Learning Generative Models across Incomparable Spaces

TL;DR

This paper introduces a method for learning generative models across incomparable spaces using Gromov-Wasserstein distance, enabling control over specific distribution aspects and broadening applications in manifold, relational, and cross-domain learning.

Contribution

It proposes a novel framework that leverages Gromov-Wasserstein distance to learn and steer generative models across spaces that are not directly comparable.

Findings

Successfully learns distributions across incomparable spaces.

Enables steering of generated distributions towards target properties.

Applicable to manifold, relational, and cross-domain learning tasks.

Abstract

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.