  The magnitude of a metric space is a novel invariant that provides a measure
of the 'effective size' of a space across multiple scales, while also capturing
numerous geometrical properties, such as curvature, density, or entropy. We
develop a family of magnitude-based measures of the intrinsic diversity of
latent representations, formalising a novel notion of dissimilarity between
magnitude functions of finite metric spaces. Our measures are provably stable
under perturbations of the data, can be efficiently calculated, and enable a
rigorous multi-scale characterisation and comparison of latent representations.
We show their utility and superior performance across different domains and
tasks, including (i) the automated estimation of diversity, (ii) the detection
of mode collapse, and (iii) the evaluation of generative models for text,
image, and graph data.
