Stabilizing Invertible Neural Networks Using Mixture Models

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.

References in corpus (5)

• Conditional Generative Adversarial Nets
• The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
• Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders
• Guided Image Generation with Conditional Invertible Neural Networks
• Benchmarking Invertible Architectures on Inverse Problems

Cited by in corpus (8)

• Convolutional Proximal Neural Networks and Plug-and-Play Algorithms
• Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
• PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization
• Generalized Normalizing Flows via Markov Chains
• Efficient approximation of high-dimensional exponentials by tensornetworks
• Resampling Base Distributions of Normalizing Flows
• Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces
• Proximal Residual Flows for Bayesian Inverse Problems