In today's column, I delve into a novel approach to unraveling the complexities of generative AI and large language models (LLMs) by utilizing the mathematical concept of Markov chains. For those unfamiliar, Markov chains are a method learned in statistical courses, and they can provide insights into AI and LLM processes. Markov chains model processes as a series of states or steps, moving from one state to another based on probability. For example, consider a trip to the DMV: you move from the check-in window to either a processing or a clean-up window based on probabilities of the needed clerical process. Similarly, Markov chains involve states and transitions based on statistical probabilities, as first conceptualized by Russian mathematician Andrey Markov in 1913 when analyzing letter sequences in literary texts. Generative AI, such as ChatGPT and other LLMs, operates on similar state-based transitions by transforming written content into tokenized data points and predicting the next possible token based on probabilities.

While researchers strive to comprehend these AI processes, applying Markov chains might reveal more about AI's seemingly mysterious behaviors. Recent studies explore viewing LLMs as Markov chains, suggesting structured state transitions and calculating predictions from limited vocabularies and context windows. Some industry professionals debate whether Markov chains can fully unlock the AI complexities, but early indicators show that these models might approximate AI token operations under certain constraints. Despite limitations, particularly concerning Markov chains' traditional focus on current states without accounting for previous states, researchers push the boundaries by examining their applicability in generative AI. Ongoing studies aim to shed light on advanced AI capabilities through Markov's concepts, signifying potential but not yet definitive insights into AI operations. The evolving research landscape continues to question and refine our understanding of generative AI through classical mathematical frameworks like Markov chains, promising ongoing discovery in AI's capabilities and internal mechanics.