Harmonic Theory and Machine Learning

Abstract

A natural inference mechanism is presented : the Black Box problem is transformed into a Dirichlet's problem on the closed cube. Then it is solved in closed polynomial form, together with a Mean-Value theorem and a Maximum Principle.A generalization to Polytopes and a reduction of any Dirichlet problem on compacta is mapp ed into a unit cub e in more dimensions.An algorithm for calculating the solution is suggested.

Keywords

• neural networks
• machine learning
• potential theory
• polynomial approximation