A radial basis function network-based upon the concept of function approximation - is a kind of artificial neural network that uses radial basis functions to define a node's output (given a set of inputs). The output of the network consists of a linear combination of radial basis functions of the inputs and neuron parameters.

Radial basis function (RBF) networks (also referred to as RBFNN for Radial Basis Function Neural Networks) will have three separate layers: an input layer, a hidden layer, and a linear output layer. The input layer will be a set of several nodes that transfer transition the input values to the second (or hidden) layer where activation patterns are applied. These patterns will be selected radial basis functions that best fit the application or objective. This transformation occurs in a non-linear fashion. The third layer (or output layer) provides the response of the network to the activation or RFB functions applied to the inputs. In an RFB network, the transformation from the hidden layer to the output layer is nonlinear.

A radial basis function network is a neural network usually approached by viewing the design as a curve-fitting (guesstimate) problem in a high dimensional space. Learning is equivalent to finding a multidimensional function that provides a best fit to the training data, with the criterion for best fit being measured in some statistical sense.

Generally, RBF networks seem to have the advantages of a more easily understood design, generalization ability, and a record of good tolerance to "noise" within the data.

The properties of RBF networks make it a very good choice for designing control systems that are required to be very flexible in that they must continually evaluate the various paths to completion and determine the most efficient. The study most famous in using RBF networks is in solving the traveling salesman problem (finding the shortest closed path between a group of cities).