Deep Neural Networks: A Formulation Via Non-Archimedean Analysis
W. A. Zúñiga-Galindo
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.