| Abstract: |
| We show that solutions of the Boltzmann equation can be uniformly approximated, in suitable Wasserstein metrics, by measure-theoretic transformer models. Our approach is based on a pushforward representation of Boltzmann dynamics induced by the Nanbu stochastic particle system, in which the evolution of a tagged particle depends on an underlying context consisting of the initial velocity distribution and a Poisson random measure encoding collision events. In this formulation, the fundamental objects (or tokens) consist of velocity-path pairs, where the paths are Radon measures describing jump sequences. By exploiting this structure, we place the Boltzmann pushforward representation within the scope of recent universality results for measure-theoretic transformers. |
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