Complexity control methods of chaos dynamics in recurrent neural networks

摘要

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 e{sub}λ = (λ - λ {sup}(obj)){sup}2/2 by a gradient method, where λ is the largest Lyapunov exponent of the network and λ{sup}(obj) is a desired exponent. A 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.