Is Chaos Good for Learning?
J. C. Sprott
Department of Physics
University of Wisconsin - Madison
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
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Fig. 1. A representative sequence of 32 points from the training
set at the onset of chaos.
Fig. 2. Lyapunov exponent as a function of A
logistic map, showing the accumulation point at A
3.4699456718... where chaos onsets.
Fig. 3. Three typical instances of the training showing how the
decreases with training trial.
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. 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