Learning Generative Models across Incomparable Spaces
This work addresses the need for more adaptable generative models in machine learning, particularly for tasks requiring selective feature learning, but it appears incremental as it builds upon existing GAN frameworks with a relational discrepancy measure.
The paper tackles the problem of learning generative models that capture only certain aspects of a reference distribution while modifying others, such as style or dimension, by proposing an approach based on the Gromov-Wasserstein distance. The result is a flexible framework applicable to manifold learning, relational learning, and cross-domain learning, though no concrete performance numbers are provided.
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.