Geiringer theorems: from population genetics to computational intelligence, memory evolutive systems and Hebbian learning

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 wi...

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Bibliographic Details
Published in:Natural computing Vol. 12; no. 4; pp. 473 - 484
Main Authors: Mitavskiy, Boris S., Tuci, Elio, Cannings, Chris, Rowe, Jonathan, He, Jun
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2013
Springer Nature B.V
Subjects:
Artificial Intelligence
Complex Systems
Computer Science
Computers
Evolutionary Biology
Intelligent design
Memory
Monte Carlo simulation
Population genetics
Processor Architectures
Theorems
Theory of Computation
Hebbian learning
Monte-Carlo tree search
Geiringer theorems
Memory evolutive systems
Partially observable Markov decision processes
Reinforcement learning
ISSN:1567-7818, 1572-9796
Online Access:Get full text
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Summary: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 and multiple edges. 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.
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ISSN:1567-7818
1572-9796
DOI:10.1007/s11047-013-9395-4