arXiv subjects
Publications and source records attributed to Elka Korutcheva.
We study the first-order transition in the model of a simple perceptron with continuous weights and large, bit finite value of the inputs. Making the analogy with the usual finite-size physical systems, we calculate the shift and the rounding exponents near the transition point. In the case of a general perceptron with larger variety of inputs, the analysis only gives bounds for the exponents.
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 {\em 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 on 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 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 analized, the curves of information are plotted and the phase diagrams are built.
We calculate the mutual information (MI) of a two-layered neural network with noiseless, continuous inputs and binary, stochastic outputs under several assumptions on the synaptic efficiencies. The interesting regime corresponds to the limit where the number of both input and output units is large but their ratio is kept fixed at a value $α$. We first present a solution for the MI using the replica technique with a replica symmetric (RS) ansatz. Then we find an exact solution for this quantity valid in a neighborhood of $α= 0$. An analysis of this solution shows that the system must have a phase transition at some finite value of $α$. This transition shows a singularity in the third derivative of the MI. As the RS solution turns out to be infinitely differentiable, it could be regarded as a smooth approximation to the MI. This is checked numerically in the validity domain of the exact solution.
We investigate the critical dynamics of the time-dependent Landau-Ginzburg model with non conserved n-component order parameter (Model A) in the presence of long-range correlated quenched impurities. We use a special kind of long-range correlations, previously introduced by Weinrib and Halperin. Using a double expansion in εand δwe calculate the critical exponent z up to second order on the small parameters. We show that the quenched impurities of this kind affect the critical dynamics already in first order of εand δ, leading to a relevant correction for the mean field value of the exponent z