Complexity of deep computations via topology of function spaces

TL;DR

This paper employs topological and model-theoretic methods to analyze the complexity of deep and limit computations, introducing new complexity classes and characterizing approximability of deep computations.

Contribution

It introduces a novel approach combining topology of function spaces and model theory to classify and analyze the complexity of deep computations.

Findings

Identification of new complexity classes via Rosenthal compacta

Characterization of approximability of deep computations

Application of Shelah's independence to computation topology

Abstract

We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of model theory, specifically, the concept of \emph{independence} from Shelah's classification theory, to translate between topology and computation. We use the theory of Rosenthal compacta to characterize approximablility of deep computations, both deterministically and probabilistically.