Nonlinear dynamics and chaos in information processing neural networks

We consider a number of possible roles of complex dynamics and chaos in information processing by neural networks. First, we review the working principles of some well-known neural networks, and then discuss a number of approaches to utilization of chaos in neural networks. Our main goal is to present a novel view of the problem of chaos in information processing. We demonstrate that chaos emerges naturally in controls when a neural network forms a controlling part of a more complex system. We show that such neural networks can enhance e‐ciency by using chaos for explorations in a method known as Reinforcement Learning. A discussion on Hamiltonian neural networks is also included.

[1]  Kazuyuki Aihara,et al.  Chaotic simulated annealing by a neural network model with transient chaos , 1995, Neural Networks.

[2]  Stephen Grossberg,et al.  Nonlinear neural networks: Principles, mechanisms, and architectures , 1988, Neural Networks.

[3]  E. Gardner The space of interactions in neural network models , 1988 .

[4]  Mohamad H. Hassoun,et al.  Associative neural memories , 1993 .

[5]  Claude F. Touzet,et al.  Neural reinforcement learning for behaviour synthesis , 1997, Robotics Auton. Syst..

[6]  Vladimir Cherkassky,et al.  Learning from data , 1998 .

[7]  Amanda J. C. Sharkey,et al.  On Combining Artificial Neural Nets , 1996, Connect. Sci..

[8]  Rolf Pfeifer,et al.  Understanding intelligence , 2020, Inequality by Design.

[9]  Harry F. Olson,et al.  Phonetic typewriter , 1957 .

[10]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[11]  Robert A. Lordo,et al.  Learning from Data: Concepts, Theory, and Methods , 2001, Technometrics.

[12]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[13]  M. Arbib Brains, Machines, and Mathematics , 1987, Springer US.

[14]  Richard S. Sutton,et al.  Neuronlike adaptive elements that can solve difficult learning control problems , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  M. K. Ali,et al.  LEARNING, EXPLORATION AND CHAOTIC POLICIES , 2000 .

[16]  E. Izhikevich,et al.  Oscillatory Neurocomputers with Dynamic Connectivity , 1999 .

[17]  Leon O. Chua,et al.  ASSOCIATIVE AND RANDOM ACCESS MEMORY USING ONE-DIMENSIONAL MAPS , 1992 .

[18]  Stephen Grossberg,et al.  ART 3: Hierarchical search using chemical transmitters in self-organizing pattern recognition architectures , 1990, Neural Networks.

[19]  D. J. Albers,et al.  Routes to Chaos in Neural Networks with Random Weights , 1998 .

[20]  Leon Glass Chaos in neural systems , 1998 .

[21]  Sabino Gadaleta,et al.  Optimal chaos control through reinforcement learning. , 1999, Chaos.

[22]  Stephen Grossberg,et al.  A massively parallel architecture for a self-organizing neural pattern recognition machine , 1988, Comput. Vis. Graph. Image Process..

[23]  Alexander S. Dmitriev,et al.  Information processing in 1-D systems with chaos , 1997 .

[24]  Stephen Grossberg,et al.  Art 2: Self-Organization Of Stable Category Recognition Codes For Analog Input Patterns , 1988, Other Conferences.

[25]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Soumitro Banerjee,et al.  Robust Chaos , 1998, chao-dyn/9803001.

[27]  W. Freeman,et al.  Role of chaotic dynamics in neural plasticity. , 1994, Progress in brain research.

[28]  Walter J. Freeman,et al.  TUTORIAL ON NEUROBIOLOGY: FROM SINGLE NEURONS TO BRAIN CHAOS , 1992 .

[29]  Andrew G. Barto,et al.  Reinforcement learning , 1998 .

[30]  Z. Tan,et al.  Pattern Recognition Using Chaotic Neural Networks , 1998 .

[31]  M. K. Ali,et al.  PATTERN RECOGNITION IN A NEURAL NETWORK WITH CHAOS , 1998 .

[32]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Péter Érdi,et al.  Chaos and learning in the olfactory bulb , 1995, Int. J. Intell. Syst..

[34]  Masahiko Morita,et al.  Associative memory with nonmonotone dynamics , 1993, Neural Networks.

[35]  Yong Yao,et al.  Central pattern generating and recognizing in olfactory bulb: A correlation learning rule , 1988, Neural Networks.

[36]  Qing Yang,et al.  Pattern recognition by a distributed neural network: An industrial application , 1991, Neural Networks.

[37]  D. Sofge THE ROLE OF EXPLORATION IN LEARNING CONTROL , 1992 .

[38]  A G Barto,et al.  Toward a modern theory of adaptive networks: expectation and prediction. , 1981, Psychological review.

[39]  Gerald Sommer,et al.  Pattern Recognition by Self-Organizing Neural Networks , 1994 .

[40]  M. K. Ali,et al.  Chaotic neural control. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Eduardo D. Sontag,et al.  Neural Networks for Control , 1993 .

