Learning Random Numbers: a MATLAB Anomaly

We describe how dependencies between random numbers generated with some popular pseudorandom number generators can be detected using general purpose machine learning techniques. This is a novel approach, since usually, pseudorandom number generators are evaluated using tests specifically designed for this purpose. Such specific tests are more sensitive. Hence, detecting the dependence using machine learning methods implies that the dependence is indeed very strong. The most important example of a generator, where dependencies may easily be found using our approach, is Matlab’s function rand if the method state is used. This method was the default in Matlab versions between 5 (1995) and 7.3 (2006b), i.e. for more than 10 years. In order to evaluate the strength of the dependence in it, we used the same machine learning tools to detect dependencies in some other random number generators, which are known to be bad or insufficient for large simulations: the infamous RANDU, ANSIC, the oldest generator in C library, Minimal Standard generator, suggested by Park and Miller in 1988, and the rand function in Microsoft C compiler.