On the effect of network modularity on evolutionary search

Modularity is an omnipresent feature of biological neural networks. It is also a cornerstone of indirect genetic encodings and developmental evolutionary algorithms for neural networks. Modularity may give evolution the ability to reflect regularities in the environment in its solutions, thus making good solutions easier to find. Furthermore, it has been proposed that the density of highly fit solutions is higher in modular networks than in non-modular networks. In this paper we investigate how the degree of modularity in neural networks affects the search landscape for neuroevolution. We use multi-objective evolution to explicitly guide evolution towards modular and non-modular areas of network search space. We find that the fitness landscape is radically different in these different areas, but that network modularity is not accompanied by increased efficiency on a modular classification task. We therefore cannot find support for the popular assumption that modular networks are “better” than non-modular networks.

[1]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[2]  Per Kristian Lehre,et al.  Phenotypic complexity and local variations in neutral degree , 2007, Biosyst..

[3]  U. Alon,et al.  Spontaneous evolution of modularity and network motifs. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[4]  J. Pollack,et al.  Coevolving High-Level Representations , 1993 .

[5]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[6]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Frédéric Gruau,et al.  Automatic Definition of Modular Neural Networks , 1994, Adapt. Behav..

[8]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[9]  O. Sporns.  Small-world connectivity, motif composition, and complexity of fractal neuronal connections. , 2006, Bio Systems.

[10]  J. Hawkins,et al.  On Intelligence , 2004 .

[11]  J. Fuster.  Network memory , 1997, Trends in Neurosciences.

[12]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex Adaptive Systems.

[13]  V. Mountcastle.  The columnar organization of the neocortex. , 1997, Brain : a journal of neurology.

[14]  Almut Schüz.  Neuroanatomy in a computational perspective , 1998 .

[15]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[18]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[19]  W. Banzhaf,et al.  Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence. , 2006, Bio Systems.

[20]  Leslie G. Valiant,et al.  Evolvability , 2009, JACM.

[21]  John R. Koza,et al.  Genetic programming 2 - automatic discovery of reusable programs , 1994, Complex adaptive systems.

[22]  J. Bullinaria.  To Modularize or Not To Modularize ? , 2002 .

[23]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.