Spectral Geometry for Deep Learning: Compression and Hallucination Detection via Random Matrix Theory

2026-01-24

AI Summary

This work addresses the challenges of insufficient reliability and high computational cost in large language models and deep neural networks. By integrating spectral geometry with random matrix theory, the authors propose EigenTrack—a method that monitors the dynamic evolution of eigenvalue spectra of hidden activations in real time to effectively detect hallucinations and out-of-distribution behaviors. Furthermore, they introduce the RMT-KD framework, which leverages spectral component selection to perform iterative knowledge distillation for efficient model compression. The proposed approach not only offers an interpretable mechanism for monitoring model uncertainty but also significantly enhances inference efficiency while preserving model accuracy.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to address both problems by analyzing the eigenvalue structure of hidden activations. The first contribution, EigenTrack, is a real-time method for detecting hallucinations and out-of-distribution behavior in language and vision-language models using spectral features and their temporal dynamics. The second contribution, RMT-KD, is a principled compression method that identifies informative spectral components and applies iterative knowledge distillation to produce compact and efficient models while preserving accuracy. Together, these results show that spectral statistics provide interpretable and robust signals for monitoring uncertainty and guiding compression in large-scale neural networks.

Problem

• hallucination
• computational cost
• reliability
• out-of-distribution
• model compression

Innovation

• spectral geometry
• random matrix theory
• hallucination detection
• model compression
• knowledge distillation