Fiber bundles and receptive neural fields

Some networks, like RBF networks or Kohonen feature maps, can be viewed as mappings from an input manifold (the signal space) to a neural receptive field, generally lower dimensional. The activation of a neuron, given by application of a smooth function to a weighted norm of the difference between the input and the so called center of the cell, can be thought as a membership value to a one point set. Generalizing this approach leads to the concept of halo around a set. The base set and its halo constitute a topological pair and can be provided with a membership function. The resulting triples are then used as total and base space for a fibered structure that provides a general framework for dealing with neural fields.