Finite State Machines and Recurrent Neural Networks -- Automata and Dynamical Systems Approaches

dc.contributor.authorTino, Peteren_US
dc.contributor.authorHorne, Bill G.en_US
dc.contributor.authorGiles, C. Leeen_US
dc.description.abstractWe present two approaches to the analysis of the relationship between a recurrent neural network (RNN) and the finite state machine \( {\cal M} \) the network is able to exactly mimic. First, the network is treated as a state machine and the relationship between the RNN and \( {\cal M} \) is established in the context of algebraic theory of automata. In the second approach, the RNN is viewed as a set of discrete-time dynamical systems associated with input symbols of \( {\cal M} \). In particular, issues concerning network representation of loops and cycles in the state transition diagram of \( {\cal M} \) are shown to provide a basis for the interpretation of learning process from the point of view of bifurcation analysis. The circumstances under which a loop corresponding to an input symbol \( x \) is represented by an attractive fixed point of the underlying dynamical system associated with \( x \) are investigated. For the case of two recurrent neurons, under some assumptions on weight values, bifurcations can be understood in the geometrical context of intersection of increasing and decreasing parts of curves defining fixed points. The most typical bifurcation responsible for the creation of a new fixed point is the saddle node bifurcation. (Also cross-referenced as UMIACS-TR-95-1)en_US
dc.format.extent2528013 bytes
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
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3396en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-95-1en_US
dc.titleFinite State Machines and Recurrent Neural Networks -- Automata and Dynamical Systems Approachesen_US
dc.typeTechnical Reporten_US
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