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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers
Asaki Saito, Akihiro Yamaguchi · 2017-06-20 · via cs.IT updates on arXiv.org

We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact computation. In particular, we clarify a way to properly prepare a set of initial points (i.e., seeds), which is needed when generating multiple pseudorandom sequences. With this seed selection method, we can distribute the initial points almost uniformly in the unit interval and can also guarantee that the orbits starting from them do not merge. We also report results of a large variety of tests indicating that the generated pseudorandom sequences have good statistical properties as well as an advantage over what is probably the most popular generator, the Mersenne Twister MT19937.

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