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...

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...

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...

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.

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington–Kirkpatrick Ising spin glass with random...

Replica symmetry breaking solutions for the new replica anzats, related to general ultrametric spaces, are investigated. A variant of analysis on trees is developed and applied to the computation of the n→0 limit in the new replica anzats.

Replica trick turns out to be a powerful method to deal with disordered systems. Nevertheless, if several replicas are involved, calculations become technically difficult in the presence of a spontaneous symmetry breaking. Given a Parisi Replica Symmetry Breaking (RSB) scheme, the Fourier...

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and Nγ edges, with 1γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the...

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.