On (not) learning the M\"obius function

ArXi:2604.23427v1 Announce Type: cross We prove lower bounds on learning the M\"obius 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 M\"obius with digital characters of various finite abelian groups, where the group is dictated by the type of input data the algorithm is given.