Lucas Teixeira

Lauren Greenspan, David Berman, Aryeh Brill et al.

Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and guaranteeing bounds on the influence of fine-grained structure that is discarded as irrelevant noise. We posit that the renormalisation framework from physics can meet this need by offering technical tools that can overcome limitations of current methods. Moreover, relevant work from adjacent fields has now matured to a point where scattered research threads can be synthesized into practical, theory-informed tools. To combine these threads in an AI safety context, we propose a unifying research agenda -- \emph{scale-aware interpretability} -- to develop formal machinery and interpretability tools that have robustness and faithfulness properties supported by statistical physics.

Adam S. Shai, Sarah E. Marzen, Lucas Teixeira et al.

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.

Nischal Mainali, Lucas Teixeira

Transformer models exhibit remarkable in-context learning (ICL), adapting to novel tasks from examples within their context, yet the underlying mechanisms remain largely mysterious. Here, we provide an exact analytical characterization of ICL emergence by deriving the closed-form stochastic gradient descent (SGD) dynamics for a simplified linear transformer performing regression tasks. Our analysis reveals key properties: (1) a natural separation of timescales directly governed by the input data's covariance structure, leading to staged learning; (2) an exact description of how ICL develops, including fixed points corresponding to learned algorithms and conservation laws constraining the dynamics; and (3) surprisingly nonlinear learning behavior despite the model's linearity. We hypothesize this phenomenology extends to non-linear models. To test this, we introduce theory-inspired macroscopic measures (spectral rank dynamics, subspace stability) and use them to provide mechanistic explanations for (1) the sudden emergence of ICL in attention-only networks and (2) delayed generalization (grokking) in modular arithmetic models. Our work offers an exact dynamical model for ICL and theoretically grounded tools for analyzing complex transformer training.