How Delays Affect Neural Dynamics and Learning

IEEE Transactions on Neural Networks

Volumn 5, Issue 4, 1994, Pages 612-621

  Baldi, Pierre ^a   Atiya, Amir F ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b QANTXX Inc ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER ARCHITECTURE; COMPUTER NETWORKS; LEARNING SYSTEMS; MAN MACHINE SYSTEMS; MATHEMATICAL MODELS;

COMMUNICATION DELAYS; NEURAL DYNAMICS;

NEURAL NETWORKS;

EID: 0028468031     PISSN: 10459227     EISSN: 19410093     Source Type: Journal    
DOI: 10.1109/72.298231     Document Type: Article

References (30)

1. A. Atiya and P. Baldi, “Oscillations and synchronizations in neural networks: An exploration of the labeling hypothesis,” Int. J. Neural Systems, vol. 1, no. 2, 103–124, 1989.
2. A. Atiya and A. G. Parlos, Spatio-Temporal Neural Networks with Applications to Nonlinear System Identification. Preprint, 1992.
3. P. Baldi and R. Meir, “Computing with arrays of coupled oscillators: An application to preattentive texture discrimination,” Neural Computation, vol. 2, pp. 458–471, 1990.
4. P. Baldi, “Gradient descent learning algorithms and limitations in dynamical systems,” in Back-propagation: Theory, Architectures and Applications, Y. Chauvin and D. E. Rumelhart Eds. Hillside, NJ: Lawrence Erlbaum Associates, 1994.
5. S. Busenberg, D. C. Fischer, and M. Martelli, “Better bounds for periodic solutions of differential equations in banach spaces,” in Proceedings of the American Mathematical Society, vol. 96, no. 2, 376–378, 1986.
6. S. Busenberg and M. Martelli, “Bounds for the period of periodic orbits of dynamical systems,” J. Differential Equations, vol. 67, pp. 359–371, 1987.
7. C. E. Carr and M. Konishi, “Axonal delay lines for time measurement in the owl's brainstem,” PNAS USA, vol. 85, pp. 8311–8315, 1988.
8. F. Crick and C. Koch, “Toward a neurobiological theory of consciousness,” in Seminars in the Neurosciences, vol. 2, pp. 263–275, 1990.
9. B. de Vries and J. C. Principe, “A theory for neural networks with time delays,” in Advances in Neural Information Processing Systems, vol. 3, R. P. Lippmann, J. E. Moody and D. S. Touretzky, Eds. San Matteo, CA: Morgan Kaufmann, 1991, pp. 162–168.
10. C. M. Gray, P. König, A. K. Engel, and W. Singer, “Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties,” Nature, vol. 338, pp. 334–337, 1989.
11. K. P. Hadeler and J. Tomiuk, “Periodic solutions of difference differential equations,” Arch. Rat. Mech. Anal., vol. 65, pp. 87–95, 1977.
12. J. K. Hale, Theory of Functional Differential Equations. New York: Springer Verlag, 1977.
13. J. K. Hale, “Nonlinear Oscillations in Equations with Delays,” in Nonlinear Oscillations in Biology, in Lecture Notes in Applied Mathematics, vol. 17, F. C. Hoppensteadt, Ed. Providence, RI, USA: American Mathematical Society, 1979.
14. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopfield Bifurcation. London Mathematical Society, Lecture Note Series 41, Cambridge: Cambridge University Press, 1981.
15. M. W. Hirsch, “Convergence in neural networks,” in Proc. 1987 Int. Conf. Neural Networks, San Diego, CA, 1987.
16. J. J. Hopfield, (1984) “Neurons with graded response have collective computational properties like those of two-state neurons,” PNAS USA, vol. 81, pp. 3088–3092, 1984.
17. N. Kopell and G. B. Ermentrout, “Coupled oscillators and the design of central pattern generators,” Mathematical Biosciences, vol. 90, pp. 87–109, 1988.
18. S. G. Lisberger and T. J. Sejnowski, Computational Analysis Predicts Sites of Motor Learning in the Vestibulo-Ocular Reflex. Preprint, 1991.
19. C. M. Marcus and R. M. Westervelt, “Stability of analog neural networks with delay,” Physical Review A, vol. 39, no. 1, 347–359, 1989.
20. E. Niebur, H. G. Schuster, and D. M. Kammen, “Collective frequencies and metastability in networks of limit cycle oscillators with time delay,” Physical Review Letters, vol. 67, no. 20, 2753–2756, 1991.
21. B. Pearlmutter, “Learning state space trajectories in recurrent neural networks,” Neural Computation, vol. 1, no. 2, 263–269, 1989.
22. F. J. Pineda, “Generalization of back-propagation to recurrent neural networks,” Physical Review Letters, vol. 59, no. 19, pp. 2229–2232, 1987.
23. H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, “Local and global self-entrainments in oscillator lattices,” Progress in Theoretical Physics, vol. 77, no. 5, pp. 1005–1010, 1987.
24. H. Smith, “Monotone semiflows generated by functional differential equations,” J. Differential Equations, vol. 66, no. 420–442, 1987.
25. H. Sompolinsky, D. Golomb, and D. Kleinfeld, “Global processing of visual stimuli in a neural network of coupled oscillators,” PNAS USA, vol. 87, pp. 7200–7204, 1990.
26. K. P. Unnikrishnan, J. J. Hopfield, and D. W. Tank, “Connected-digit speaker dependent speech recognition using a neural network with time-delayed connections,” IEEE Trans. Signal Processing, vol. 39, no. 3, pp. 698–713, 1991.
27. U. Van der Heide, Analysis of Neural Networks. New York: Springer Verlag, 1980.
28. C. von der Malsburg, “The Correlation Theory of Brain Function.” Internal Report 81–2, Department of Neurobiology, Max Planck Institute for Biophysical Chemistry, 1981.
29. R. J. Williams and D. Zipser, “A learning algorithm for continually running fully recurrent neural networks,” Neural Computation, vol. 1, no. 2, 270–280, 1989.
30. M. A. Wilson and J. M. Bower, “A computer simulation of oscillatory behavior in primary visual cortex,” Neural Computation, vol. 3, no. 4, 498–509, 1991.