  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.
