Universal Induction with Varying Sets of Combinators

TL;DR

This paper explores adaptive combinator sets in universal induction using genetic programming, demonstrating improved efficiency and task-specific optimization in combinatory logic-based systems.

Contribution

It introduces an approach for adaptively selecting combinator sets in universal induction, enhancing efficiency and task-specific performance.

Findings

Low-complexity tasks are solved more efficiently than brute force methods.

Useful combinators can be identified and incorporated to simplify complex tasks.

Optimal combinator sets vary with the specific task, requiring adaptive selection.

Abstract

Universal induction is a crucial issue in AGI. Its practical applicability can be achieved by the choice of the reference machine or representation of algorithms agreed with the environment. This machine should be updatable for solving subsequent tasks more efficiently. We study this problem on an example of combinatory logic as the very simple Turing-complete reference machine, which enables modifying program representations by introducing different sets of primitive combinators. Genetic programming system is used to search for combinator expressions, which are easily decomposed into sub-expressions being recombined in crossover. Our experiments show that low-complexity induction or prediction tasks can be solved by the developed system (much more efficiently than using brute force); useful combinators can be revealed and included into the representation simplifying more difficult tasks. However, optimal sets of combinators depend on the specific task, so the reference machine should be adaptively chosen in coordination with the search engine.