tf.keras.losses.CosineSimilarity

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. 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))

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 for more details.
name Optional name for the op.

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 this custom training tutorial for more details.
name (Optional) name for the loss.
**kwargs The keyword arguments that are passed on to fn.

Methods

from_config

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Instantiates a Loss from its config (output of get_config()).

Args
config Output of get_config().

Returns
A Loss instance.

get_config

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Returns the config dictionary for a Loss instance.

__call__

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Invokes the Loss instance.

Args
y_true Ground truth values. shape = [batch_size, d0, .. dN], except sparse loss functions such as sparse categorical crossentropy where shape = [batch_size, d0, .. dN-1]
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 ondN-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.