Neural network learning as an inverse problem

Capability of generalization in learning of neural networks from examples can be modelled using regularization, which has been developed as a tool for improving stability of solutions of inverse problems. Such problems are typically described by integral operators. It is shown that learning from examples can be reformulated as an inverse problem defined by an evaluation operator. This reformulation leads to an analytical description of an optimal input/output function of a network with kernel units, which can be employed to design a learning algorithm based on a numerical solution of a system of linear equations.