Geometrically Enriched Latent Spaces
This work addresses interpretability issues in generative models for researchers and practitioners, though it appears incremental as it builds on existing methods with a geometric twist.
The paper tackles the problem of misleading biases in generative models by proposing a Riemannian manifold ambient space instead of Euclidean, which improves interpretability of learned representations.
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space. Instead, we consider the ambient space to be a Riemannian manifold, which allows for encoding domain knowledge through the associated Riemannian metric. Shortest paths can then be defined accordingly in the latent space to both follow the learned manifold and respect the ambient geometry. Through careful design of the ambient metric we can ensure that shortest paths are well-behaved even for deterministic generators that otherwise would exhibit a misleading bias. Experimentally we show that our approach improves interpretability of learned representations both using stochastic and deterministic generators.