Research
On (not) learning the Mobius function
arXiv:2604.23427v1 Announce Type: cross Abstract: We prove lower bounds on learning the Mobius or Liouville function with a variety of standard learning techniques, including kernel methods, noisy gra
arXiv:2604.23427v1 Announce Type: cross Abstract: We prove lower bounds on learning the Mobius or Liouville function with a variety of standard learning techniques, including kernel methods, noisy gradient methods, and correlational statistical query algorithms. These results follow from quantitative bounds on the correlation of Mobius with digital characters of various finite abelian groups, where the group is dictated by the type of input data the algorithm is given. Using residues mod p for many different primes corresponds to a cyclic group, and using the base p expansion for a fixed prime corresponds to an elementary abelian p-group. We also note that lower bounds of this form are closely related to certain types of digital prime number theorems.
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Source: arXiv cs.LG | 2026-04-28