Natural Computing

, Volume 12, Issue 4, pp 473–484 | Cite as

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

  • Boris S. Mitavskiy
  • Elio Tuci
  • Chris Cannings
  • Jonathan Rowe
  • Jun He


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.


Geiringer theorems Partially observable Markov decision processes Monte-Carlo tree search Reinforcement learning Memory evolutive systems Hebbian learning 



This work has been supported by the EPSRC EP/I009809/1 “Evolutionary Approximation Algorithms for Optimization: Algorithm Design and Complexity Analysis” Grant.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Boris S. Mitavskiy
    • 1
  • Elio Tuci
    • 1
  • Chris Cannings
    • 2
  • Jonathan Rowe
    • 3
  • Jun He
    • 1
  1. 1.Department of Computer ScienceAberystwyth UniversityAberystwythUK
  2. 2.School of Mathematics and StatisticsUniversity of SheffieldSheffieldEngland, UK
  3. 3.School of Computer ScienceUniversity of BirminghamEdgbastonUK

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