Deep Neural Networks: A Formulation Via Non-Archimedean Analysis

2024/01/31 by Zúñiga-Galindo, W. A. · 1 citation
#11S85 #65D15 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural and Evolutionary Computing (cs.NE) #Primary 68T07 #Secondary 41A30

paper · doi:10.48550/arxiv.2402.00094

Abstract

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval.

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