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Computational Capabilities of Recurrent NARX Neural Networks

dc.contributor.authorSiegelmann, Hava T.en_US
dc.contributor.authorHorne, Bill G.en_US
dc.contributor.authorGiles, C. Leeen_US
dc.description.abstractRecently, fully connected recurrent neural networks have been proven to be computationally rich --- at least as powerful as Turing machines. This work focuses on another network which is popular in control applications and has been found to be very effective at learning a variety of problems. These networks are based upon Nonlinear AutoRegressive models with eXogenous Inputs (NARX models), and are therefore called {\em NARX networks}. As opposed to other recurrent networks, NARX networks have a limited feedback which comes only from the output neuron rather than from hidden states. They are formalized by \[ y(t) = \Psi \left( \rule[-1ex]{0em}{3ex} u(t-n_u), \ldots, u(t-1), u(t), y(t-n_y), \ldots, y(t-1) \right), \] where $u(t)$ and $y(t)$ represent input and output of the network at time $t$, $n_u$ and $n_y$ are the input and output order, and the function $\Psi$ is the mapping performed by a Multilayer Perceptron. We constructively prove that the NARX networks with a finite number of parameters are computationally as strong as fully connected recurrent networks and thus Turing machines. We conclude that in theory one can use the NARX models, rather than conventional recurrent networks without any computational loss even though their feedback is limited. Furthermore, these results raise the issue of what amount of feedback or recurrence is necessary for any network to be Turing equivalent and what restrictions on feedback limit computational power. (Also cross-referenced as UMIACS-TR-95-12)en_US
dc.format.extent423139 bytes
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3408en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-95-12en_US
dc.titleComputational Capabilities of Recurrent NARX Neural Networksen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US

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