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Learning to imitate stochastic time series in a compositional way by chaos. (English) Zbl 1396.68099
Summary: This study shows that a mixture of RNN experts model can acquire the ability to generate sequences that are combination of multiple primitive patterns by means of self-organizing chaos. By training the model, each expert learns a primitive sequence pattern, and a gating network learns to imitate stochastic switching of the multiple primitives via 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 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.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Software:
LSTM
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