From Directions to Regions: Decomposing Activations in Language Models via Local Geometry

Activation decomposition methods in language models are tightly coupled to geometric assumptions on how concepts are realized in activation space. Existing approaches search for individual global directions, implicitly assuming linear separability, which overlooks concepts with nonlinear or multi-dimensional structure. In this work, we leverage Mixture of Factor Analyzers (MFA) as a scalable, unsupervised alternative that models the activation space as a collection of Gaussian regions with their local covariance structure. MFA decomposes activations into two compositional geometric objects: the region's centroid in activation space, and the local variation from the centroid. We train large-scale MFAs for Llama-3.1-8B and Gemma-2-2B, and show they capture complex, nonlinear structures in activation space. Moreover, evaluations on localization and steering benchmarks show that MFA outperforms unsupervised baselines, is competitive with supervised localization methods, and often achieves stronger steering performance than sparse autoencoders. Together, our findings position local geometry, expressed through subspaces, as a promising unit of analysis for scalable concept discovery and model control, accounting for complex structures that isolated directions fail to capture.

Pretrained LLMs Learn Multiple Types of Uncertainty

Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we study how well LLMs capture uncertainty, without explicitly being trained for that. We show that, if considering uncertainty as a linear concept in the model's latent space, it might indeed be captured, even after only pretraining. We further show that, though unintuitive, LLMs appear to capture several different types of uncertainty, each of which can be useful to predict the correctness for a specific task or benchmark. Furthermore, we provide in-depth results such as demonstrating a correlation between our correction prediction and the model's ability to abstain from misinformation using words, and the lack of impact of model scaling for capturing uncertainty. Finally, we claim that unifying the uncertainty types as a single one using instruction-tuning or [IDK]-token tuning is helpful for the model in terms of correctness prediction.