Linear Representations

The Geometry of Categorical and Hierarchical Concepts in LLMs

Building upon our ICML 2024 paper, we formalize the representations of categorical concepts in LLMs as convex polytopes and further show that hierarchically related concepts are represented as orthogonal vectors. Accepted to ICLR 2025 for oral presentation.

The Linear Representation Hypothesis and the Geometry of LLMs

We formalize different notions of linear representations in LLMs (e.g., linear probes and steering vectors) and unify those notions by identifying an inner product that encodes semantic structure. Published in ICML 2024.