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

 dc.contributor.author Tino, Peter en_US dc.contributor.author Horne, Bill G. en_US dc.contributor.author Giles, C. Lee en_US dc.date.accessioned 2004-05-31T22:29:38Z dc.date.available 2004-05-31T22:29:38Z dc.date.created 1995-01 en_US dc.date.issued 1998-10-15 en_US dc.identifier.uri http://hdl.handle.net/1903/687 dc.description.abstract We 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.extent 2528013 bytes dc.format.mimetype application/postscript dc.language.iso en_US dc.relation.ispartofseries UM Computer Science Department; CS-TR-3396 en_US dc.relation.ispartofseries UMIACS; UMIACS-TR-95-1 en_US dc.title Finite State Machines and Recurrent Neural Networks -- Automata and Dynamical Systems Approaches en_US dc.type Technical Report en_US dc.relation.isAvailableAt Digital Repository at the University of Maryland en_US dc.relation.isAvailableAt University of Maryland (College Park, Md.) en_US dc.relation.isAvailableAt Tech Reports in Computer Science and Engineering en_US dc.relation.isAvailableAt UMIACS Technical Reports en_US
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