Introducing Curvature to the Label Space

TL;DR

This paper proposes adding curvature to the label space in classification tasks to better reflect real-world class relationships, moving beyond the limitations of one-hot encoding.

Contribution

It introduces a curvature-based approach to label space using a metric tensor, providing a flexible, learning-algorithm agnostic solution for more accurate class relationship representation.

Findings

The curvature approach better models class similarities and differences.

The method is compatible with existing learning algorithms.

Future work includes autoencoder-based metric parameterizations.

Abstract

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.