Internal representation in networks of nonmonotonic processing units

Connectionist networks that use nonmonotonic transfer functions tend to adopt highly structured internal representations, revealed as vertical banding in density plots of internal unit activities. Recent work has shown this banding to be easily analyzed allowing for the extraction of symbolic descriptions of the solution encoded in the network. While the banding phenomenon is well documented, the properties that give rise to this structure have never been formalized. In this paper we detail the geometry that underlies the internal unit activity clustering that banding represents. These results distinguish the operation of nonmonotonic units from that of traditional sigmoid devices in terms of the mechanism by which they carve up the input space