► Keras 3 API documentation / Losses / Regression losses

Regression losses

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MeanSquaredError class

keras.losses.MeanSquaredError(
    reduction="sum_over_batch_size", name="mean_squared_error", dtype=None
)

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

Formula:

loss = mean(square(y_true - y_pred))

Arguments

  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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MeanAbsoluteError class

keras.losses.MeanAbsoluteError(
    reduction="sum_over_batch_size", name="mean_absolute_error", dtype=None
)

Computes the mean of absolute difference between labels and predictions.

Formula:

loss = mean(abs(y_true - y_pred))

Arguments

  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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MeanAbsolutePercentageError class

keras.losses.MeanAbsolutePercentageError(
    reduction="sum_over_batch_size", name="mean_absolute_percentage_error", dtype=None
)

Computes the mean absolute percentage error between y_true & y_pred.

Formula:

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

Arguments

  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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MeanSquaredLogarithmicError class

keras.losses.MeanSquaredLogarithmicError(
    reduction="sum_over_batch_size", name="mean_squared_logarithmic_error", dtype=None
)

Computes the mean squared logarithmic error between y_true & y_pred.

Formula:

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

Arguments

  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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CosineSimilarity class

keras.losses.CosineSimilarity(
    axis=-1, reduction="sum_over_batch_size", name="cosine_similarity", dtype=None
)

Computes the cosine similarity between y_true & y_pred.

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. 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.

Formula:

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

Arguments

  • axis: The axis along which the cosine similarity is computed (the features axis). Defaults to -1.
  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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Huber class

keras.losses.Huber(
    delta=1.0, reduction="sum_over_batch_size", name="huber_loss", dtype=None
)

Computes the Huber loss between y_true & y_pred.

Formula:

for x in error:
    if abs(x) <= delta:
        loss.append(0.5 * x^2)
    elif abs(x) > delta:
        loss.append(delta * abs(x) - 0.5 * delta^2)

loss = mean(loss, axis=-1)

See: Huber loss.

Arguments

  • delta: A float, the point where the Huber loss function changes from a quadratic to linear.
  • reduction: Type of reduction to apply to loss. Options are "sum", "sum_over_batch_size" or None. Defaults to "sum_over_batch_size".
  • name: Optional name for the instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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LogCosh class

keras.losses.LogCosh(reduction="sum_over_batch_size", name="log_cosh", dtype=None)

Computes the logarithm of the hyperbolic cosine of the prediction error.

Formula:

error = y_pred - y_true
logcosh = mean(log((exp(error) + exp(-error))/2), axis=-1)`

where x is the error y_pred - y_true.

Arguments

  • reduction: Type of reduction to apply to loss. Options are "sum", "sum_over_batch_size" or None. Defaults to "sum_over_batch_size".
  • name: Optional name for the instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

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Tversky class

keras.losses.Tversky(
    alpha=0.5, beta=0.5, reduction="sum_over_batch_size", name="tversky", dtype=None
)

Computes the Tversky loss value between y_true and y_pred.

This loss function is weighted by the alpha and beta coefficients that penalize false positives and false negatives.

With alpha=0.5 and beta=0.5, the loss value becomes equivalent to Dice Loss.

Arguments

  • alpha: The coefficient controlling incidence of false positives. Defaults to 0.5.
  • beta: The coefficient controlling incidence of false negatives. Defaults to 0.5.
  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

Returns

Tversky loss value.

Reference

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Dice class

keras.losses.Dice(
    reduction="sum_over_batch_size", name="dice", axis=None, dtype=None
)

Computes the Dice loss value between y_true and y_pred.

Formula:

loss = 1 - (2 * sum(y_true * y_pred)) / (sum(y_true) + sum(y_pred))

Arguments

  • reduction: Type of reduction to apply to the loss. In almost all cases this should be "sum_over_batch_size". Supported options are "sum", "sum_over_batch_size" or None.
  • name: Optional name for the loss instance.
  • axis: Tuple for which dimensions the loss is calculated. Defaults to None.
  • dtype: The dtype of the loss's computations. Defaults to None, which means using keras.backend.floatx(). keras.backend.floatx() is a "float32" unless set to different value (via keras.backend.set_floatx()). If a keras.DTypePolicy is provided, then the compute_dtype will be utilized.

Returns

Dice loss value.

Example

>>> y_true = [[[[1.0], [1.0]], [[0.0], [0.0]]],
...           [[[1.0], [1.0]], [[0.0], [0.0]]]]
>>> y_pred = [[[[0.0], [1.0]], [[0.0], [1.0]]],
...           [[[0.4], [0.0]], [[0.0], [0.9]]]]
>>> axis = (1, 2, 3)
>>> loss = keras.losses.dice(y_true, y_pred, axis=axis)
>>> assert loss.shape == (2,)
>>> loss
array([0.5, 0.75757575], shape=(2,), dtype=float32)

>>> loss = keras.losses.dice(y_true, y_pred)
>>> assert loss.shape == ()
>>> loss
array(0.6164384, shape=(), dtype=float32)

>>> y_true = np.array(y_true)
>>> y_pred = np.array(y_pred)
>>> loss = keras.losses.Dice(axis=axis, reduction=None)(y_true, y_pred)
>>> assert loss.shape == (2,)
>>> loss
array([0.5, 0.75757575], shape=(2,), dtype=float32)

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mean_squared_error function

keras.losses.mean_squared_error(y_true, y_pred)

Computes the mean squared error between labels and predictions.

