Synthetic Data and Generative AI

Chapter 11: High quality random numbers for data synthetization

Abstract

High quality random numbers are critical in large-scale simulations such as data synthetization. I discuss a new test of randomness for pseudorandom number generators (PRNG), to detect subtle patterns in binary sequences. The test shows that congruential PRNGs, even the best ones, have flaws that can be exacerbated by the choice of the seed. This includes the Mersenne twister used in many programming languages including Python. I also show that the digits of some numbers such as $\sqrt{2205}$, conjectured to be perfectly random, fail this new test, despite the fact that they pass all ...