  We investigate dynamics of recurrent neural networks with correlated noise to
analyze the noise's effect. The mechanism of correlated firing has been
analyzed in various models, but its functional roles have not been discussed in
sufficient detail. Aoyagi and Aoki have shown that the state transition of a
network is invoked by synchronous spikes. We introduce two types of noise to
each neuron: thermal independent noise and correlated noise. Due to the effects
of correlated noise, the correlation between neural inputs cannot be ignored,
so the behavior of the network has sample dependence. We discuss two types of
associative memory models: one with auto- and weak cross-correlation
connections and one with hierarchically correlated patterns. The former is
similar in structure to Aoyagi and Aoki's model. We show that stochastic
transition can be presented by correlated rather than thermal noise. In the
latter, we show stochastic transition from a memory state to a mixture state
using correlated noise. To analyze the stochastic transitions, we derive a
macroscopic dynamic description as a recurrence relation form of a probability
density function when the correlated noise exists. Computer simulations agree
with theoretical results.
