Proposed in this paper is a network which uses basis functions based on products of the input space variables raised to a variable power. These basis functions are introduced in regions of confusion obtained through vector quantization of the input space based on patterns which are erroneously classified by a simple linear classifier. The overall effect is thus of directly generating relevant higher order combinations of the input data in regions of maximum confusion. We present the complete architecture of the network and derive a training algorithm. Results using two synthetic data sets are provided.