FIFTH system for general-purpose connectionist computation

TL;DR

This paper introduces a new formal framework for general-purpose connectionist computation based on information propagation networks with unbounded recursion, bridging theory and practical programming.

Contribution

It develops a Turing-complete connectionist model within a declarative framework related to constraint logic programming, enabling high-level semantics and solving complex search problems.

Findings

Connectionist computations can be understood through high-level programming semantics.

The framework allows solving NP-hard search problems more efficiently.

It bridges the gap between theoretical models and practical programming applications.

Abstract

To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more theoretical than practical significance. We instead develop connectionist computation within the framework of information propagation networks extended with unbounded recursion, which is related to constraint logic programming and is more declarative than the semantics typically used in practical programming, but is still formally known to be Turing-complete. This approach yields contributions to the theory and practice of both connectionist computation and programming languages. Connectionist computations are carried out in a way that lets them communicate with, and be understood and interrogated directly in terms of the high-level semantics of a general-purpose programming language. Meanwhile, difficult (unbounded-dimension, NP-hard) search problems in programming that have previously been left to the programmer to solve in a heuristic, domain-specific way are solved uniformly a priori in a way that approximately achieves information-theoretic limits on performance.