Metric Space Magnitude for Evaluating the Diversity of Latent Representations
This provides a rigorous multi-scale method for evaluating latent representation diversity, addressing a key challenge in generative modeling and representation learning.
The paper tackles the problem of evaluating diversity in latent representations by developing magnitude-based measures that formalize dissimilarity between magnitude functions of finite metric spaces, showing superior performance in automated diversity estimation, mode collapse detection, and generative model evaluation across text, image, and graph data.
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.