Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems

2023/09/21 by Nathan Buskulic, Buskulic, Nathan, Jalal Fadili +3 · 4 citations
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Neural Networks and Applications #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2309.12128

openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Neural networks have become a prominent approach to solve inverse problems in recent years. While a plethora of such methods was developed to solve inverse problems empirically, we are still lacking clear theoretical guarantees for these methods. On the other hand, many works proved convergence to optimal solutions of neural networks in a more general setting using overparametrization as a way to control the Neural Tangent Kernel. In this work we investigate how to bridge these two worlds and we provide deterministic convergence and recovery guarantees for the class of unsupervised feedforward multilayer neural networks trained to solve inverse problems. We also derive overparametrization bounds under which a two-layers Deep Inverse Prior network with smooth activation function will benefit from our guarantees.

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