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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| Veröffentlicht in: | Natural computing Jg. 12; H. 4; S. 473 - 484 |
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| 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 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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| AbstractList | Issue Title: Part 1: Special Issue: Frontiers of Natural Computing Part 2: Special issue: Asynchronous cellular automata and applications 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.[PUBLICATION 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 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. |
| Author | Tuci, Elio Rowe, Jonathan Mitavskiy, Boris S. Cannings, Chris He, Jun |
| Author_xml | – sequence: 1 givenname: Boris S. surname: Mitavskiy fullname: Mitavskiy, Boris S. email: bom4@aber.ac.uk organization: Department of Computer Science, Aberystwyth University – sequence: 2 givenname: Elio surname: Tuci fullname: Tuci, Elio organization: Department of Computer Science, Aberystwyth University – sequence: 3 givenname: Chris surname: Cannings fullname: Cannings, Chris organization: School of Mathematics and Statistics, University of Sheffield – sequence: 4 givenname: Jonathan surname: Rowe fullname: Rowe, Jonathan organization: School of Computer Science, University of Birmingham – sequence: 5 givenname: Jun surname: He fullname: He, Jun organization: Department of Computer Science, Aberystwyth University |
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| Cites_doi | 10.1214/aoms/1177731313 10.1007/s10710-007-9038-6 10.1108/17563781211208233 10.1080/0308107042000193534 10.1162/evco.2009.17.3.343 10.1007/978-1-4612-9839-7 10.2307/1427934 10.1007/s10516-005-6001-0 10.1093/genetics/34.6.665 10.1109/CEC.2007.4424799 10.1007/11903697_91 10.1142/7438 10.1145/225058.225088 10.1145/2460239.2460252 10.1093/genetics/33.6.548 10.1007/11513575_9 10.1007/3-540-55027-5_23 |
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| DOI | 10.1007/s11047-013-9395-4 |
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| Keywords | Hebbian learning Monte-Carlo tree search Geiringer theorems Memory evolutive systems Partially observable Markov decision processes Reinforcement learning |
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| References | Weng (CR26) 2012 Ehresmann, Smeonov, Simeonov, Smith, Ehresmann (CR6) 2012 Auger, Doerr (CR3) 2011 Ehresmann, Baas, Vanbremeersch (CR5) 2004; 33 Agrawal (CR1) 1995; 27 CR17 CR16 Barr, Wells (CR4) 1998 CR14 Geiringer (CR9) 1944; 15 Mc Lane (CR13) 1971 Mitavskiy, Rowe, Cannings (CR20) 2012; 5 Mitavskiy, Rowe (CR18) 2006; 14 Hebb (CR12) 1949 Auer (CR2) 2002; 3 CR25 CR24 Geiringer (CR11) 1949; 34 Mitavskiy, Rowe, Wright, Schmitt (CR22) 2008; 17 CR23 CR21 Ehresmann, Vanbremeersch (CR7) 2006; 16 Mitavskiy, Cannings (CR15) 2009; 17 Geiringer (CR10) 1948; 33 Ehresmann, Vanbremeersch (CR8) 2007 J Weng (9395_CR26) 2012 H Geiringer (9395_CR10) 1948; 33 A Ehresmann (9395_CR5) 2004; 33 A Auger (9395_CR3) 2011 A Ehresmann (9395_CR8) 2007 B Mitavskiy (9395_CR15) 2009; 17 P Auer (9395_CR2) 2002; 3 M Barr (9395_CR4) 1998 9395_CR17 9395_CR16 B Mitavskiy (9395_CR18) 2006; 14 9395_CR14 A Ehresmann (9395_CR6) 2012 A Ehresmann (9395_CR7) 2006; 16 H Geiringer (9395_CR9) 1944; 15 S Mc Lane (9395_CR13) 1971 DO Hebb (9395_CR12) 1949 B Mitavskiy (9395_CR22) 2008; 17 R Agrawal (9395_CR1) 1995; 27 9395_CR21 B Mitavskiy (9395_CR20) 2012; 5 H Geiringer (9395_CR11) 1949; 34 9395_CR25 9395_CR24 9395_CR23 |
