Learning to imitate stochastic time series in a compositional way by   chaos
  This study shows that a mixture of RNN experts model can acquire the ability to generate sequences combining multiple primitive patterns by means of self-organizing chaos. By training of the model, each expert learns a primitive sequence pattern, and a gating network learns to imitate stochastic switching of the multiple primitives via a chaotic dynamics, utilizing a sensitive dependence on initial conditions. As a demonstration, we present a numerical simulation in which the model learns Markov chain switching among some Lissajous curves by a chaotic dynamics. Our analysis shows that by using a sufficient amount of training data, balanced with the network memory capacity, it is possible to satisfy the conditions for embedding the target stochastic sequences into a chaotic dynamical system. It is also shown that reconstruction of a stochastic time series by a chaotic model can be stabilized by adding a negligible amount of noise to the dynamics of the model. 
Jun Namikawa and Jun Tani