Stochastic Symmetry-breaking in a Gaussian Hopfield-model

1 Infinitely many states and stochastic symmetry in a Gaussian Potts - Hopfield model

Fluctuations of the Free Energy in the high temperature Hopfield Model

We consider the Hopfield model of size N and with p ∼ tN patterns, in the whole high temperature (paramagnetic) region. Our result is that the partition function has log-normal fluctuations. It is obtained by extending to the present model the method of the interpolating Brownian Motions used in [10] for the Sherrington-Kirkpatrick model. We view the load t of the memory as a dynamical paramete...

The Ashkin-Teller neural network near saturation

The thermodynamic and retrieval properties of the Ashkin-Teller neural network model storing an infinite number of patterns are examined in the replica-symmetric mean-field approximation. In particular, for linked patterns temperature-capacity phase diagrams are derived for different values of the two-neuron and four-neuron coupling strengths. This model can be considered as a particular non-tr...

Storage Capacity of Kernel Associative Memories

This contribution discusses the thermodynamic phases and storage capacity of an extension of the Hopfield-Little model of associative memory via kernel functions. The analysis is presented for the case of polynomial and Gaussian kernels in a replica symmetry ansatz. As a general result we found for both kernels that the storage capacity increases considerably compared to the Hopfield-Little model.

Bifurcation as the Source of Polymorphism

In this paper we present a symmetry breaking bifurcationbased analysis of a Lotka-Volterra model of competing populations. We describe conditions under which equilibria of the population model can be uninvadable by other phenotypes, which is a necessary condition for the solution to be evolutionarily relevant. We focus on the first branching process that occurs when a monomorphic population los...