State-Space Modeling in Natural Language

In many real-world applications, the goal is to infer the latent dynamics of an underlying process from a sequence of observations. Traditionally, state-space models such as hidden Markov models (HMMs) have been used to represent dynamic systems by positing a discrete or continuous latent state space, where states evolve according to a transition model and observations follow an emission model. However, these models are typically limited to structured observations and numerical state representations that are often not interpretable or identifiable. In this paper, we propose a new class of state-space models that formulates state inference and prediction as language tasks, both the transition and emission models implemented by a large language model (LLM). In our model, latent states are represented as concise natural-language descriptions, while observations may comprise large and unstructured text corpora. We develop a post-training procedure to fine-tune LLMs for state inference and prediction, inspired by variational inference algorithms in classical state-space modeling. We demonstrate the promise of this approach through preliminary experiments on disease progression modeling from clinical notes, and on modeling geopolitical relationships using news articles.