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

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. 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 Voronovska...

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