=-1) assert np.array_equal(loss.numpy(), np.maximum(0., neg - pos + 1.))

Args: y_true: The ground truth values. y_true values are expected to be 0 or 1. y_pred: The predicted values.

Returns: Categorical hinge loss values.

cosine_similarity function

tensorflow.keras.losses.cosine_similarity(y_true, y_pred, axis=-1)

Computes the cosine similarity between labels and predictions.

Note that it is a number between -1 and 1. When it is a negative number between -1 and 0, 0 indicates orthogonality and values closer to -1 indicate greater similarity. The values closer to 1 indicate greater dissimilarity. This makes it usable as a loss function in a setting where you try to maximize the proximity between predictions and targets. If either y_true or y_pred is a zero vector, cosine similarity will be 0 regardless of the proximity between predictions and targets.

loss = -sum(l2_norm(y_true) * l2_norm(y_pred))

Standalone usage:

y_true = [[0., 1.], [1., 1.], [1., 1.]] y_pred = [[1., 0.], [1., 1.], [-1., -1.]] loss = tf.keras.losses.cosine_similarity(y_true, y_pred, axis=1) loss.numpy() array([-0., -0.999, 0.999], dtype=float32)

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

Returns: Cosine similarity tensor.

deserialize function

tensorflow.keras.losses.deserialize(name, custom_objects=None)

Deserializes a serialized loss class/function instance.

Arguments: name: Loss configuration. custom_objects: Optional dictionary mapping names (strings) to custom objects (classes and functions) to be considered during deserialization.

Returns: A Keras Loss instance or a loss function.

get function

tensorflow.keras.losses.get(identifier)

Retrieves a Keras loss as a function/Loss class instance.

The identifier may be the string name of a loss function or Loss class.

loss = tf.keras.losses.get("categorical_crossentropy") type(loss) loss = tf.keras.losses.get("CategoricalCrossentropy") type(loss)

You can also specify config of the loss to this function by passing dict containing class_name and config as an identifier. Also note that the class_name must map to a Loss class

identifier = {"class_name": "CategoricalCrossentropy", ... "config": {"from_logits": True}} loss = tf.keras.losses.get(identifier) type(loss)

Arguments: identifier: A loss identifier. One of None or string name of a loss function/class or loss configuration dictionary or a loss function or a loss class instance

Returns: A Keras loss as a function/ Loss class instance.

Raises: ValueError: If identifier cannot be interpreted.

hinge function

tensorflow.keras.losses.hinge(y_true, y_pred)

Computes the hinge loss between y_true and y_pred.

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

Standalone usage:

y_true = np.random.choice([-1, 1], size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.hinge(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), ... np.mean(np.maximum(1. - y_true * y_pred, 0.), axis=-1))

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].

huber function

tensorflow.keras.losses.huber(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.

kl_divergence function

tensorflow.keras.losses.kl_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

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)).astype(np.float64) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.kullback_leibler_divergence(y_true, y_pred) assert loss.shape == (2,) y_true = tf.keras.backend.clip(y_true, 1e-7, 1) y_pred = tf.keras.backend.clip(y_pred, 1e-7, 1) assert np.array_equal( ... loss.numpy(), np.sum(y_true * np.log(y_true / y_pred), axis=-1))

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.

kl_divergence function

tensorflow.keras.losses.kld(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

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)).astype(np.float64) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.kullback_leibler_divergence(y_true, y_pred) assert loss.shape == (2,) y_true = tf.keras.backend.clip(y_true, 1e-7, 1) y_pred = tf.keras.backend.clip(y_pred, 1e-7, 1) assert np.array_equal( ... loss.numpy(), np.sum(y_true * np.log(y_true / y_pred), axis=-1))

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.

kl_divergence function

tensorflow.keras.losses.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

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)).astype(np.float64) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.kullback_leibler_divergence(y_true, y_pred) assert loss.shape == (2,) y_true = tf.keras.backend.clip(y_true, 1e-7, 1) y_pred = tf.keras.backend.clip(y_pred, 1e-7, 1) assert np.array_equal( ... loss.numpy(), np.sum(y_true * np.log(y_true / y_pred), axis=-1))

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.

log_cosh function

tensorflow.keras.losses.log_cosh(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.

Standalone usage:

y_true = np.random.random(size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.logcosh(y_true, y_pred) assert loss.shape == (2,) x = y_pred - y_true assert np.allclose( ... loss.numpy(), ... np.mean(x + np.log(np.exp(-2. * x) + 1.) - math_ops.log(2.), axis=-1), ... atol=1e-5)

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].

log_cosh function

tensorflow.keras.losses.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.

