Transformers Represent Belief State Geometry in their Residual Stream

Adam Shai, Lucas Teixeira, Alexander Gietelink Oldenziel, Sarah Marzen, Paul M. Riechers

Keywords: Interpretability, Computational Mechanics, Belief State, Features, Representation

TL;DR: Transformers trained on next-token prediction learn to represent the geometry of belief updating over hidden states of the data-generating process in their residual stream.

Abstract: What computational structure are we building into large language models when we train them on next-token prediction? Here, we present evidence that this structure is given by the meta-dynamics of belief updating over hidden states of the data- generating process. Leveraging the theory of optimal prediction, we anticipate and then find that belief states are linearly represented in the residual stream of transformers, even in cases where the predicted belief state geometry has highly nontrivial fractal structure. We investigate cases where the belief state geometry is represented in the final residual stream or distributed across the residual streams of multiple layers, providing a framework to explain these observations. Furthermore we demonstrate that the inferred belief states contain information about the entire future, beyond the local next-token prediction that the transformers are explicitly trained on. Our work provides a general framework connecting the structure of training data to the geometric structure of activations inside transformers.

Primary Area: Interpretability and explainability

Submission Number: 9570