Formula:

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

Example

>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_squared_error(y_true, y_pred)

Arguments

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

Returns

Mean squared error values with shape = [batch_size, d0, .. dN-1].

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mean_absolute_error function

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)

Arguments

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

Returns

Mean absolute error values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_absolute_error(y_true, y_pred)

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mean_absolute_percentage_error function

keras.losses.mean_absolute_percentage_error(y_true, y_pred)

Computes the mean absolute percentage error between y_true & y_pred.

Formula:

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

Division by zero is prevented by dividing by maximum(y_true, epsilon) where epsilon = keras.backend.epsilon() (default to 1e-7).

Arguments

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

Returns

Mean absolute percentage error values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.random(size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_absolute_percentage_error(y_true, y_pred)

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mean_squared_logarithmic_error function

keras.losses.mean_squared_logarithmic_error(y_true, y_pred)

Computes the mean squared logarithmic error between y_true & y_pred.

Formula:

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

Note that y_pred and y_true cannot be less or equal to 0. Negative values and 0 values will be replaced with keras.backend.epsilon() (default to 1e-7).

Arguments

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

Returns

Mean squared logarithmic error values with shape = [batch_size, d0, .. dN-1].

Example

>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_squared_logarithmic_error(y_true, y_pred)

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cosine_similarity function

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

Computes the cosine similarity between labels and predictions.

Formula:

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

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. 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.

Arguments

  • y_true: Tensor of true targets.
  • y_pred: Tensor of predicted targets.
  • axis: Axis along which to determine similarity. Defaults to -1.

Returns

Cosine similarity tensor.

Example

>>> y_true = [[0., 1.], [1., 1.], [1., 1.]]
>>> y_pred = [[1., 0.], [1., 1.], [-1., -1.]]
>>> loss = keras.losses.cosine_similarity(y_true, y_pred, axis=-1)
[-0., -0.99999994, 0.99999994]

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huber function

keras.losses.huber(y_true, y_pred, delta=1.0)

Computes Huber loss value.

Formula:

for x in error:
    if abs(x) <= delta:
        loss.append(0.5 * x^2)
    elif abs(x) > delta:
        loss.append(delta * abs(x) - 0.5 * delta^2)

loss = mean(loss, axis=-1)

See: Huber loss.

Example

>>> y_true = [[0, 1], [0, 0]]
>>> y_pred = [[0.6, 0.4], [0.4, 0.6]]
>>> loss = keras.losses.huber(y_true, y_pred)
0.155

Arguments

  • 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. Defaults to 1.0.

Returns

Tensor with one scalar loss entry per sample.

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log_cosh function

keras.losses.log_cosh(y_true, y_pred)

Logarithm of the hyperbolic cosine of the prediction error.

Formula:

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

Note that 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.

Example

>>> y_true = [[0., 1.], [0., 0.]]
>>> y_pred = [[1., 1.], [0., 0.]]
>>> loss = keras.losses.log_cosh(y_true, y_pred)
0.108

Arguments

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

Returns

Logcosh error values with shape = [batch_size, d0, .. dN-1].

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tversky function

keras.losses.tversky(y_true, y_pred, alpha=0.5, beta=0.5)

Computes the Tversky loss value between y_true and y_pred.

This loss function is weighted by the alpha and beta coefficients that penalize false positives and false negatives.

With alpha=0.5 and beta=0.5, the loss value becomes equivalent to Dice Loss.

Arguments

  • y_true: tensor of true targets.
  • y_pred: tensor of predicted targets.
  • alpha: coefficient controlling incidence of false positives.
  • beta: coefficient controlling incidence of false negatives.

Returns

Tversky loss value.

Reference

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dice function

keras.losses.dice(y_true, y_pred, axis=None)

Computes the Dice loss value between y_true and y_pred.

Formula:

loss = 1 - (2 * sum(y_true * y_pred)) / (sum(y_true) + sum(y_pred))

Arguments

  • y_true: tensor of true targets.
  • y_pred: tensor of predicted targets.
  • axis: tuple for which dimensions the loss is calculated

Returns

Dice loss value.

Regression losses
MeanSquaredError class
MeanAbsoluteError class
MeanAbsolutePercentageError class
MeanSquaredLogarithmicError class
CosineSimilarity class
Huber class
LogCosh class
Tversky class
Dice class
mean_squared_error function
mean_absolute_error function
mean_absolute_percentage_error function
mean_squared_logarithmic_error function
cosine_similarity function
huber function
log_cosh function
tversky function
dice function