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.
Haagerup,The best constants in the Khintchine inequality, Studia Mathematica, 70(3):231–283, (1981)
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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.