Elman topology with sigma–pi units: An application to the modeling of verbal hallucinations in schizophrenia

The development of neural network models has greatly enhanced the comprehension of cognitive phenomena. Here, we show that models using multiplicative processing of inputs are both powerful and simple to train and understand. We believe they are valuable tools for cognitive explorations. Our model can be viewed as a subclass of networks built on sigma-pi units and we show how to derive the Kronecker product representation from the classical sigma-pi unit. We also show how the connectivity requirements of the Kronecker product can be relaxed considering statistical arguments. We use the multiplicative network to implement what we call an Elman topology, that is, a simple recurrent network (SRN) that supports aspects of language processing. As an application, we model the appearance of hallucinated voices after network damage, and show that we can reproduce results previously obtained with SRNs concerning the pathology of schizophrenia.