Three lectures on Fourier analysis and learning theory

TL;DR

This paper discusses recent advances in Fourier analysis on discrete hypercubes, highlighting the use of classical inequalities like Bohnenblust--Hille in learning low-degree Boolean functions and exploring quantum and classical Fourier analysis progress.

Contribution

It reviews recent progress connecting Fourier analysis, Bohnenblust--Hille inequality, and learning theory, including applications to quantum systems.

Findings

Bohnenblust--Hille inequality aids in learning low-degree Boolean functions

Progress in discrete quantum systems analysis using Fourier methods

Enhanced understanding of classical Fourier analysis applications

Abstract

Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the context of learning low-degree Boolean functions. In these lecture notes, we explore this line of research and discuss recent progress in discrete quantum systems and classical Fourier analysis.