Correlation of Firing in Layered Associative Neural Networks

There is growing interest in a phenomenon called the ``synfire chain'', in which firings of neurons propagate from pool to pool in the chain. The mechanism of the synfire chain has been analyzed by many resarchers. Keeping the synfire chain phenomenon in mind, we investigate a layered associative memory neural network model, in which patterns are embedded in connections between neurons. In this model, we also include uniform noise in connections, which induces common input in the next layer. Such common input in layers generate correlated firings of neurons. We theoretically obtain the evolution of retrieval states in the case of infinite pattern loading. We find that the overlap between patterns and neuronal states is not given as a deterministic quantity, but is described by a probability distribution defined over the emsemble of synaptic matrices. Our simulation results are in excellent agreement with theoretical calculations.