Geiringer Theorems: From Population Genetics to Computational Intelligence, Memory Evolutive Systems and Hebbian Learning

TL;DR

This paper explores the extension of Geiringer theorems to computational intelligence, proposing new algorithms inspired by biological neural network models and their connection to Hebbian learning.

Contribution

It introduces novel dynamic parallel algorithms based on Geiringer theorems for use in reinforcement learning and Monte-Carlo tree search, inspired by a category-theoretic model of cognition.

Findings

Algorithms involve independent agents on directed graphs with loops

Connection established between algorithms and Hebbian learning

Provides a category-theoretic framework for cognition

Abstract

The classical Geiringer theorem addresses the limiting frequency of occurrence of various alleles after repeated application of crossover. It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action evaluation at the chance nodes. The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time. The algorithms involve independent agents traversing a dynamically constructed directed graph that possibly has loops. A rather elegant and profound category-theoretic model of cognition in biological neural networks developed by a well-known French mathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan Paul Vanbremeersch over the last thirty years provides a hint at the connection between such algorithms and Hebbian learning.