Softmax Geometry

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. (Figure courtesy: Kiho Park)

The Geometry of Categorical and Hierarchical Concepts in LLMs

Building upon our recent work, we formalize the representations of categorical concepts in LLMs as convex polytopes and further show that hierarchical relations between concepts are represented as orthogonality. Under Review. (Figure courtesy: Kiho Park)