Exact Interpolation and Learning in Quadratic Neural Networks

A quadratic matrix mapping scheme is presented where exact interpolation for a set of input vectors is achieved. Analogies are drawn with radial-basis function (RBF) neural networks. The environment of definition is the complex domain, with the real domain being a special case. The network is further defined for the integers where it acts as a perfect hashing function. This network can be trained with gradient descend, the perceptron algorithm and a novel matrix pseudoinverse method. The XOR problem is solved in a variety of ways. The weights of the output neuron are fixed; they are the inputs themselves.