Boolean networks which learn to compute
Through a training procedure based on simulated annealing, Boolean networks can ‘learn’ to perform specific tasks. As an example, a network implementing a binary adder has been obtained after a training procedure based on a small number of examples of binary addition, thus showing a generalization capability. Depending on problem complexity, network size, and number of examples used in the training, different learning regimes occur. For small networks an exact analysis of the statistical mechanics of the system shows that learning takes place as a phase transition. The ‘simplicity’ of a problem can be related to its entropy. Simple problems are those that are thermodynamically favored.
KeywordsSimulated Annealing Boolean Function Training Procedure Boolean Network Generalization Capability
Unable to display preview. Download preview PDF.
- 1.Hopfield, J.J: Proc. Nat. Acad. Sci. USA, Vol. 79 p. 2254 (1982)Google Scholar
- 2.Amit, D.J., Gutfreund, H. and H. Sompolinsky: Phys. Rev. A, Vol. 32 p. 1007 (1985)Google Scholar
- 3.Amit, D.J., Gutfreund, H. and H. Sompolinsky: Phys. Rev. Lett.: Vol. 55 p. 1530 (1985)Google Scholar
- 4.Parisi, G.: Jour. Phys. A (Math. Gen.), Vol. 19 p. L675 (1986)Google Scholar
- 5.Personnaz, L., Guyon, I. and G. Dreyfus: in Disordered Systems and Biological Organization, (Eds. E. Bienenstock et al.), Springer & Verlag (1986)Google Scholar
- 6.Sejnowsky, T.J. and C. Rosenberg: John Hopkins University Tech. Rep., Vol. 86/01 (1986)Google Scholar
- 7.Hinton, G.E., and T.J. Sejnowsky: Proc. IEEE Comp. Soc. Conference on Computer Vision and Pattern Recognition, p. 488 (1983)Google Scholar
- 8.Cruz, C.A., Hanson, W.A. and J.Y. Tam: in Neural Networks for Computing, Am. Inst. of Phys. Proc., Vol. 151 (1986)Google Scholar
- 9.Patarnello, S. and P. Carnevali: Europhys. Letts., Vol.4(4) p. 503 (1987)Google Scholar
- 10.Kirkpatrick, S. Gelatt, S.D. and M.P. Vecchi: Science, Vol. 220, p. 671 (1983)Google Scholar
- 11.Carnevali, P. and S. Patarnello: Europhys. Letts., in PressGoogle Scholar