Optimal basins of attraction in randomly sparse neural network models

The size of the basin of attraction for randomly sparse neural networks with optimal interactions is calculated. For all values of the storage ratio, alpha =p/C<2, where p is the number of random uncorrelated patterns and C is the connectivity, the basin of attraction is finite, while for alpha <0.42, the basin of attraction is (almost) 100%.

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

[2]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[3]  B. Derrida,et al.  Random networks of automata: a simple annealed approximation , 1986 .

[4]  Thomas B. Kepler,et al.  Domains of attraction in neural networks , 1988 .

[5]  E. Gardner,et al.  Zero temperature parallel dynamics for infinite range spin glasses and neural networks , 1987 .

[6]  E. Gardner,et al.  Maximum Storage Capacity in Neural Networks , 1987 .

[7]  Thomas M. Cover,et al.  Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition , 1965, IEEE Trans. Electron. Comput..

[8]  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.

[9]  D. Amit,et al.  Statistical mechanics of neural networks near saturation , 1987 .

[10]  S. Venkatesh.  Epsilon capacity of neural networks , 1987 .

[11]  W. Krauth,et al.  Learning algorithms with optimal stability in neural networks , 1987 .

[12]  P. Leath,et al.  The failure distribution in percolation models of breakdown , 1987 .

[13]  Marc Mézard,et al.  The roles of stability and symmetry in the dynamics of neural networks , 1988 .

[14]  B. Forrest.  Content-addressability and learning in neural networks , 1988 .

[15]  E. Gardner,et al.  Optimal storage properties of neural network models , 1988 .

[16]  Sompolinsky,et al.  Storing infinite numbers of patterns in a spin-glass model of neural networks. , 1985, Physical review letters.

[17]  E. Gardner.  Multiconnected neural network models , 1987 .

[18]  E. Gardner,et al.  An Exactly Solvable Asymmetric Neural Network Model , 1987 .