Related papers: Parallel dynamics of extremely diluted symmetric Q…
This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise…
Using a probabilistic approach we study the parallel dynamics of fully connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown to exist at zero temperature. A recursive scheme is set up to determine the time…
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 retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical…
Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature…
The time evolution of the local field in symmetric Q-Ising neural networks is studied for arbitrary Q. In particular, the structure of the noise and the appearance of gaps in the probability distribution are discussed. Results are presented…
In this work we solve the dynamics of pattern diluted associative networks, evolving via sequential Glauber update. We derive dynamical equations for the order parameters, that quantify the simultaneous pattern recall of the system, and…
We consider the dynamics of diluted neural networks with clipped and adapting synapses. Unlike previous studies, the learning rate is kept constant as the connectivity tends to infinity: the synapses evolve on a time scale intermediate…
We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…
We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is…
We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
The time evolution of the extremely diluted Blume-Emery-Griffiths neural network model is studied, and a detailed equilibrium phase diagram is obtained exhibiting pattern retrieval, fluctuation retrieval and self-sustained activity phases.…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
Control of large-scale networked systems often necessitates the availability of complex models for the interactions amongst the agents. However in many applications, building accurate models of agents or interactions amongst them might be…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution…
The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one…
The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied in extension of a recent work on…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…