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 (19)

• Conditional Generative Adversarial Nets
• Categorical Reparameterization with Gumbel-Softmax
• An Introduction to Variational Autoencoders
• Improved Training of Wasserstein GANs
• The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
• General state space Markov chains and MCMC algorithms
• Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders
• Guided Image Generation with Conditional Invertible Neural Networks
• Multiplicative Normalizing Flows for Variational Bayesian Neural Networks
• Generalized Denoising Auto-Encoders as Generative Models
• Analyzing Inverse Problems with Invertible Neural Networks
• Deep Bayesian Inversion
• Disconnected Manifold Learning for Generative Adversarial Networks
• Parseval Proximal Neural Networks
• Stellar Parameter Determination from Photometry using Invertible Neural Networks
• Benchmarking Invertible Architectures on Inverse Problems
• Understanding and Mitigating Exploding Inverses in Invertible Neural Networks
• A RAD approach to deep mixture models
• Gaussian mixture models with Wasserstein distance

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