System-size resonance in a binary attractor neural network.

System size resonance (SSR) is a phenomenon in which the response of a system is optimal for a certain finite size, but poorer as the size goes to zero or infinity. In order to show SSR effects in binary attractor neural networks, we study the response of a network, in the ferromagnetic phase, to an external, time-dependent stimulus. Under the presence of such a stimulus, the network shows SSR, as is demonstrated by the measure of the signal amplification both analytically and by simulation.

Time evolution of the extremely diluted Blume-Emery-Griffiths neural network.

A study of the time evolution and a stability analysis of the phases in the extremely diluted Blume-Emery-Griffiths neural network model are shown to yield new phase diagrams in which fluctuation retrieval may drive pattern retrieval. It is shown that saddle-point solutions associated with fluctuation overlaps slow down the flow of the network states towards the retrieval fixed points. A comparison of the performance with other three-state networks is also presented.

Finite-size scaling in disordered systems.

The critical behavior of a quenched random hypercubic sample of linear size L is considered, within the "random-T(c)" field-theoretical model, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension d=4-epsilon and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.

Three-state neural network: from mutual information to the Hamiltonian.

The mutual information, I, of the three-state neural network can be obtained exactly for the mean-field architecture, as a function of three macroscopic parameters: the overlap, the neural activity and the activity-overlap, i.e., the overlap restricted to the active neurons. We perform an expansion of I on the overlap and the activity-overlap, around their values for neurons almost independent of the patterns. From this expansion we obtain an expression for a Hamiltonian which optimizes the retrieval properties of this system. This Hamiltonian has the form of a disordered Blume-Emery-Griffiths model. The dynamics corresponding to this Hamiltonian is found. As a special characteristic of such a network, we see that information can survive even if no overlap is present. Hence the basin of attraction of the patterns and the retrieval capacity is much larger than for the Hopfield network. The extreme diluted version is analyzed, the curves of information are plotted and the phase diagrams are built.

Blind source separation in the presence of weak sources.

We investigate the information processing of a linear mixture of independent sources of different magnitudes. In particular we consider the case where a number m of the sources can be considered as "strong" as compared to the other ones, the "weak" sources. We find that it is preferable to perform blind source separation in the space spanned by the strong sources, and that this can be easily done by first projecting the signal onto the m largest principal components. We illustrate the analytical results with numerical simulations.