Stabilizing Invertible Neural Networks Using Mixture Models
This addresses stability issues in invertible neural networks for researchers and practitioners in inverse problems, though it is incremental as it modifies an existing approach.
The paper tackles the problem of unstable invertible neural networks in solving inverse problems by controlling Lipschitz constants, and finds that using a Gaussian mixture model instead of a standard normal latent distribution resolves this issue, leading to significantly improved sampling quality in multimodal applications.
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.