Abstract
An unsupervised trained, chaotic BAM composed of units with saturated limits logistic function can extract intrinsic features of data and exhibit various associative dynamics for different values of transmission parameters of the neurons’ activation functions during recall. The output behavior of its units can be a fixed point or periodic attractor, a constrained aperiodic attractor consisting of one or more stored patterns, or a chaotic attractor. This characteristic indicates that the model is a promising technique that can be applied to information processing, such as pattern recognition and memory recall. However, controlling the amount of output variability and stabilizing it in a desired attractor is a crucial issue in practice. In this work it is shown that the transmission parameters of the units’ activation functions play a significant role in identifying the output behavior. Using different time-series generated by the trained network, Largest Lyapunov Exponent is computed for different values of transmission parameter. Then, critical values of this parameter that lead to the highest chaotic behavior for each unit are stored and used to set the network during recall. Interaction between some chaotic feature units and some fixed-point ones produces desired behaviors with various degrees of uncertainty. An evolutionary algorithm is then introduced to find the units that should work chaotically to generate the desired behavior. Achievement of this method implies that such a controlled chaotic feature extracting BAM can be feasibly applied to information processing.
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Kosko B (1988) Bidirectional associative memories. IEEE Trans Syst Man Cybern 18(1): 49–60
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8): 2554–2558
Ott E (1993) Chaos in dynamical systems. Cambridge University Press, Cambridge
Babloyantz A, Lourenco C (1996) Brain chaos and computation. Int J Neural Syst 7: 461–471
Dafilis MP, Liley DTJ, Cadusch PJ (2001) Robust chaos in a model of the electroencephalogram: implications for brain dynamics. Chaos 11: 474–478
Korn H, Faure P (2003) Is there chaos in the brain? II. Experimental evidence and related models. Comptes Rendus Biologies 326(9): 787–840
Tsuda I (2001) Towards an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24(4): 793–847
Arieli A, Sterkin A, Grinvald A, Aertsen A (1996) Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses. Science 273(5283): 1868–1871
Kaplan D, Glass L (1995) Understanding nonlinear dynamics, 1 edn. Springer, New York
Freeman WJ (1985) Strange attractors in the olfactory system of rabbits. Electroencephalogr. Clin. Neurophysiol 61
Freeman WJ (1987) Simulation of EEG chaotic patterns with adynamic model of the olfactory system. Biol Cybern 56: 139–150
Freeman WJ, Barrie JM (1994) Chaotic oscillations and the genesis of meaning in cerebral cortex. Springer, Berlin, pp 13–37
Yao Y, Freeman WJ (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Netw 3: 153–170
Andreyev YV, Belsky YL, Dmitriev AS, Kuminov DA (1996) Information processing using dynamical chaos: neural networks implementation. IEEE Trans Neural Netw 7(2): 290–299
Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 44(6–7): 333–339
Chen L, Aihara K (1999) Global searching ability of chaotic neural networks. IEEE Trans Circuits Syst 46(8): 974–993
Chen S, Shih C (2004) Asymptotic behaviors in a transiently chaotic neural network. Discret Contin Dyn Syst 10(3): 805–826
Crook N, Goh W, Hawara M (2007) Pattern recall in networks of chaotic neurons. BioSystems 87: 267–274
Lee RST (2006) Lee-associator: a chaotic auto-associative network for progressive memory recalling. Neural Netw 19(5): 644–666
Sprott JC, Albers DJ, Dechert WE (1998) Routes to chaos in neural networks with random weights. Int J Bifurcation Chaos 8(7): 1463–1478
Choi MY, Huberman BA (1983) Dynamic behavior of nonlinear networks. Phys Rev A 28: 1204–1206
Sandler Y, Yu M (1990) Model of neural networks with selective memorization and chaotic behavior. Phys Lett A 144: 462–466
Zhenkun H, Xinghua W, Chunhua F (2010) Multiperiodicity of periodically oscillated discrete-time neural networks with transient excitatory self-connections and sigmoidal nonlinearities. IEEE Trans Neural Netw 21: 1643–1655
Zhenkun H, Mohamad S, Honghua B (2010) Multiperiodicity analysis and numerical simulation of discrete-time transiently chaotic non-autonomous neural networks with time-varying delays. Commun Nonlinear Sci Numeri Simul 15: 1348–1357
Chartier S, Boukadoum M (2006) A chaotic bidirectional associative memory. Proceedings of Maghrebian conference on software engineering and artificial intelligence, pp 498–501
Chartier S, Boukadoum M (2006) A bidirectional heteroassociative memory for binary and grey-level patterns. IEEE Trans Neural Netw 17(2): 385–396
Chartier S, Proulx R (2005) NDRAM: Nonlinear dynamic recurrent associative memory for learning bipolar and nonbipolar correlated patterns. IEEE Trans Neural Netw 16(6): 1393–1400
Giguère G, Chartier S, Proulx R, Lina J (2007a) Category development and reorganization using a bidirectional associative memory-inspired architecture. Proceedings of the 8th international conference on cognitive modeling, pp 97–102
Giguère G, Chartier S, Proulx R, Lina J (2007b) Creating perceptual features using a BAM architecture. Proceedings of the 29th annual cognitive science society, pp 1025–1030
Chartier S, Renaud P, Boukadoum M (2008) A nonlinear dynamic artificial neural network model of memory. New Ideas in Psychol 26(2): 252–277
He G, Chan L, Aihara K (2008) Associative memory with a controlled chaotic neural network. Neurocomputing 71: 2794–2805
He G, Shrimali MD, Aihara K (2008) Threshold control of chaotic neural network. Neural Netw 21: 114–121
Krishnaiah J, Kumar CS, Faruqi MA (2006) Modeling and control of chaotic processes through their bifurcation diagrams generated with the help of recurrent neural network models. J Process Control 16: 67–79
Xia M, Fang J, Tang Y, Wang Z (2010) Dynamic depression control of chaotic neural networks for associative memory. Neurocomputing 73: 776–783
He G, Cao Z, Zhu P, Ogura H (2003) Controlling chaos in a chaotic neural network. Neural Netw 16: 1195–1200
Chartier S, Giguère G, Renaud P, Lina J, Proulx R (2007) FEBAM: A feature-extracting bidirectional associative memory. Proceedings of the international joint conference on neural networks, pp 1679–1684
Haykin S (1999) Neural networks: a comprehensive foundation. Prentice-Hall, Englewood Cliffs
Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10: 161–195
Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16: 153–164
Sprott JC (2003) Chaos and time-series analysis. Oxford University Press, Oxford
Adachi M, Aihara K (1997) Associative dynamics in a chaotic neural network. Neural Netw 10(1): 83–98
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Nejadgholi, I., Seyyedsalehi, S.A. & Chartier, S. A Chaotic Feature Extracting BAM and Its Application in Implementing Memory Search. Neural Process Lett 36, 69–99 (2012). https://doi.org/10.1007/s11063-012-9223-3
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DOI: https://doi.org/10.1007/s11063-012-9223-3