Global dynamics in neural networks. III

Global dynamics in neural networks. III,10.1109/IJCNN.1991.155358,Fernanda Botelho,Max Garzon

Global dynamics in neural networks. III   (Citations: 3)
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A transform is introduced that maps discrete neural network dynamics to almost everywhere topologically conjugate dynamical systems on the unit interval. In many cases this correspondence gives rise to continuous conjugates, in which case the transform preserves entropy. The transform also allows transfer of many dynamical properties of continuous systems to a large class of infinite discrete neural networks. For instance, it is proved that the network dynamics of very simple classes of neural networks, even with highly symmetric weights and architectures, have chaotic regions of evolution (in the sense of existence of scrambled sets and configurations of arbitrarily large periods). These results raise the possibility of fully modeling parallel computability on real-valued dynamical systems by discrete neural nets
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    • ...(For an interesting approach to computations on nets of unbounded size, see [14, 15, 18, 19].)...

    Pekka Orponen. Neural Networks and Complexity Theory

    • ...The main tool is a transform for neural networks regarded as dynamical systems on the Cantor sct [8,9,11] to dynamical systems on the euclidean unit n-dimensional cubes...
    • ...of the middle Cantor set of the unit interval in the real line R satisfying certain conditions (continuity and some finiteness conditions -see [8,9,10]...

    Fernanda Botelhoet al. Global dynamics in neural networks. III

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