Researchers Uncover Algorithms Behind LLM In-Context Learning for HMMs.

Large language models (LLMs) have demonstrated a remarkable ability to predict subsequent observations from Hidden Markov Models (HMMs) through in-context learning (ICL). However, the precise algorithms underpinning this capability have remained elusive, with previous research proposing various candidates without reaching a consensus or grounding them in the models' internal workings. This new study aims to bridge this knowledge gap. The researchers employed a three-stage methodology. Initially, they empirically compared LLM behavior against a range of potential algorithms, narrowing the field to three distinct classes. They found that no single class fully explained LLM behavior across all HMM configurations and sequence lengths. Following this, theoretical connections between these three classes were established, demonstrating how each could be implemented within a Transformer architecture, which was validated using a small, trained Transformer model. Finally, the study introduced the Principal Activations Probe (PAP), a novel layer-wise probing and intervention technique. Applied to pre-trained LLMs, PAP allowed the isolation of algorithmic signals within the models' activations. This revealed low-dimensional linear representations that directly influence predictions and correlate with ICL performance. PAP also showed how these representations adapt to different HMM regimes and localized distinct computational stages to specific layers within the LLM. These findings collectively advance the understanding of the internal mechanisms enabling LLMs to perform in-context learning on HMMs.