Random Multiplicative Functions with Periodic Weights

What the math gives to ML

The paper constructs a reproducible source of structured complex randomness by assigning independent unit-circle phases to primes and extending them completely multiplicatively, then shows that periodic modulation behaves asymptotically Gaussian after excluding integers with small prime factors. This could replace explicitly stored random positional features or dropout masks: a short prime-phase seed deterministically generates a long sequence. The most plausible transfer is a structured random positional-encoding module, with the rough-number restriction intended to reduce non-Gaussian multiplicative collisions. The idea is speculative and should be tested against ordinary random Fourier features for covariance quality, memory, and downstream accuracy.