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1 July 1990 Feedback network with space-invariant coupling
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Proceedings Volume 1319, Optics in Complex Systems; (1990)
Event: 15th International Optics in Complex Systems, 1990, Garmisch, Germany
We present a feedback system where a picture u(t) circulates under successive application of a convolution operation with the kernel h and of a nonlinearity NL: t1(t + 1) = NL((u(t)*h)1) . (1) This system represents a special class of neural networks: it is space invariant. In comparison to space variant neuronal networks it can be implement much easier, for example by Fast Fourier Transform, or even optically. Nevertheless, it exhibits a broad spectrum of behavior: there may be deterministic chaos in space and time, i. e. the system is unpredictable in principle and displays no fixed points, or stable structures may evolve.' Certain convolution kernels may lead to the evolution of stable structures, i. e. fixed points, that look like patterns from nature, for example like crystals or like magnetic domains.' In experiments described in 2 we observed that the stable structures can be disturbed quite heavily and are yet autoassociativly restored during a couple of iteration cycles. Here we show how to adjust the kernel h in order to obtain a certain desired stable state u of eq. 1, and how to apply the system to shift invariant pattern recognition.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Gerd Haeusler and Eberhardt Lange "Feedback network with space-invariant coupling", Proc. SPIE 1319, Optics in Complex Systems, (1 July 1990);

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