Abstract
An approach to analyze neural networks based on harmonic analysis of Boolean functions is presented. It is shown how this technique can be applied to answer the following two fundamental questions: (1) What is the computational power of a polynomial threshold element with respect to linear threshold elements? (2) Is it possible to get exponentially many spurious memories when the outer-product method for programming the Hopfield model is used? The basic concepts of harmonic analysis of Boolean functions are introduced, and two applications to neural networks are mentioned. The first application is related to feedforward networks. The second application is related to the Hopfield model.