The relative entropy D KL ( P ∥ ∥ Q ) can be thought of geometrically as a statistical distance, a measure of how far the distribution Q is from the distribution P. Geometrically it is a divergence : an asymmetric, generalized form of squared distance. The cross-entropy H ( P , Q ) is itself such a measurement (formally a loss function), but it cannot be thought of as a distance, since H ( P , P ) =: H ( P ) is not zero. This can be fixed by subtracting H ( P ) to make D KL ( P ∥ ∥ Q ) agree more closely with our notion of distance, as the excess loss. The resulting function is asymmetric, and while this can be symmetrized (see § Symmetrised divergence), the asymmetric form is more useful. See § Interpretations for more on the geometric interpretation.