We investigate storage capacity and generalization ability for two types of fully connected layered neural networks with non-monotonic transfer functions; random patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network in which a non-monotonic transfer...

We investigate storage capacity of two types of fully connected layered neural networks with sparse coding when binary patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network, in which a transfer function of even layers is different from that of odd...

In this paper, a new approximate formula to probability integral is deduced using theoretical analysis combining with computer numerical simulation. The absolute storage capacity of the Hopfield neural network is analyzed with this approximate formula and a more strict result is obtained.

In this paper, the storage capacity of the Q-state complex phasor neural network is analysed with the signal-to-noise theory. The results indicate that the storage capacity of the model approaches that of the Hopfield model if the number Q is small; while the storage capacity is proportional to...

We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian mean field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which...

A family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of the replica approach are computed.

We make an estimation of a maximizer of posterior marginals (MPM) as for a multi-valued information symbol by a code-division multiple access (CDMA) demodulator using a multi-valued spreading code sequence within a framework of a Bayesian inference. We calculate an estimation error of the CDMA...

The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the perceptron-based code saturates the theoretically achievable limit in...

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways...