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Structure and Redundancy in Large Language Models: A Spectral Study via Random Matrix Theory
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Structure and Redundancy in Large Language Models: A Spectral Study via Random Matrix Theory

#Large Language Models #Random Matrix Theory #Spectral Analysis #Model Compression #Hallucination Detection #Deep Learning #Knowledge Distillation #EigenTrack

📌 Key Takeaways

  • Research addresses reliability and efficiency challenges in large language models using Spectral Geometry and Random Matrix Theory
  • EigenTrack provides real-time detection of hallucinations and out-of-distribution behavior in AI models
  • RMT-KD offers a method to compress deep networks while preserving accuracy
  • The framework analyzes eigenvalue dynamics to distinguish structured representations from noise
  • The approach could reduce computational and energy demands of AI systems

📖 Full Retelling

Computer science researcher Davide Ettori from Politecnico di Milano published a groundbreaking thesis on February 25, 2026, that addresses reliability and efficiency challenges in large language models through Spectral Geometry and Random Matrix Theory, aiming to combat issues like hallucinations and excessive computational demands. The research introduces a unified framework that analyzes eigenvalue dynamics of hidden activations across layers and inputs, providing interpretable insights into model behavior by distinguishing structured representations from noise-dominated variability. This approach tackles two persistent problems in modern AI systems: their tendency to produce unreliable outputs and their growing resource requirements. One major contribution is EigenTrack, a real-time method for detecting hallucinations and out-of-distribution behavior in large language and vision-language models. By transforming streaming activations into spectral descriptors such as entropy, variance, and deviations from statistical baselines, the system can identify reliability failures before they manifest in model outputs while offering insights into representation dynamics through lightweight recurrent classifiers. The second significant contribution is RMT-KD, a principled approach to compressing deep networks through random matrix theoretic knowledge distillation. By identifying outlier eigenvalues in activation spectra as carriers of task-relevant information, RMT-KD progressively projects networks onto lower-dimensional subspaces. This method creates significantly more compact and energy-efficient models while preserving accuracy and maintaining a hardware-friendly dense structure, potentially revolutionizing how large AI systems are deployed in resource-constrained environments.

🏷️ Themes

Machine Learning, AI Efficiency, Model Reliability

📚 Related People & Topics

Spectral analysis

Topics referred to by the same term

Spectral analysis or spectrum analysis is analysis in terms of a spectrum of frequencies or related quantities such as energies, eigenvalues, etc. In specific areas it may refer to: Spectroscopy in chemistry and physics, a method of analyzing the properties of matter from their electromagnetic in...

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Random matrix

Matrix-valued random variable

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they becom...

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Large language model

Type of machine learning model

A large language model (LLM) is a language model trained with self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially language generation. The largest and most capable LLMs are generative pre-trained transformers (GPTs) that provide the c...

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Original Source
--> Computer Science > Machine Learning arXiv:2602.22345 [Submitted on 25 Feb 2026] Title: Structure and Redundancy in Large Language Models: A Spectral Study via Random Matrix Theory Authors: Davide Ettori View a PDF of the paper titled Structure and Redundancy in Large Language Models: A Spectral Study via Random Matrix Theory, by Davide Ettori View PDF HTML Abstract: This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory . As deep networks and large language models continue to scale, their internal behavior becomes increasingly opaque, leading to hallucinations, fragile generalization under distribution shift, and growing computational and energy demands. By analyzing the eigenvalue dynamics of hidden activations across layers and inputs, this work shows that spectral statistics provide a compact, stable, and interpretable lens on model behavior, capable of separating structured, causal representations from noise-dominated variability. Within this framework, the first contribution, EigenTrack, introduces a real-time method for detecting hallucinations and out-of-distribution behavior in large language and vision-language models. EigenTrack transforms streaming activations into spectral descriptors such as entropy, variance, and deviations from the Marchenko-Pastur baseline, and models their temporal evolution using lightweight recurrent classifiers, enabling early detection of reliability failures before they appear in model outputs while offering interpretable insight into representation dynamics. The second contribution, RMT-KD, presents a principled approach to compressing deep networks via random matrix theoretic knowledge distillation. By interpreting outlier eigenvalues in activation spectra as carriers of task-relevant information, RMT-KD progressively projects networks onto lower-dimensional subspaces through...
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arxiv.org

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