Self Normalizing Flows

TL;DR

Self Normalizing Flows introduce a flexible training framework that replaces costly gradient computations with learned approximations, enabling efficient and stable training of complex normalizing flow models with improved performance.

Contribution

The paper proposes a novel method that reduces computational complexity in normalizing flows by using learned approximate inverses, allowing for more flexible and efficient model training.

Findings

Reduced computational complexity from O(D^3) to O(D^2) per layer.

Models are stable and achieve similar likelihoods as exact gradient methods.

Training is faster and outperforms functionally constrained models.

Abstract

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $\mathcal{O}(D^3)$ to $\mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while training more quickly and surpassing the performance of functionally constrained counterparts.