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Computer Science > Computation and Language

arXiv:2406.01506 (cs)
[Submitted on 3 Jun 2024]

Title:The Geometry of Categorical and Hierarchical Concepts in Large
Language Models

Authors:Kiho Park, Yo Joong Choe, Yibo Jiang, Victor Veitch
View a PDF of the paper titled The Geometry of Categorical and
Hierarchical Concepts in Large Language Models, by Kiho Park and 3
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    Abstract:Understanding how semantic meaning is encoded in the
    representation spaces of large language models is a fundamental
    problem in interpretability. In this paper, we study the two
    foundational questions in this area. First, how are categorical
    concepts, such as {'mammal', 'bird', 'reptile', 'fish'},
    represented? Second, how are hierarchical relations between
    concepts encoded? For example, how is the fact that 'dog' is a
    kind of 'mammal' encoded? We show how to extend the linear
    representation hypothesis to answer these questions. We find a
    remarkably simple structure: simple categorical concepts are
    represented as simplices, hierarchically related concepts are
    orthogonal in a sense we make precise, and (in consequence)
    complex concepts are represented as polytopes constructed from
    direct sums of simplices, reflecting the hierarchical structure.
    We validate these theoretical results on the Gemma large language
    model, estimating representations for 957 hierarchically related
    concepts using data from WordNet.

Comments: Code is available at this https URL
          Computation and Language (cs.CL); Artificial Intelligence
Subjects: (cs.AI); Machine Learning (cs.LG); Machine Learning
          (stat.ML)
Cite as:  arXiv:2406.01506 [cs.CL]
          (or arXiv:2406.01506v1 [cs.CL] for this version)
          https://doi.org/10.48550/arXiv.2406.01506
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Kiho Park [view email]
[v1] Mon, 3 Jun 2024 16:34:01 UTC (6,202 KB)
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