Implications of Möbius Randomness for ML prediction of μ(n)

Ascertain whether the Möbius Randomness principle—asserting that the Möbius function μ(n) has negligible correlation with polynomial-time computable functions—implies that polynomial-time machine learning models should struggle to predict μ(n), or whether machine learning can instead act as an approximate probabilistic oracle achieving nontrivial predictive power for μ(n).

Background

The Möbius Randomness paradigm posits that μ(n) exhibits little to no correlation with low-complexity, polynomial-time computable functions. The paper raises the question of how this paradigm interfaces with modern machine learning, which could be viewed as producing polynomial-time predictors from data.

The authors explicitly pose whether Möbius Randomness entails limitations on ML-based prediction accuracy for μ(n) or whether ML might serve as an approximate oracle capable of nontrivial prediction. They conclude that this issue remains unresolved.