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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 11 (2000), S. 113-129 
    ISSN: 1573-773X
    Keywords: virtual input layer ; neural network training ; fast learning ; SVD
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A new methodology for neural learning is presented. Only a single iteration is needed to train a feed-forward network with near-optimal results. This is achieved by introducing a key modification to the conventional multi-layer architecture. A virtual input layer is implemented, which is connected to the nominal input layer by a special nonlinear transfer function, and to the first hidden layer by regular (linear) synapses. A sequence of alternating direction singular value decompositions is then used to determine precisely the inter-layer synaptic weights. This computational paradigm exploits the known separability of the linear (inter-layer propagation) and nonlinear (neuron activation) aspects of information transfer within a neural network. Examples show that the trained neural networks generalize well.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 29 (1982), S. 363-374 
    ISSN: 1572-9613
    Keywords: Linear transport (Boltzmann) operator ; two-dimensional spectrum ; spectral decomposition ; generalized eigenfunction expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The spectral decomposition theorem is proved for linear transport operators with separable scattering kernels and energy-dependent collision frequency in both one- and three-dimensional geometries.
    Type of Medium: Electronic Resource
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