Complex Valued, Multi-Layer Hopfield Neural Network

Based on a Complex Valued Neural Network (CVNNs) with the neurons placed in multiple layers, several interesting associative memories are proposed and their dynamics is investigated. Specifically, the synaptic weight matrix was chosen to be Block Hermitian, Block Jacobi, Block Toeplitz and Block Hankel. It is reasoned that in the case of such structured multilayer CVNNs, an interesting Convergence theorem holds true which enables that utilization of such an Artificial Neural Network as an associative memory. It is expected that the CVNNs proposed in this research paper have biological significance.