Transformers predict LCG sequences in-context for fixed moduli up to 2^32 and unseen moduli up to 2^16 by learning the modulus factorization and digit-wise periodic structure.
Computationally easy, spectrally good multipliers for congruential pseudorandom number generators
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abstract
Congruential pseudorandom number generators rely on good multipliers, that is, integers that have good performance with respect to the spectral test. We provide lists of multipliers with a good lattice structure up to dimension eight and up to lag eight for generators with typical power-of-two moduli, analyzing in detail multipliers close to the square root of the modulus, whose product can be computed quickly.
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(How) Can Transformers Predict Pseudo-Random Numbers?
Transformers predict LCG sequences in-context for fixed moduli up to 2^32 and unseen moduli up to 2^16 by learning the modulus factorization and digit-wise periodic structure.