Adaptive classification of temporal signals in fixed-weight recurrent neural networks: An existence proof

Neural Computation

Volumn 20, Issue 10, 2008, Pages 2564-2596

  Tyukin, Ivan Y ^a,b   Prokhorov, Danil ^c   Van Leeuwen, Cees ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^c TOYOTA TECHNICAL CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53349180261     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2008.05-07-527     Document Type: Article

References (32)

1. Back, A., & Chen, T. (2002). Universal approximation of multiple nonlinear operators by neural networks. Neural Computation, 14, 2561-2566.
2. Broer, H. W., Dumortier, F., Stiren, S. J. van, & Takens, F. (1991). Structure in dynamics: Finite dimensional deterministic studies. Amsterdam: North-Holland.
3. Cao, C., Annaswamy, A., & Kojic, A. (2003). Parameter convergence in nonlinearly parameterized systems. IEEE Trans. on Automatic Control, 48(3), 397-411.
4. Chen, T., & Amari, S. (2001). Stability of asymmetric Hopfield networks. IEEE Transactions on Neural Networks, 12(1), 159-163.
5. Chen, T., & Chen, H. (1995). Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Transactions on Neural Networks, 6(4), 911-917.
6. Cohen, M., & Grossberg, S. (1983). Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics, 13, 815-826.
7. Conant, R. C., & Ashby, W. R. (1970). Every good regulator of a system must be a model of that system. Int. J. Syst. Sci., 1, 89-98.
8. Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Math. of Control, Signals and Systems, 2, 303-314.
9. Feldkamp, L., & Puskorius, G. (1997). Fixed-weight controller for multiple systems. In Proc. of the IEEE International Joint Conference on Neural Networks (pp. 2268-2272). Piscataway, NJ: IEEE Press.
10. Feldkamp, L., Puskorius, G., & Moore, P. (1996). Adaptation from fixed weight dynamic networks. In Proc. of the IEEE International Conference on Neural Networks. Piscataway, NJ: IEEE Press.
11. Fuchs, A., & Haken, H. (1988a). Pattern recognition and associative memory as dynamical processes in a synergetic system, I: Translational variance, selective attention, and decomposition of scenes. Biological Cybernetics, 60, 17-22.
12. Fuchs, A., & Haken, H. (1988b). Pattern recognition and associative memory as dynamical processes in a synergetic system, II: Decomposition of complex scenes, simultaneous invariance with respect to translation, rotation, and scaling. Biological Cybernetics, 60, 107-109.
13. Gorban, A. (2004). Singularities of transition processes in dynamical systems: Qualitative theory of critical delays. Electronic Journal of Differential Equations, Monograph 5. Available online at http://ejde.math.unt.edu.
14. Guckenheimer, J., & Holmes, P. (2002). Nonlinear oscillations, dynamical systems and bifurcations of vector fields. New York: Springer.
15. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. PNAS, 79, 2554-2558.
16. Kaneko, K., & Tsuda, I. (2003). Chaotic itinerancy. Chaos, 13(3), 926-936.
17. Khalil, H. (2002). Nonlinear systems (3d ed.). Upper Saddle River, NJ: Prentice Hall.
18. Lo, J. (2001). Adaptive vs. accommodative neural networks for adaptive system identification. In Proc. of the IEEE International Joint Conference on Neural Networks (pp. 1279-1284). Piscataway, NJ: IEEE Press.
19. Loria, A., Panteley, E., Popovic, D., & Teel, A. (2003). Persistency of excitation for uniform convergence in nonlinear control systems. Available online at http://arxiv.org/abs/math/0301335.
20. Lu, W., & Chen, T. (2003). New conditions on global stability of Cohen-Grossberg neural networks. Neural Computation, 15, 1173-1189.
21. Michel, A., Farrel, J. A., & Porod, W. (1989). Qualitative analysis of neural networks. IEEE Transactions on Circuits and Systems, 36, 229-243.
22. Milnor, J. (1985). On the concept of attractor. Commun. Math. Phys., 99, 177-195.
23. Pavlov, A., Wouw, N. van de, & Nijmeijer, H. (2006). Uniform output regulation of nonlinear systems: A convergent dynamics approach. Boston: Birkhauser.
24. Prokhorov, D. V., Feldkamp, L. A., & Tyukin, I. Y. (2002, May). Adaptive behavior with fixed weights in recurrent neural networks. In Proc. of IEEE International Joint Conference on Neural Networks (Vol. 3, pp. 2018-2022). Piscataway, NJ: IEEE Press.
25. Sontag, E. (2003). Adaptation and regulation with signal detection implies internal model. Systems and Control Letters, 50, 119-126.
26. Tsodyks, M. V., Pawelzik, K., & Markram, H. (1998). Neural networks with dynamic synapses. Neural Computation, 10, 821-835.
27. Tsuda, I. (1991). Chaotic itinerancy as a dynamical basis of hermeneutics in brain and mind. World Futures, 32, 167-184.
28. Tsuda, I., & Fujii, H. (2004). A complex systems approach to an interpretation of dynamic brain activity I: Chaotic itinerancy can provide a mathematical basis for information processing in cortical transitory and nonstationary dynamics. Lecture Notes in Computer Science, 3146, 109-128.
29. Tyukin, I., Steur, E., Nijmeijer, H., & van Leeuwen, C. (2008). Non-uniform small-gain theorems for systems with unstable invariant sets. SIAM Journal on Control and Optimization, 47(2), 849-882.
30. Tyukin, I. Y., Prokhorov, D. V., & van Leeuwen, C. (2007). Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parameterization. IEEE Transactions on Automatic Control, 52(9), 1543-1559.
31. Yang, H., & Dillon, T. (1994). Exponential stability and oscillation of Hopfield networks. IEEE Transactions on Neural Networks, 5, 719-729.
32. Younger, S., Conwell, P., & Cotter, N. (1999). Fixed-weight on-line learning. IEEE Trans, on Neural Networks, 10(2), 272-283.