Is Chaos Good for Learning?

J. C. Sprott
Department of Physics
University of Wisconsin - Madison

ABSTRACT

This paper demonstrates that an artificial neural network training on time-series data from the logistic map at the onset of chaos trains more effectively when it is weakly chaotic. This suggests that a modest amount of chaos in the brain in addition to the ever present random noise might be beneficial for learning. In such a case, human subjects might exhibit an increased Lyapunov exponent in their EEG recordings during the performance of creative tasks, suggesting a possible line of future research.

Ref: J. C. Sprott,  Nonlinear Dynamics, Psychology, and Life Sciences 17, 223-232  (2013).

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Fig. 1

Fig. 1. A representative sequence of 32 points from the training set at the onset of chaos.

Fig. 2

Fig. 2. Lyapunov exponent as a function of A for the logistic map, showing the accumulation point at A = 3.4699456718... where chaos onsets.

Fig. 3

Fig. 3. Three typical instances of the training showing how the error e decreases with training trial.
Fig. 4

Fig. 4. Typical variation of the Lyapunov exponent during one instance of the training as the error decreases, showing how positive and negative regions are visited.
Fig. 5

Fig. 5. Average learning rate as a function of Lyapunov exponent in the vicinity of the solution at lambda = 0 showing that weak chaos (positive lambda) is beneficial for learning in this artificial network.