Approximability of deep computations
Logic
2026-01-28 v7
Abstract
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of the series, we characterize deep computations that are bona fide computable, and prove the existence of deep equilibria, which hitherto have been found only empirically in deep learning. A subsequent paper will study the complexity of ultracomputations. Our approach adapts and combines technology from topology of function spaces, structural Ramsey theory, topological dynamics, and model theory.
Cite
@article{arxiv.2409.06064,
title = {Approximability of deep computations},
author = {Samson Alva and Eduardo Dueñez and Jose Iovino and Claire Walton},
journal= {arXiv preprint arXiv:2409.06064},
year = {2026}
}