Large Language Models as Markov Chains
Authors: name: Oussama Zekri, name: Ambroise Odonnat, name: Abdelhakim Benechehab, name: Linus Bleistein, name: Nicolas Boullé, name: Ievgen Redko

Large language models (LLMs) have proven to be remarkably efficient, both
across a wide range of natural language processing tasks and well beyond them.
However, a comprehensive theoretical analysis of the origins of their
impressive performance remains elusive. In this paper, we approach this
challenging task by drawing an equivalence between generic autoregressive
language models with vocabulary of size T and context window of size K and
Markov chains defined on a finite state space of size O(T^K). We
derive several surprising findings related to the existence of a stationary
distribution of Markov chains that capture the inference power of LLMs, their
speed of convergence to it, and the influence of the temperature on the latter.
We then prove pre-training and in-context generalization bounds and show how
the drawn equivalence allows us to enrich their interpretation. Finally, we
illustrate our theoretical guarantees with experiments on several recent LLMs
to highlight how they capture the behavior observed in practice.