Standalone usage:

y_true = np.random.random(size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.logcosh(y_true, y_pred) assert loss.shape == (2,) x = y_pred - y_true assert np.allclose( ... loss.numpy(), ... np.mean(x + np.log(np.exp(-2. * x) + 1.) - math_ops.log(2.), axis=-1), ... atol=1e-5)

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].

mean_absolute_error function

tensorflow.keras.losses.mae(y_true, y_pred)

Computes the mean absolute error between labels and predictions.

loss = mean(abs(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.abs(y_true - y_pred), axis=-1))

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].

mean_absolute_percentage_error function

tensorflow.keras.losses.mape(y_true, y_pred)

Computes the mean absolute percentage error between y_true and y_pred.

loss = 100 * mean(abs((y_true - y_pred) / y_true), axis=-1)

Standalone usage:

y_true = np.random.random(size=(2, 3)) y_true = np.maximum(y_true, 1e-7) # Prevent division by zero y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_percentage_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), ... 100. * np.mean(np.abs((y_true - y_pred) / y_true), axis=-1))

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].

mean_absolute_error function

tensorflow.keras.losses.mean_absolute_error(y_true, y_pred)

Computes the mean absolute error between labels and predictions.

loss = mean(abs(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.abs(y_true - y_pred), axis=-1))

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].

mean_absolute_percentage_error function

tensorflow.keras.losses.mean_absolute_percentage_error(y_true, y_pred)

Computes the mean absolute percentage error between y_true and y_pred.

loss = 100 * mean(abs((y_true - y_pred) / y_true), axis=-1)

Standalone usage:

y_true = np.random.random(size=(2, 3)) y_true = np.maximum(y_true, 1e-7) # Prevent division by zero y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_absolute_percentage_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), ... 100. * np.mean(np.abs((y_true - y_pred) / y_true), axis=-1))

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].

mean_squared_error function

tensorflow.keras.losses.mean_squared_error(y_true, y_pred)

Computes the mean squared error between labels and predictions.

After computing the squared distance between the inputs, the mean value over the last dimension is returned.

loss = mean(square(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.square(y_true - y_pred), axis=-1))

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].

mean_squared_logarithmic_error function

tensorflow.keras.losses.mean_squared_logarithmic_error(y_true, y_pred)

Computes the mean squared logarithmic error between y_true and y_pred.

loss = mean(square(log(y_true + 1) - log(y_pred + 1)), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_logarithmic_error(y_true, y_pred) assert loss.shape == (2,) y_true = np.maximum(y_true, 1e-7) y_pred = np.maximum(y_pred, 1e-7) assert np.allclose( ... loss.numpy(), ... np.mean( ... np.square(np.log(y_true + 1.) - np.log(y_pred + 1.)), axis=-1))

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].

mean_squared_error function

tensorflow.keras.losses.mse(y_true, y_pred)

Computes the mean squared error between labels and predictions.

After computing the squared distance between the inputs, the mean value over the last dimension is returned.

loss = mean(square(y_true - y_pred), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_error(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), np.mean(np.square(y_true - y_pred), axis=-1))

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].

mean_squared_logarithmic_error function

tensorflow.keras.losses.msle(y_true, y_pred)

Computes the mean squared logarithmic error between y_true and y_pred.

loss = mean(square(log(y_true + 1) - log(y_pred + 1)), axis=-1)

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.mean_squared_logarithmic_error(y_true, y_pred) assert loss.shape == (2,) y_true = np.maximum(y_true, 1e-7) y_pred = np.maximum(y_pred, 1e-7) assert np.allclose( ... loss.numpy(), ... np.mean( ... np.square(np.log(y_true + 1.) - np.log(y_pred + 1.)), axis=-1))

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].

poisson function

tensorflow.keras.losses.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).

Standalone usage:

y_true = np.random.randint(0, 2, size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.poisson(y_true, y_pred) assert loss.shape == (2,) y_pred = y_pred + 1e-7 assert np.allclose( ... loss.numpy(), np.mean(y_pred - y_true * np.log(y_pred), axis=-1), ... atol=1e-5)

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.

serialize function

tensorflow.keras.losses.serialize(loss)

Serializes loss function or Loss instance.

Arguments: loss: A Keras Loss instance or a loss function.

Returns: Loss configuration dictionary.

sparse_categorical_crossentropy function

tensorflow.keras.losses.sparse_categorical_crossentropy(y_true, y_pred, from_logits=False, axis=-1)

Computes the sparse categorical crossentropy loss.

Standalone usage:

y_true = [1, 2] y_pred = [[0.05, 0.95, 0], [0.1, 0.8, 0.1]] loss = tf.keras.losses.sparse_categorical_crossentropy(y_true, y_pred) assert loss.shape == (2,) loss.numpy() array([0.0513, 2.303], dtype=float32)

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.

squared_hinge function

tensorflow.keras.losses.squared_hinge(y_true, y_pred)

Computes the squared hinge loss between y_true and y_pred.

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

Standalone usage:

y_true = np.random.choice([-1, 1], size=(2, 3)) y_pred = np.random.random(size=(2, 3)) loss = tf.keras.losses.squared_hinge(y_true, y_pred) assert loss.shape == (2,) assert np.array_equal( ... loss.numpy(), ... np.mean(np.square(np.maximum(1. - y_true * y_pred, 0.)), axis=-1))

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].