Abstract
In this research paper, a complex valued generalization of associative memory synthesized by Hopfield is considered and it is proved that it is impossible to synthesize such a neural network with desired unitary stable states when the dimension of the network (number of neurons) is odd. The linear algebraic structure of such a neural network is discussed. Using Sylvester construction of Hadamard matrix of suitable dimension, an algorithm to synthesize such a complex Hopfield neural network is discussed. Also, it is discussed how to synthesize real / complex valued associative memories with desired energy landscape (i.e. desired stable states and desired energy values of associated quadratic energy function).
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References
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proceedings of National Academy of Sciences 79, 2554–2558 (1982). USA
[MGZ] Muezzinoglu, M.K., Guzelis, C., Zurada, J.M.: A new design method for the complex-valued multistate hopfield associative memory. IEEE Transactions on Neural Networks 14(4), July 2003
Rama Murthy, G., Praveen, D.: Complex-valued Neural Associative Memory on the Complex hypercube. IEEE Conference on Cybernetics and Intelligent Systems, Singapore, December 1-3, 2004
Rama Murthy, G.: Optimal Signal Design for Magnetic and Optical Recording Channels. Bellcore Technical Memorandum, TM-NWT-018026, April 1st, 1991
Rama Murthy, G., Nischal, B.: Hopfield-Amari Neural Network : Minimization of Quadratic forms. The 6th International Conference on Soft Computing and Intelligent Systems, Kobe Convention Center(Kobe Portopia Hotel), Kobe, Japan, November 20-24, 2012
Hirose, A.: Complex Valued Neural Networks: Theories and Applications. World scientific publishing Co, November 2003
Rama Murthy, G., Praveen, D.: A novel associative memory on the complex hypercube lattice. In: 16th European Symposium on Artificial Neural Networks, April 2008
Rama Murthy, G.: Some novel real/ complex valued neural network models. In: Advances in Soft Computing, Springer Series on Computational Intelligence: Theory and Applications, Proceedings of 9th Fuzzy days, Dortmund, Germany, September 18-20 2006
Jagadeesh, G., Praveen, D., Rama Murthy, G.: Heteroassociative memories on the complex hypercube. In: Proceedings of 20th IJCAI Workshop on Complex Valued Neural Networks, January 6-12, 2007
Sree Hari Rao, V., Rama Murthy, G.: Global dynamics of a class of complex valued neural networks. In: Special Issue on CVNNS of International Journal of Neural Systems, April 2008
Rama Murthy, G.: Infinite Population, Complex Valued State Neural Network on the Complex Hypercube. In: Proceedings of International Conference on Cognitive Science (2004)
Rama Murthy, G.: Multidimensional Neural Networks-Unified Theory. New Age International Publishers. New Delhi (2007)
Goles, E., Fogelman, F., Pellegrin, D.: Decreasing energy functions as a tool for studying threshold networks. Discrete Applied Mathematics 12, 261–277 (1985)
Bruck, J.: On the Convergence Properties of the Hopfield Model. Proceeding of the IEEE 78(10), October 1990
Zhu, X., Wei, W.: Fixed points of complex-valued bidirectional associative memory. Journal of Computational and Applied Mathematics 236, 753–758 (2011)
Kosko, B.: Bidirectional Associative Memories. IEEE Transactions on Systems, Man and Cybernetics 18(1), January/February 1988
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Murthy, G.R., Gabbouj, M. (2015). Existence and Synthesis of Complex Hopfield Type Associative Memories. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2015. Lecture Notes in Computer Science(), vol 9095. Springer, Cham. https://doi.org/10.1007/978-3-319-19222-2_30
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DOI: https://doi.org/10.1007/978-3-319-19222-2_30
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