[42]  S. A. Barton Two-dimensional movement controlled by a chaotic neural network , 1995, Autom..

[43]  Hayakawa,et al.  Effects of the chaotic noise on the performance of a neural network model for optimization problems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[44]  S. Grossberg,et al.  ART 2: self-organization of stable category recognition codes for analog input patterns. , 1987, Applied optics.

[45]  Alvin Shrier,et al.  Chaos in neurobiology , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[46]  R. Hecht-Nielsen Counterpropagation networks. , 1987, Applied optics.

[47]  E. Izhikevich,et al.  Weakly connected neural networks , 1997 .

[48]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[49]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[50]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[51]  L Delpuech,et al.  Models of Neural Networks, Deuxième édition, E Domany, JL van Hemmen, K Schulten. Springer Verlag, Marseille (1995) , 1997 .

[52]  Kazuyuki Aihara,et al.  Associative Dynamics in a Chaotic Neural Network , 1997, Neural Networks.

[53]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[54]  Teuvo Kohonen,et al.  The 'neural' phonetic typewriter , 1988, Computer.

[55]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[56]  A. S. Dmitriyev,et al.  CHAOTIC SCANNING AND RECOGNITION OF IMAGES IN NEURON-LIKE SYSTEMS WITH LEARNING , 1994 .

[57]  J.A. Anderson,et al.  Neural Network Models for Pattern Recognition and Associative Memory , 2002 .

[58]  E. M. Izhikevich,et al.  A POSSIBLE ROLE OF CHAOS IN NEUROSYSTEMS , 1992 .

[59]  Kate Smith-Miles,et al.  A unified framework for chaotic neural-network approaches to combinatorial optimization , 1999, IEEE Trans. Neural Networks.

[60]  Masahiro Nakagawa,et al.  A Chaos Associative Model with a Sinusoidal Activation Function , 1999 .

[61]  W. Freeman The physiology of perception. , 1991, Scientific American.

[62]  Ichiro Tsuda,et al.  Dynamic link of memory--Chaotic memory map in nonequilibrium neural networks , 1992, Neural Networks.

[63]  F. Pasemann A simple chaotic neuron , 1997 .

[64]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[65]  Hiroaki Kurokawa,et al.  A learning algorithm for oscillatory cellular neural networks , 1999, Neural Networks.

[66]  Frank H. Eeckman,et al.  A normal form projection algorithm for associative memory , 1993 .

[67]  J. Doyne Farmer,et al.  A Rosetta stone for connectionism , 1990 .

[68]  Yong Yao,et al.  Model of biological pattern recognition with spatially chaotic dynamics , 1990, Neural Networks.

[69]  Amanda J. C. Sharkey,et al.  Combining Artificial Neural Nets: Ensemble and Modular Multi-Net Systems , 1999 .

[70]  Stephen Grossberg,et al.  ARTMAP: supervised real-time learning and classification of nonstationary data by a self-organizing neural network , 1991, [1991 Proceedings] IEEE Conference on Neural Networks for Ocean Engineering.

[71]  R. Penrose,et al.  Shadows of the Mind , 1994 .

[72]  Z. Tan,et al.  PATTERN RECOGNITION WITH STOCHASTIC RESONANCE IN A GENERIC NEURAL NETWORK , 2000 .

[73]  B. Baird Nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb , 1986 .

[74]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[75]  Zhou Chang-song,et al.  Chaotic neural network with nonlinear self-feedback and its application in optimization , 1997, Neurocomputing.

[76]  Thomas W. Ryan,et al.  VARIATIONS ON ADAPTIVE RESONANCE. , 1987 .

[77]  Donald A. Sofge,et al.  Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches , 1992 .

[78]  M. K. Ali,et al.  Robust chaos in neural networks , 2000 .

[79]  D. Obradovic,et al.  Combining Artificial Neural Nets , 1999, Perspectives in Neural Computing.

[80]  Shin Ishii,et al.  A network of chaotic elements for information processing , 1996, Neural Networks.

[81]  Tony R. Martinez,et al.  Quantum associative memory , 2000, Inf. Sci..

[82]  Pineda,et al.  Generalization of back-propagation to recurrent neural networks. , 1987, Physical review letters.

[83]  Walter J. Freeman Qualitative Overview of Population Neurodynamics , 1994 .

[84]  Jun Nishii,et al.  A learning model for oscillatory networks , 1998, Neural Networks.

[85]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[86]  R. Bellman Dynamic programming. , 1957, Science.

[87]  G. Kane Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations, vol 2: Psychological and Biological Models , 1994 .

[88]  James Glanz Sharpening the Senses With Neural 'Noise' , 1997, Science.

[89]  A. Babloyantz,et al.  Low-dimensional chaos in an instance of epilepsy. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[90]  Z. Tan,et al.  ASSOCIATIVE MEMORY USING SYNCHRONIZATION IN A CHAOTIC NEURAL NETWORK , 2001 .

[91]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems , 1996, Springer US.