2 research outputs found
Multiplicative versus additive noise in multi-state neural networks
The effects of a variable amount of random dilution of the synaptic couplings
in Q-Ising multi-state neural networks with Hebbian learning are examined. A
fraction of the couplings is explicitly allowed to be anti-Hebbian. Random
dilution represents the dying or pruning of synapses and, hence, a static
disruption of the learning process which can be considered as a form of
multiplicative noise in the learning rule. Both parallel and sequential
updating of the neurons can be treated. Symmetric dilution in the statics of
the network is studied using the mean-field theory approach of statistical
mechanics. General dilution, including asymmetric pruning of the couplings, is
examined using the generating functional (path integral) approach of disordered
systems. It is shown that random dilution acts as additive gaussian noise in
the Hebbian learning rule with a mean zero and a variance depending on the
connectivity of the network and on the symmetry. Furthermore, a scaling factor
appears that essentially measures the average amount of anti-Hebbian couplings.Comment: 15 pages, 5 figures, to appear in the proceedings of the Conference
on Noise in Complex Systems and Stochastic Dynamics II (SPIE International
An associative network with spatially organized connectivity
We investigate the properties of an autoassociative network of
threshold-linear units whose synaptic connectivity is spatially structured and
asymmetric. Since the methods of equilibrium statistical mechanics cannot be
applied to such a network due to the lack of a Hamiltonian, we approach the
problem through a signal-to-noise analysis, that we adapt to spatially
organized networks. The conditions are analyzed for the appearance of stable,
spatially non-uniform profiles of activity with large overlaps with one of the
stored patterns. It is also shown, with simulations and analytic results, that
the storage capacity does not decrease much when the connectivity of the
network becomes short range. In addition, the method used here enables us to
calculate exactly the storage capacity of a randomly connected network with
arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA