Distribution of the activities in a diluted neural network

The dynamics of asymmetrically diluted neural networks can be solved exactly. In the present work, the distribution of the neural activities is calculated analytically for zero-temperature parallel dynamics. This distribution depends on the number of stored patterns and is a continuous function in the good retrieval phase. The continuous part of the distribution of activities is due to the asymmetry of the synapses since it is known that networks with symmetric interactions always have a distribution of activities which is a sum of a few delta functions. The expression for the distribution of activities is also given for a mixture of two patterns which have a non-zero overlap.

[1]  D. R. Bowman,et al.  Spin-glass theory in the Bethe approximation: Insights and problems , 1982 .

[2]  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.

[3]  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.

[4]  A. Bray,et al.  Phase diagrams for dilute spin glasses , 1985 .

[5]  H. Orland.  Mean-field theory for optimization problems , 1985 .

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

[7]  Sompolinsky,et al.  Spin-glass models of neural networks. , 1985, Physical review. A, General physics.

[8]  G. Parisi,et al.  Asymmetric neural networks and the process of learning , 1986 .

[9]  M. Thouless.  Spin-glass on a Bethe lattice. , 1986, Physical review letters.

[10]  Kanter,et al.  Mean-field theory of spin-glasses with finite coordination number. , 1987, Physical review letters.

[11]  M. Mézard,et al.  Mean-field theory of randomly frustrated systems with finite connectivity , 1987 .

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

[13]  Meir,et al.  Exact solution of a layered neural network model. , 1987, Physical review letters.

[14]  Replica symmetric solutions in the Ising spin glass: the tree approximation , 1987 .

[15]  J. Nadal,et al.  Learning and forgetting on asymmetric, diluted neural networks , 1987 .

[16]  Eytan Domany,et al.  Stochastic dynamics of a layered neural network. Exact solution , 1987 .

[17]  P. Mottishaw,et al.  Replica Symmetry Breaking and the Spin-Glass on a Bethe Lattice , 1987 .

[18]  Kree,et al.  Continuous-time dynamics of asymmetrically diluted neural networks. , 1987, Physical review. A, General physics.

[19]  The continuous distribution function of the effective fields of the Ising spin glass of the ±J model , 1987 .

[20]  Bernard Derrida,et al.  Distribution of local magnetisations in random networks of automata , 1987 .

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

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

[23]  Meir,et al.  Chaotic behavior of a layered neural network. , 1988, Physical review. A, General physics.

[24]  Ron Meir.  Extensions of a solvable feed forward neural network , 1988 .

[25]  Meir,et al.  Layered feed-forward neural network with exactly soluble dynamics. , 1988, Physical review. A, General physics.

[26]  Gutfreund,et al.  Processing of temporal sequences in neural networks. , 1988, Physical review letters.

[27]  Henrik Flyvbjerg,et al.  An order parameter for networks of automata , 1988 .

[28]  Ising spin glass in the Bethe approximation at zero temperature , 1988 .

[29]  A. Noest.  Associative Memory in Sparse Phasor Neural Networks , 1988 .

[30]  Coolen,et al.  Image evolution in Hopfield networks. , 1988, Physical review. A, General physics.

[31]  Ising spin glass in a field zero temperature in the Bethe approximation , 1988 .

[32]  Inhomogeneous magnetization in dilute asymmetric and symmetric systems. , 1988, Physical review letters.