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Learning with complex dynamics

An important aspect of an autonomous system is its ability to make continuous information processing of input data from a (rapidly) changing environment. We have developed a recurrent neural network, with asymmetric connections and distance-dependent delays (Liljenström 1991), that makes use of its complex dynamics for achieving a fast and accurate association process. The model is mimicking the olfactory cortex in its structure and dynamics, but the results are generic. The dynamics can be controlled by a single parameter, giving point attractor, limit cycle, or strange attractor behavior, corresponding to different perceptual states (Liljenström 1992), (Liljenström and Wu 1993). A change in this parameter thus regulates the sensitivity/stability of the system, depending on the demands or current situation (Wu and Liljenström 1994).

For any given static or time-varying input pattern the system compares the induced (oscillatory) network activity with previously stored patterns, at gradually increasing sensitivity. If unable to make a match within a certain period, the current input is stored as a new limit cycle memory state (Liljenström 1995). This is shown in the figure below, where the activity of two arbitrary network units are plotted against each other for one simulated second.

The oscillatory dynamics can enhance weak signals and speed up information processing considerably, whereas an (initial) chaotic-like behavior can enhance system sensitivity and flexibility (Liljenström 1995). System dynamics and functions is also affected by the intrinsic noise level. A change in this level can result in state transitions, e.g. between two oscillatory states, or from an oscillatory to a chaotic state. Memory recall (convergence) time can even be minimized for certain optimal noise levels (Liljenström and Wu 1995). (Liljenström and Wu 1995). (Liljenström and Wu 1994), These findings could have important technical implications, in particular for real-time pattern recognition. A recent parallel implementation of the current model on the Connection Machine gives great improvement in speed and resolution of the dynamical simulations (Wilhelmsson and Liljenström 1993) .

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