Universal approximation by generalized mellin approximate identity neural networks

Abstract

This study considers sufficient and also necessary conditions for the universal approximation capability of three-layer feedforward generalized Mellin approximate identity neural networks. Our approach consists of three steps. In the first step, we introduce a notion of generalized Mellin approximate identity. In the second step, we prove a theorem by using this notion to show convolution linear operators of generalized Mellin approximate identity with a continuous function f on ℝ+ with a compact support converges uniformly to f. In the third step, we establish a main theorem by using those previous steps. The theorem shows universal approximation by generalized Mellin approximate identity neural networks.