Large-scale language models (LLMs) operate in extremely high-dimensional state spaces, where both token embeddings and their hidden representations create complex dependencies that are not easily reduced to classical Markov structures. In this paper, we explore a theoretically feasible approximation of LLM dynamics using N-order additive Markov chains. Such models allow the conditional probability of the next token to be decomposed into a superposition of contributions from multiple historical depths, reducing the combinatorial explosion typically associated with high-order Markov processes. The main result of the work is the establishment of a correspondence between an additive multi-step chain and a chain with a step-wise memory function. This equivalence allowed the introduction of the concept of information temperature not only for stepwise but also for additive N-order Markov chains.
@article{arxiv.2603.04412,
title = {Additive Multi-Step Markov Chains and the Curse of Dimensionality in Large Language Models},
author = {O. V. Usatenko and S. S. Melnyk and G. M. Pritula},
journal= {arXiv preprint arXiv:2603.04412},
year = {2026}
}