  One-hot encoding is a labelling system that embeds classes as standard basis
vectors in a label space. Despite seeing near-universal use in supervised
categorical classification tasks, the scheme is problematic in its geometric
implication that, as all classes are equally distant, all classes are equally
different. This is inconsistent with most, if not all, real-world tasks due to
the prevalence of ancestral and convergent relationships generating a varying
degree of morphological similarity across classes. We address this issue by
introducing curvature to the label-space using a metric tensor as a
self-regulating method that better represents these relationships as a bolt-on,
learning-algorithm agnostic solution. We propose both general constraints and
specific statistical parameterizations of the metric and identify a direction
for future research using autoencoder-based parameterizations.
