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

摘要

The classical Geiringer theorem addresses the limiting frequency ofoccurrence of various alleles after repeated application of crossover. It hasbeen adopted to the setting of evolutionary algorithms and, a lot morerecently, reinforcement learning and Monte-Carlo tree search methodology tocope with a rather challenging question of action evaluation at the chancenodes. The theorem motivates novel dynamic parallel algorithms that areexplicitly described in the current paper for the first time. The algorithmsinvolve independent agents traversing a dynamically constructed directed graphthat possibly has loops. A rather elegant and profound category-theoretic modelof cognition in biological neural networks developed by a well-known Frenchmathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan PaulVanbremeersch over the last thirty years provides a hint at the connectionbetween such algorithms and Hebbian learning.