Title: Learning, generalisation, and functional entropy in random automata networks

Authors: Alireza Goudarzi; Christof Teuscher; Natali Gulbahce; Thimo Rohlf

Addresses: Department of Computer Science, Portland State University, 1900 SW 4th Ave., Portland, OR 97201, USA ' Department of Electrical and Computer Engineering, Portland State University, 1900 SW 4th Ave., Portland, OR 97201, USA ' Department of Cellular and Molecular Pharmacology, University of California, San Francisco (UCSF), 1700 4th, San Francisco, CA 94158, USA ' Interdisciplinary Centre for Bioinformatics, University Leipzig, Haertelstr. 16-18, D-04107 Leipzig, Germany; Epigenomics Project, iSSB, Genopole Campus 1, 5 Rue Henri Desbrueres, F-91034 Evry, France; Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany

Abstract: It has been shown (Van den Broeck and Kawai, 1990; Patarnello and Carnevali, 1987) that feedforward Boolean networks can learn to perform specific simple tasks and generalise well if only a subset of the learning examples is provided for learning. Here, we extend this body of work and show experimentally that random Boolean networks (RBNs), where both the interconnections and the Boolean transfer functions are chosen at random initially, can be evolved by using a state-topology evolution to solve simple tasks. We measure the learning and generalisation performance, investigate the influence of the average node connectivity K, the system size N, and introduce a new measure that allows to better describe the network's learning and generalisation behaviour. We show that the connectivity of the maximum entropy networks scales as a power-law of the system size N. Our results show that networks with higher average connectivity K (supercritical) achieve higher memorisation and partial generalisation. However, near critical connectivity, the networks show a higher perfect generalisation on the even-odd task.

Keywords: adaptation; learning; generalisation; automata networks; random Boolean networks; RBNs; robustness; network information processing; functional entropy; average node connectivity; system size.

DOI: 10.1504/IJAACS.2014.065198

International Journal of Autonomous and Adaptive Communications Systems, 2014 Vol.7 No.3, pp.295 - 314

Published online: 29 Oct 2014 *

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