Stabilizing Invertible Neural Networks Using Mixture Models

TL;DR

This paper investigates invertible neural networks for inverse problems, showing that using Gaussian mixture models instead of standard normal distributions stabilizes Lipschitz constants and improves sampling quality.

Contribution

The paper introduces a method to control Lipschitz constants in invertible neural networks by replacing the latent distribution with a Gaussian mixture model, enhancing stability and performance.

Findings

Replacing standard normal with Gaussian mixture models stabilizes Lipschitz constants.

Numerical simulations show improved sampling in multimodal applications.

The approach reduces errors in inverse problem solutions.

Abstract

In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks. Without such an control, numerical simulations are prone to errors and not much is gained against traditional approaches. Fortunately, our analysis indicates that changing the latent distribution from a standard normal one to a Gaussian mixture model resolves the issue of exploding Lipschitz constants. Indeed, numerical simulations confirm that this modification leads to significantly improved sampling quality in multimodal applications.