The Möbius function restricted to squarefrees up to R has Fourier ratio at least R to the power -1/4 minus epsilon, forcing any uniform learner for the class to use Omega(R) samples.
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When the Fourier ratio of a time series is small, its largest values can be additively generated by a small set using only coefficients from {-1,0,1}.
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Arithmetic functions and learning theory
The Möbius function restricted to squarefrees up to R has Fourier ratio at least R to the power -1/4 minus epsilon, forcing any uniform learner for the class to use Omega(R) samples.
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Large values in time series and additive combinatorics
When the Fourier ratio of a time series is small, its largest values can be additively generated by a small set using only coefficients from {-1,0,1}.