Quadratic neural networks for solving inverse problems

2023/12/20 by Leon Frischauf, Otmar Scherzer, Frischauf, Leon +3 · 1 citation
Computer Science · Mathematics · #42C40 #45Q05 #65F20 #65J22 #FOS: Mathematics #Neural Networks and Applications #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2401.09445

openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is that such functions can approximate typical test cases, such as the Shepp-Logan phantom, better, than standard neural networks. Moreover, we show that the convergence analysis of numerical methods for solving inverse problems with shallow generalized neural network functions leads to more intuitive convergence conditions, than for deep affine linear neural networks.

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