Lifting Architectural Constraints of Injective Flows
Peter Sorrenson, Felix Draxler, Armand Rousselot, Sander Hummerich, Lea Zimmermann, Ullrich Koethe
Abstract
Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.
BibTeX
@inproceedings{
sorrenson2024lifting,
title={Lifting Architectural Constraints of Injective Flows},
author={Peter Sorrenson and Felix Draxler and Armand Rousselot and Sander Hummerich and Lea Zimmermann and Ullrich Koethe},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=kBNIx4Biq4}
}