Stabilizing invertible neural networks using mixture models. (12th July 2021)

• Record Type: Journal Article
• Authors: Hagemann, Paul; Neumayer, Sebastian
• Is Part Of: Inverse problems. Volume 37:Number 8(2021)
• Publication Date: 2021-07-12
• Subjects: invertible neural networks -- mixture models -- inverse problems -- numerical stability -- multimodal problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abe928
• Languages: English
• ISSNs: 0266-5611

Abstract

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 a 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.