Learning and Generalization in Random Automata Networks
Abstract
It has been shown [7,6] that feedforward Boolean networks can learn to perform specific simple tasks and generalize 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 generalization 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 generalization behavior. Our results show that networks with higher average connectivity K (supercritical) achieve higher memorization and partial generalization. However, near critical connectivity, the networks show a higher perfect generalization on the even-odd task.
Keywords
Boolean Function Input Space Mapping Task Boolean Network Learning ProbabilityPreview
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References
- 1.Aleksander, I.: Random logic nets: Stability and adaptation. International Journal of Man-Machine Studies 5, 115–131 (1973)CrossRefGoogle Scholar
- 2.Aleksander, I.: From Wisard to Magnus: A family of weightless virtual neural machines. In: Austin, J. (ed.) RAM-Based Neural Networks. Progress in Neural Processing, vol. 9. World Scientific (1998)Google Scholar
- 3.Aleksander, I., Thomas, W.V., Bowden, P.A.: WISARD: A radical step foward in image recognition. Sensor Review 4, 120–124 (1984)CrossRefGoogle Scholar
- 4.Amari, S.I.: Characteristics of randomly connected threshold-element networks and network systems. Proceedings of the IEEE 59(1), 35–47 (1971)MathSciNetCrossRefGoogle Scholar
- 5.Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)MATHGoogle Scholar
- 6.Carnevali, P., Patarnello, S.: Exhaustive thermodynamical analysis of Boolean learning networks. Europhysics Letters 4(10), 1199–1204 (1987)CrossRefGoogle Scholar
- 7.Van den Broeck, C., Kawai, R.: Learning in feedforward Boolean networks. Physical Review A 42(10), 6210–6218 (1990)CrossRefGoogle Scholar
- 8.Gershenson, C.: Classification of random Boolean networks. In: Standish, R.K., Bedau, M.A., Abbass, H.A. (eds.) Artificial Life VIII. Proceedings of the Eight International Conference on Artificial Life, pp. 1–8. MIT Press, Cambridge, MA (2003)Google Scholar
- 9.Kauffman, S.A.: Metabolic stability and epigenesis in randomly connected genetic nets. Journal of Theoretical Biology 22, 437–467 (1968)CrossRefGoogle Scholar
- 10.Kauffman, S.A.: Emergent properties in random complex automata. Physica D 10(1-2), 145–156 (1984)MathSciNetCrossRefGoogle Scholar
- 11.Kauffman, S.A.: The Origins of Order: Self–Organization and Selection in Evolution. Oxford University Press, New York (1993)Google Scholar
- 12.Lawson, J., Wolpert, D.H.: Adaptive programming of unconventional nano-architectures. Journal of Computational and Theoretical Nanoscience 3, 272–279 (2006)Google Scholar
- 13.Lizier, J., Prokopenko, M., Zomaya, A.: The information dynamics of phase transitions in random boolean networks. In: Bullock, S., Noble, J., Watson, R., Bedau, M.A. (eds.) Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pp. 374–381. MIT Press, Cambridge (2008)Google Scholar
- 14.Martland, D.: Auto-associative pattern storage using synchronous boolean networks. In: Proceedings of the First IEEE International Conference on Neural Networks, San Diego, CA, vol. III, pp. 355–366 (1987)Google Scholar
- 15.Martland, D.: Behaviour of autonomous (synchronous) boolean networks. In: Proceedings of the First IEEE International Conference on Neural Networks, San Diego, CA, vol. II, pp. 243–250 (1987)Google Scholar
- 16.Patarnello, A., Carnevali, P.: Learning networks of neurons with Boolean logic. Europhysics Letters 4(4), 503–508 (1987)CrossRefGoogle Scholar
- 17.Patarnello, S., Carnevali, P.: Learning capabilities of boolean networks. In: Aleksander, I. (ed.) Neural Computing Architectures: The Design of Brain-Like Machines, ch. 7, pp. 117–129. North Oxford Academic, London (1989)Google Scholar
- 18.Rozonoér, L.I.: Random logical nets I. Automation and Remote Control 5, 773–781 (1969); translation of Avtomatika i TelemekhanikaGoogle Scholar
- 19.Selfridge, O.G.: “Pandemonium”: A paradigm for learning. In: Mechanisation of Thought Processes: Proceedings of a Symposium Held at the National Physical Laboratory, pp. 513–526 (1958)Google Scholar
- 20.Selfridge, O.G., Neisser, U.: Pattern recognition by machine. Scientific American 203(2), 60–68 (1960)CrossRefGoogle Scholar
- 21.Teuscher, C.: Turing’s Connectionism. An Investigation of Neural Network Architectures. Springer, London (2002)MATHGoogle Scholar
- 22.Teuscher, C., Gulbahce, N., Rohlf, T.: Learning and generalization in random Boolean networks. In: Dynamics Days 2007: International Conference on Chaos and Nonlinear Dynamics, Boston, MA, January 3-6 (2007)Google Scholar
- 23.Teuscher, C., Gulbahce, N., Rohlf, T.: An assessment of random dynamical network automata for nanoelectronics. International Journal of Nanotechnology and Molecular Computation 1(4), 39–57 (2009)CrossRefGoogle Scholar
- 24.Tour, J., Van Zandt, W.L., Husband, C.P., Husband, S.M., Wilson, L.S., Franzon, P.D., Nackashi, D.P.: Nanocell logic gates for molecular computing. IEEE Transactions on Nanotechnology 1(2), 100–109 (2002)CrossRefGoogle Scholar
- 25.Turing, A.M.: Intelligent machinery. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 5, pp. 3–23. Edinburgh University Press, Edinburgh (1969)Google Scholar
- 26.Weisbuch, G.: Dynamique des systèmes complexes: Une introduction aux réseaux d’automates. InterEditions, France (1989)Google Scholar
- 27.Weisbuch, G.: Complex Systems Dynamics: An Introduction to Automata Networks. Lecture Notes, Santa Fe Institute, Studies in the Sciences of Complexity, vol. 2. Addison-Wesley, Redwood City (1991)Google Scholar
- 28.Wittaker, E.T., Robinson, G.: The trapezoidal and parabolic rules. In: The Calculus of Observations: A Treatise on Numerical Mathematics, pp. 156–158. Dover, New York (1969)Google Scholar