Large Language Models as Markov Chains
Keywords: Large language models, Markov chain, in-context learning, generalization bounds, convergence analysis
TL;DR: We draw an equivalence between LLMs and Markov chains and derive theoretical results, including generalization bounds, on LLMs.
Abstract: 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 auto-regressive language models with vocabulary of size $T$ and context window of size $K$ and Markov chains defined on a finite state space of size $\mathcal{O}(T^K)$. 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.
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 2574
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