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Series on theoretical computer science – ident: CR25 – volume: 15 start-page: 25 year: 1944 end-page: 57 ident: CR9 article-title: On the probability of linkage in mendelian heredity publication-title: Ann Math Stat doi: 10.1214/aoms/1177731313 – ident: CR23 – year: 2007 ident: CR8 publication-title: Memory evolutive systems: hierarchy, emergence, cognition, studies in multidisciplinarity – ident: CR21 – volume: 33 start-page: 548 year: 1948 end-page: 564 ident: CR10 article-title: On the mathematics of random mating in case of different recombination values for males and females publication-title: Genetics – volume: 17 start-page: 109 issue: 3 year: 2008 end-page: 123 ident: CR22 article-title: Quotients of Markov chains and asymptotic properties of the stationary distribution of the Markov chain associated to an evolutionary algorithm publication-title: Genet Program Evol Mach doi: 10.1007/s10710-007-9038-6 – year: 1949 ident: CR12 publication-title: The organization of behavior – volume: 5 start-page: 36 issue: 1 year: 2012 end-page: 90 ident: CR20 article-title: A version of Geiringer-like theorem for decision making in the environments with randomness and incomplete information publication-title: Int J Intell Comput Cybern doi: 10.1108/17563781211208233 – volume: 33 start-page: 553 issue: 5 year: 2004 end-page: 568 ident: CR5 article-title: Hyperstructures and memory evolutive systems publication-title: Int J Gen Syst doi: 10.1080/0308107042000193534 – ident: CR17 – volume: 17 start-page: 343 issue: 3 year: 2009 end-page: 377 ident: CR15 article-title: Estimating the ratios of the stationary distributions of Markov chains modeling evolutionary algorithms using the quotient construction method publication-title: Evol Comput doi: 10.1162/evco.2009.17.3.343 – year: 1971 ident: CR13 publication-title: Categories for the working mathematician doi: 10.1007/978-1-4612-9839-7 – volume: 3 start-page: 397 year: 2002 end-page: 422 ident: CR2 article-title: Using confidence bounds for exploration–exploitation trade-offs publication-title: J Mach Learn Res – volume: 27 start-page: 1054 year: 1995 end-page: 1078 ident: CR1 article-title: Sample mean based index policies with (log ) regret for the multi-armed bandit problem publication-title: Adv Appl Probab doi: 10.2307/1427934 – year: 2012 ident: CR26 publication-title: Natural and artificial intelligence – volume: 16 start-page: 165 year: 2006 end-page: 214 ident: CR7 article-title: The memory evolutive systems as a model of Rosens organisms publication-title: Axiomathes doi: 10.1007/s10516-005-6001-0 – year: 2012 ident: CR6 article-title: Wlimes: towards a theoretical framework for wandering logic intelligence memory evolutive systems publication-title: Integral biomathics: tracing the road to reality – ident: CR24 – volume: 34 start-page: 665 year: 1949 ident: 9395_CR11 publication-title: Genetics doi: 10.1093/genetics/34.6.665 – ident: 9395_CR21 doi: 10.1109/CEC.2007.4424799 – ident: 9395_CR14 doi: 10.1007/11903697_91 – volume-title: Integral biomathics: tracing the road to reality year: 2012 ident: 9395_CR6 – volume-title: Memory evolutive systems: hierarchy, emergence, cognition, studies in multidisciplinarity year: 2007 ident: 9395_CR8 – volume: 15 start-page: 25 year: 1944 ident: 9395_CR9 publication-title: Ann Math Stat doi: 10.1214/aoms/1177731313 – volume-title: Theory of randomized search heuristics. 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| Title | Geiringer theorems: from population genetics to computational intelligence, memory evolutive systems and Hebbian learning |
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