Geometric Lens: Verbalizing Hidden Representations of an LLM From First Principles

Sun, 19 Jul 2026 03:10:00 -0400

[This is an introductory blog for the new paper Laguerre Geometry for Interpreting Large Language Models and the GitHub repository Geometric Lens.]

LLM Lens: What does an internal vector mean?

Anthropic’s recent paper on the “J-Lens” (Jacobian Lens) has revived interest in reading the “thoughts” inside Large Language Models. The idea of placing a “lens” at an LLM’s hidden layers isn’t new. It dates back to the Logit Lens, and has since evolved into a family of variants, including Tuned Lens and Patchscopes. But as we build new lenses, we keep hitting the same wall: what are we actually reading? How do we know that what we read is “correct”? Is there even a ground truth for the “meaning” of an internal state? These questions remain largely unanswered.

Large Language Models Are Secretly Voronoi Diagrams

Sun, 19 Jul 2026 16:56:51 -0400

[This is an introductory blog for the new paper Laguerre Geometry for Interpreting Large Language Models and the GitHub repository Geometric Lens.]

Large Language Models (LLMs) have achieved remarkable breakthroughs not only in general question-answering and conversation, but also in coding, mathematical reasoning, multimodal (image, audio, and video) generation, and scientific discovery. Yet, although every atomic internal computation within an LLM is ontologically well understood, the reason these computations, when composed, give rise to a high degree of intelligence remains largely epistemologically opaque—warranting deeper scientific inquiry.

Interpret LLM

Geometric Lens: Verbalizing Hidden Representations of an LLM From First Principles

LLM Lens: What does an internal vector mean?

Large Language Models Are Secretly Voronoi Diagrams