Complexity Control Methods of Chaos Dynamics in Recurrent Neural Networks.

概要

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This paper demonstrates that the Lyapunov exponents of recurrent neural networks can be controlled by our proposed methods. One of the control methods minimizes a squared error eλ=(λ-λobj)2/2 by a gradient method, where λ is the largest Lyapunov exponent of the network and λobj is a desired exponent. λ implying the dynamical complexity is calculated by observing the state transition for a long-term period. This method is, however, computationally expensive for large-scale recurrent networks and the control is unstable for recurrent networks with chaotic dynamics since a gradient collection through time diverges due to the chaotic instability. We also propose an approximation method in order to reduce the computational cost and realize a "stable" control for chaotic networks. The new method is based on a stochastic relation which allows us to calculate the collection through time in a fashion without time evolution. Simulation results show that the approximation method can control the exponent for recurrent networks with chaotic dynamics under a restriction.
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