Implementing Radial Basis Functions Using Bump-resistor Networks

1 Implementing Radial Basis Functions Using Bump-Resistor Networks John G. Harris University of Florida EE Dept., 436 CSE Bldg 42 Gainesville, FL 32611 [email protected] .edu Abstract| 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 di erence 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-resistor 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 Delbr uck bump circuit is used to compute the Gaussian-like basis functions [2]. Below threshold the current output ts 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 Delbr uck 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]: Y = Pi cigi Pi gi (1) The bump current is used to control the conductance of the resistors in Figure 5 such that gi = G(x ti) where ti is the voltage representing the center location of each bump-resistor. The circuit now computes: Y = Pi ciG(x ti) PiG(x ti) (2) This normalized RBF or partition of unity form has been used by Moody and Darken in learning simulaGaussian Circuit