Applications of neural networks to digital communications: a survey

Various circuit architectures of simple neuron-like analog processors are considered for online solving of a system of linear equations with real constant and/or time-variable coefficients. The proposed circuit structures can be used, after slight modifications, in related problems, namely, inversion and pseudo-inversion of matrices and for solving linear and quadratic programming problems. Various ordinary differential equation formulation schemes (generally nonlinear) and corresponding circuit architectures are investigated to find which are best suited for VLSI implementations. Special emphasis is given to ill-conditioned problems. The properties and performance of the proposed circuit structures are investigated by extensive computer simulations. >

Neural networks for solving systems of linear equations and related problems

Assuming that the output function of neurons is monotonic and differentiable at any interior point in the output range, the condition necessary for a vertex of a hypercube to become a local minimum of the Hopfield neural networks and the form of the convergence region to that minimum are clarified. Based on this, a method for analyzing and suppressing spurious states in the networks is derived. It is shown that all the spurious states of the traveling salesman problem (TSP) for the Hopfield original energy function can be suppressed by the method, and the validity of the method is demonstrated by computer simulations. >

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Global convergence and suppression of spurious states of the Hopfield neural networks

A multi-input multi-output (MIMO) recurrent neural network (RNN) is used as a versatile tool for the high-speed phasor detection and the adaptive identification of control and protection signals in power systems. For the application as a phasor detector, a fast pseudo-gradient training is performed off-line to estimate the time-invariant weights of the RNN. This network is then operated in real-time, in recall mode only, to behave as a nonlinear fixed-coefficient filter. For the application as an adaptive identifier of nonlinear components, training is performed off-line for initializing the connection weights, but subsequently, they are continuously updated in real time. This results in an adaptive identifier suitable for detecting abrupt changes in complex nonlinear systems. Following an initial evaluation on synthetic signals, these two proposed RNNs are then validated using realistic waveforms generated from a series-compensated power system model.

Recurrent neural networks for phasor detection and adaptive identification in power system control and protection

For pt.I see ibid., vol.39, no.2, p.124-38 (1992). The minimax (L/sub infinity /- or Chebyshev norm) and the least absolute value (L/sub 1/-norm) optimization criteria for linear parameter estimation problems are reformulated as constrained minimization problems. For these problems appropriate energy (Lyapunov) functions are constructed which enable the problems to be mapped into systems of nonlinear ordinary differential equations. On the basis of these systems of equations, analog neuronlike network architectures are proposed and their properties are discussed. The proposed circuit structures exhibit a high degree of modularity, and in most cases a relatively small number of basic building blocks (processing units) are required to implement effective and powerful optimization algorithms. The validity and performance of the architectures are illustrated by extensive computer simulations and CMOS implementations of a general-purpose network architecture are considered. >

Neural networks for solving systems of linear equations. II. Minimax and least absolute value problems

The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT). They show both analytically and by simulation that the circuit is guaranteed to settle into the correct values within RC time constants (on the order of hundreds of nanoseconds), and they compare its performance to other on-chip DFT implementations. >

A.D. Culhane

Papers

A neural net approach to discrete Hartley and Fourier transforms