Persistent Similarity in Internal Representations of Large Language Models
Keywords: Topological Data Analysis, Persistent Homology, Large Language Models, Internal Representations, Similarity, Layer Pruning
Abstract: Understanding the decision-making processes of large language models (LLMs) is critical given their widespread applications. Towards this goal, describing the topological and geometrical properties of internal representations has recently provided valuable insights. For a more comprehensive characterization of these inherently complex spaces, we present a novel framework based on zigzag persistence, a method in topological data analysis (TDA) well-suited for describing data undergoing dynamic transformations across layers. Within this framework, we introduce persistence similarity, a new topological descriptor that quantifies the persistence and transformation of topological features such as $p$-cycles throughout the model layers. Unlike traditional similarity measures, our approach captures the entire evolutionary trajectory of these features, providing deeper insights into the internal workings of LLMs. As a practical application, we leverage persistence similarity to identify and prune layers, demonstrating comparable performance to state-of-the-art methods across several benchmark datasets. Additionally, our analysis reveals similar topological behaviors across various models and hyperparameter settings, suggesting a universal structure in LLM internal representations.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 12184
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