A spectral inverse theorem and a spectral regularity theorem show that leading eigenvectors of Fourier-denoised matrices recover quadratic Fourier structure, giving new algorithms for quadratic denoising and character decomposition.
Aaronson, Algorithms for Boolean Function Query Properties , SIAM J
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Spectral algorithms in higher-order Fourier analysis
A spectral inverse theorem and a spectral regularity theorem show that leading eigenvectors of Fourier-denoised matrices recover quadratic Fourier structure, giving new algorithms for quadratic denoising and character decomposition.