A MULTI-DIMENSIONAL ANALOG GAUSSIAN RADIAL BASlS CIRCUIT

Gaussian basis function(GBF) networks a r e powerful systems for learning and a p p r o x i m a t i n g complex input-output mappings. Networks composed of these localized receptive field u n i t s trained with efficient learning algorithms h a v e been simulated solving a variety of i n t e r e s t i n g problems. For real-time and p o r t a b l e applications however, direct hardware implementation is needed. We describe s imula ted and experimental results from the most c o m p a c t , low voltage analog Gaussian basis circuit y e t reported. We also extend our circuit to hand le large fan-in with minimal additional hardware. We show a SPICE simulation of our c i r c u i t implementing a multivalued exp o n e n t i a1 associative memory (MERAM). Neurons with response characteristics that are locally tuned to a particular range of the input variable have been found in many parts of the central nervous system[l]. Examples include cells in the somatosensory cortex that respond selectively to stimulation from localized regions of the body surface, and orientation selective cells in the visual cortex that respond selectively to stimulation which are both local in retinal position and local in angle of object orientation[2]. Computer simulations of GBF networks are sufficient for many applications. However, hardware implementation of these systems are mandatory for many real-time, or low power, portable applications such as vision and speech recognition, robotics, and numerous other interactive control and signal processing applications. For these reason, we have developed a compact, low voltage, analog circuit implementation of the GBF network. This paper first reviews the existing circuits that implement Gaussian basis functions. Then, we discuss our circuit including experimental data from a fabricated chip. To illustrate the usefulness of the approach, we describe an application using GBFs. Lastly, we summary our contribution. 2. EXISTING GAUSSIAN BASIS CIRCUITS In the past few years there have been a number hardware implementations of the radial basis function in analog[3-61, and pulse formsp]. The design by Delbruck [6] is shown in Fig. 1. It has been used in visual processing, and as a similarity computing element. It is based on a simple current correlator as shown in Fig. 2 which implements the function: I o u t = sm 1 1 1 2