(Deep) Generative Geodesics

TL;DR

This paper introduces a new Riemannian metric for generative models that measures data similarity independently of model parametrization, enabling efficient computation of geodesics for applications like clustering and visualization.

Contribution

The work presents a parametrization-agnostic Riemannian metric for generative models and demonstrates its use in computing geodesics for data analysis tasks.

Findings

The metric is independent of model parametrization.

Efficient algorithms for geodesic computation are proposed.

Applications include clustering, visualization, and interpolation.

Abstract

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization of the generative model and requires only the evaluation of its data likelihood. Moreover, the metric leads to the conceptual definition of generative distances and generative geodesics, whose computation can be done efficiently in the data space. Their approximations are proven to converge to their true values under mild conditions. We showcase three proof-of-concept applications of this global metric, including clustering, data visualization, and data interpolation, thus providing new tools to support the geometrical understanding of generative models.