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We investigate dynamics of recurrent neural networks with correlated noise toanalyze the noise's effect. The mechanism of correlated firing has beenanalyzed in various models, but its functional roles have not been discussed insufficient detail. Aoyagi and Aoki have shown that the state transition of anetwork is invoked by synchronous spikes. We introduce two types of noise toeach neuron: thermal independent noise and correlated noise. Due to the effectsof correlated noise, the correlation between neural inputs cannot be ignored,so the behavior of the network has sample dependence. We discuss two types ofassociative memory models: one with auto- and weak cross-correlationconnections and one with hierarchically correlated patterns. The former issimilar in structure to Aoyagi and Aoki's model. We show that stochastictransition can be presented by correlated rather than thermal noise. In thelatter, we show stochastic transition from a memory state to a mixture stateusing correlated noise. To analyze the stochastic transitions, we derive amacroscopic dynamic description as a recurrence relation form of a probabilitydensity function when the correlated noise exists. Computer simulations agreewith theoretical results.Comment: 21 page

Stochastic Transitions of Attractors in Associative Memory Models with Correlated Noise