A novel continuous-time neural network for realizing associative memory

A novel neural network is proposed in this paper for realizing associative memory. The main advantage of the neural network is that each prototype pattern is stored if and only if as an asymptotically stable equilibrium point. Furthermore, the basin of attraction of each desired memory pattern is distributed reasonably (in the Hamming distance sense), and an equilibrium point that is not asymptotically stable is really the state that cannot be recognized. The proposed network also has a high storage as well as the capability of learning and forgetting, and all its components can be implemented. The network considered is a very simple linear system with a projection on a closed convex set spanned by the prototype patterns. The advanced performance of the proposed network is demonstrated by means of simulation of a numerical example.

[1]  L. Personnaz,et al.  Collective computational properties of neural networks: New learning mechanisms. , 1986, Physical review. A, General physics.

[2]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[3]  Stefen Hui,et al.  Solving linear programming problems with neural networks: a comparative study , 1995, IEEE Trans. Neural Networks.

[4]  A. Michel,et al.  Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube , 1989 .

[5]  P. Hartman.  Ordinary Differential Equations , 1965 .

[6]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[7]  Wolfgang Porod,et al.  Qualitative analysis and synthesis of a class of neural networks , 1988 .

[8]  Anthony N. Michel,et al.  A learning and forgetting algorithm in associative memories: results involving pseudo-inverses , 1991 .

[9]  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.

[10]  I. Guyon,et al.  Information storage and retrieval in spin-glass like neural networks , 1985 .

[11]  Stanislaw H. Zak,et al.  On neural networks that design neural associative memories , 1997, IEEE Trans. Neural Networks.

[12]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[13]  A.N. Michel,et al.  Analysis and synthesis of a class of discrete-time neural networks described on hypercubes , 1991, IEEE Trans. Neural Networks.

[14]  Stefen Hui,et al.  Synthesis of Brain-State-in-a-Box (BSB) based associative memories , 1994, IEEE Trans. Neural Networks.

[15]  J. P. Lasalle.  The stability of dynamical systems , 1976 .

[16]  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.

[17]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[18]  Youshen Xia,et al.  Neural network for solving linear programming problems with bounded variables , 1995, IEEE Trans. Neural Networks.

[19]  Yousen Xia.  Neural network for solving extended linear programming problems , 1997, IEEE Trans. Neural Networks.

[20]  A.N. Michel,et al.  Associative memories via artificial neural networks , 1990, IEEE Control Systems Magazine.