Persistent Topological Features in Large Language Models

2024-10-14

arXiv.org

AI Summary

This work addresses the lack of interpretable mathematical characterization of internal representation dynamics in large language models (LLMs). We propose a topological analysis framework based on zigzag persistent homology, enabling the first systematic modeling of topological features—specifically *p*-cycles—along model depth, capturing their birth, persistence, and death. Innovatively, we introduce *persistent similarity*, a metric quantifying cross-layer topological evolution, and discover universal topological regularities across diverse LLMs and hyperparameter configurations. Furthermore, integrating layer redundancy identification with topology-guided pruning, we achieve efficient model compression on multiple benchmarks, matching state-of-the-art performance. This study establishes the first systematic topological perspective for understanding the geometric structure and dynamical evolution of LLM internal representations.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Web Mining and Content Analysis: Large pretrained models with web data

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 metric 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 redundant layers, demonstrating comparable performance to state-of-the-art methods across several benchmark datasets. Additionally, our analysis reveals consistent topological behaviors across various models and hyperparameter settings, suggesting a universal structure in LLM internal representations.

Problem

• Understanding decision-making in large language models
• Tracking topological feature evolution across model layers
• Applying zigzag persistence for layer pruning optimization

Innovation

• Uses zigzag persistence for dynamic data analysis
• Introduces topological descriptors tracking feature evolution
• Applies persistence for layer pruning criterion