Related papers: The Ashkin-Teller neural network near saturation
An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns…
The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The…
The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks, storing ternary patterns, are studied using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the…
The thermodynamic and retrieval properties of the Blume-Emery-Griffiths neural network with synchronous updating and variable dilution are studied using replica mean-field theory. Several forms of dilution are allowed by pruning the…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…
Ashkin-Teller type perceptron models are introduced. Their maximal capacity per number of couplings is calculated within a first-step replica-symmetry-breaking Gardner approach. The results are compared with extensive numerical simulations…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
The replica method is applied to a neural network model with state-dependent synapses built from those patterns having a correlation with the state of the system greater than a certain threshold. Replica-symmetric and first-step…
We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…
We studied the computational properties of an attractor neural network (ANN) with different network topologies. Though fully connected neural networks exhibit, in general, a good performance, they are biologically unrealistic, as it is…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…
The aim of this thesis is to compare the capacity of different models of neural networks. We start by analysing the problem solving capacity of a single perceptron using a simple combinatorial argument. After some observations on the…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…