The Linear Representation Hypothesis and the Geometry of Large Language Models

This is experimental HTML to improve accessibility. We invite you to report rendering errors. Use Alt+Y to toggle on accessible reporting links and Alt+Shift+Y to toggle off. Learn more about this project and help improve conversions. HTML conversions sometimes display errors due to content that did not convert correctly from the source. This paper uses the following packages that are not yet supported by the HTML conversion tool. Feedback on these issues are not necessary; they are known and are being worked on. Authors: achieve the best HTML results from your LaTeX submissions by following these best practices. Informally, the “linear representation hypothesis” is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does “linear representation” actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity and projection) in the representation space

The Linear Representation Hypothesis and the Geometry of Large Language Models Kiho Park Yo Joong Choe Victor Veitch Abstract Informally, the “linear representation hypothesis” is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does “linear representation” actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity and projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of linear r

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