Kantorovich--Kernel Neural Operators: Approximation Theory, Asymptotics, and Neural Network Interpretation

ArXi:2603.26418v1 Announce Type: cross This paper studies a class of multivariate Kantorovich-kernel neural network operators, including the deep Kantorovich-type neural network operators studied by Sharma and Singh. We prove density results, establish quantitative convergence estimates, derive Voronovskaya-type theorems, analyze the limits of partial differential equations for deep composite operators, prove Korovkin-type theorems, and propose inversion theorems.