(Deep) Generative Geodesics
This work provides new tools for analyzing generative models, which could benefit researchers in machine learning, but it appears incremental as it builds on existing geometric concepts.
The authors tackled the problem of understanding the global geometry of generative models by introducing a new Riemannian metric that measures similarity between data points based solely on data likelihood, and they demonstrated its applications in clustering, visualization, and interpolation.
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.