LLMs Extract Hidden Markov Model Algorithms via In-Context Learning

A recent investigation published on arXiv (2607.22646) explores the in-context learning (ICL) abilities of large language models (LLMs) in predicting future observations from Hidden Markov Models (HMMs). The researchers outline a three-step approach to uncover the foundational algorithm. Initially, they conduct empirical comparisons of LLM actions with potential algorithms, ultimately refining their focus to three categories, although no single category fully accounts for behavior across all HMM configurations and sequence lengths. Next, they establish theoretical links among these categories and demonstrate how each can be realized in-context by a Transformer, confirming this in a small trained Transformer. Finally, they present the Principal Activations Probe (PAP), a method for probing and intervening layer-wise to extract algorithmic elements from pre-trained LLMs, enhancing the understanding of LLMs' ICL mechanisms.