Toward a Sheaf-Theoretic Understanding of Compositionality in Large Language Models
Keywords: cognition, compositionality, sheaf-theory, language model evaluation
TL;DR: This paper uses a sheaf-theoretic approach to understand and evaluate compositionality in LLMs.
Abstract: Compositionality has long been considered a fundamental aspect of human cognition - enabling the learning, manipulation, and generation of natural language. Understanding how this concept applies to Large Language Models (LLMs) and how it can be effectively evaluated remains a key challenge. In this work, we explore the potential of formalizing cognitive notions from theory, such as compositionality, to develop more nuanced evaluation frameworks for LLMs. Using a sheaf-theoretic approach, we define compositionality through four distinct conditions that capture its multifaceted nature. This formalization offers a structured perspective on evaluating LLMs, moving beyond surface-level assessments to uncover deeper insights into their behavior. Our findings suggest that theoretical frameworks like this one can play a crucial role in advancing the understanding and evaluation of LLMs, providing a foundation for more comprehensive and precise performance analyses.
Primary Area: applications to neuroscience & cognitive science
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Submission Number: 14010
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