Implementing radial basis functions using bump-resistor networks - Neural Networks, 1994. IEEE World Congress on Computational Intelligence., 1994 IEEE International

Radial Basis Function (RBF) networks provide a powerful learning architecture for neural networks [6]. We have implemented a RBF network in analog VLSI using the concept of bump-resistors. A bump-resistor is a nonlinear resistor whose conductance is a Gaussian-like function of the difference of two other voltages. The width of the Gaussian basis functions may be continuously varied so that the aggregate interpolating function varies from a nearest-neighbor lookup, piecewise constant function to a globally smooth function. The bump-resis tor methodology extends to arbitrary dimensions while still preserving the radiality of the basis functions. The feedforward network architecture needs no additional circuitry other than voltage sources and the 1D bump-resistors. A nine-transistor variation of the Delbruck bump circuit is used to compute the Gaussian-like basis functions [2]. Below threshold the current output fits a Gaussian extremely well, see Figure 1. Figure 3 shows that the shape of the function deviates from the Gaussian shape above threshold. The width of the bump can to be varied by almost an order of magnitude (see Figure 4). The Delbruck bump circuit is shown in Figure A follower aggregation network shown in Figure 5 computes an average of the inputs voltages ci weighted by conductance values gi [4]: