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

Authors:
Juan C. Valle-Lisboa;Florencia Reali;Héctor Anastasía;Eduardo Mizraji
Affiliations:
Sección Biofísica, Facultad de Ciencias, Universidad de la República, Iguá 4225, Montevideo 11400, Uruguay;Sección Biofísica, Facultad de Ciencias, Universidad de la República, Iguá 4225, Montevideo 11400, Uruguay;Servicio de Psiquiatría, Hospital Militar, Montevideo, Uruguay;Sección Biofísica, Facultad de Ciencias, Universidad de la República, Iguá 4225, Montevideo 11400, Uruguay
Venue:
Neural Networks
Year:
2005

Citing 10
Cited 2

Multiplying with synapses and neurons

Single neuron computation
Vector logics: the matrix-vector representation of logical calculus

Fuzzy Sets and Systems
NMDA-based pattern discrimination in a modeled cortical neuron

Neural Computation
On the computational power of neural nets

Journal of Computer and System Sciences
Computing with the leaky integrate-and-fire neuron: logarithmic computation and multiplication

Neural Computation
Transformations of sigma-pi nets: obtaining reflected functions by reflecting weight matrices

Neural Networks
Natural Language Grammatical Inference with Recurrent Neural Networks

IEEE Transactions on Knowledge and Data Engineering
On the complexity of computing and learning with multiplicative neural networks

Neural Computation
A neural network simulation of hallucinated “voices” and associated speech perception impairments in schizophrenic patients

Journal of Cognitive Neuroscience
A cognitive architecture that solves a problem stated by Minsky

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

A non-linear index to evaluate a journal's scientific impact

Information Sciences: an International Journal
Quantized Neural Modeling: Hybrid Quantized Architecture in Elman Networks

Neural Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.