DSpace Collection: <!-- 2200 -->斉藤 朝輝 (Saito, Asaki)http://hdl.handle.net/10445/19912020-02-23T04:09:59Z2020-02-23T04:09:59ZComputation of f^{-1} Spectral Chaos Using Cubic Surdshttp://hdl.handle.net/10445/60182017-08-01T00:38:57Z2008-01-01T00:00:00ZTitle: Computation of f^{-1} Spectral Chaos Using Cubic Surds2008-01-01T00:00:00ZRealization of True Orbit Simulation Using Integer Arithmetichttp://hdl.handle.net/10445/60192017-07-27T05:41:37Z2010-01-01T00:00:00ZTitle: Realization of True Orbit Simulation Using Integer Arithmetic2010-01-01T00:00:00ZTrue Orbit Computation Using Integer Arithmetichttp://hdl.handle.net/10445/60202017-07-27T08:03:11Z2011-01-01T00:00:00ZTitle: True Orbit Computation Using Integer Arithmetic2011-01-01T00:00:00ZDynamical Singularities in Online Learning of Recurrent Neural Networkshttp://hdl.handle.net/10445/60172017-07-27T05:46:33Z2007-01-01T00:00:00ZTitle: Dynamical Singularities in Online Learning of Recurrent Neural Networks
Abstract: We numerically and theoretically demonstrate various singularities, as a dynamical system, of a simple online learning system of a recurrent neural network (RNN) where RNN performs the one-step prediction of a time series generated by a one-dimensional map. More specifically, we show first through numerical simulations that the learning system exhibits singular behaviors (“neutral behaviors”) different from ordinary chaos, such as almost zero finite-time Lyapunov exponents, as well as inaccessibility and power-law decay of the distribution of learning times (transient times). Also, we show through linear stability analysis that, as a dynamical system, the learning system is represented by a singular map whose Jacobian matrix has eigenvalue unity in the whole phase space. In particular, we state that the singularity as a dynamical system (shown by the second method) provides a basic reason for the neutral behaviors (shown by the first method) exhibited by the learning system.2007-01-01T00:00:00Z