Metric Space Magnitude for Evaluating the Diversity of Latent Representations
Katharina Limbeck, Rayna Andreeva, Rik Sarkar, Bastian Rieck
Abstract
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 the automated estimation of diversity, the detection of mode collapse, and the evaluation of generative models for text, image, and graph data.
BibTeX
@inproceedings{
limbeck2024metric,
title={Metric Space Magnitude for Evaluating the Diversity of Latent Representations},
author={Katharina Limbeck and Rayna Andreeva and Rik Sarkar and Bastian Rieck},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=glgZZAfssH}
}