Foundations Of Cognitive Science

Radial Basis Function Unit

A radial basis function unit (RBF unit) is a kind of processor in an artificial neural network. Like a value unit, it uses a Gaussian activation function. However, unlike a value unit -- and most other connectionist networks -- it uses a nonstandard net input function. The net input is the distance between the RBF unit (it will have a location in some pattern space) and another point in the same pattern space that represents the location of some input pattern (Moody & Darken, 1989; Renals, 1989). The shorter the distance, the higher the activity of the RBF unit. Thus, an RBF unit can be viewed as a Gaussian-contoured cone laid out over a pattern space which measures the proximity of some input pattern to the centre of the cone.

Because the net input function to an RBF unit is a distance, and therefore cannot be less than 0, an RBF unit's activation function is monotonic -- similar to a decreasing sigmoid in shape. This is a key difference between it and a value unit, which can have negative net inputs, and which therefore has a truly nonmonotonic activation function (Dawson, 2004).


  1. Dawson, M. R. W. (2004). Minds And Machines : Connectionism And Psychological Modeling. Malden, MA: Blackwell Pub..
  2. Moody, J., & Darken, C. J. (1989). Fast learning in networks of locally-tuned processing units. Neural computation, 1, 281-294
  3. Renals, S. (1989). Radial basis function network for speech pattern classification. Electronics letters, 25, 437-439.

(Added January 2010)