Stabilizer rank and higher-order Fourier analysis

Higher order Fourier analysis

Higher-order Fourier Analysis and Applications

Higher-Order Low-Rank Regression

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension i...

Using higher-order Fourier analysis over general fields

Higher-order Fourier analysis, developed over prime fields, has been recently used in different areas of computer science, including list decoding, algorithmic decomposition and testing. We extend the tools of higher-order Fourier analysis to analyze functions over general fields. Using these new tools, we revisit the results in the above areas. (i) For any fixed finite field K, we show that th...

On Higher-Order Fourier Analysis over Non-Prime Fields

The celebrated Weil bound for character sums says that for any low-degree polynomial P and any additive character χ, either χ(P ) is a constant function or it is distributed close to uniform. The goal of higher-order Fourier analysis is to understand the connection between the algebraic and analytic properties of polynomials (and functions, generally) at a more detailed level. For instance, wha...