6.842 Randomness and Computation

Today we will discuss two more applications of the low degree algorithm. First we will look at constant depth circuits. We will cite a theorem regarding the Fourier concentration of functions computable by constant depth circuits and we will use this theorem as well as the low degree algorithm to show how we can learn constant depth circuits. Second we will begin to develop the theory need to learn functions of halfspaces. To do this we will explore the notion of noise sensitivity which will ultimately allow us to bound the Fourier concentration of these types of functions and learn them through the low degree algorithm.