Spectral Signatures of Large Language Models
2026-07-03 • Computation and Language
Computation and LanguageArtificial Intelligence
AI summaryⓘ
The authors address the challenge of organizing and comparing a large variety of big language models, which can differ a lot in how they're built. They use a technique that looks at the shape of the models' weight matrices, specifically their spectral properties, to create a unique and simple 'signature' for each model. This signature doesn't need any data to calculate, works efficiently, and helps track models' history, group similar ones, and estimate how well they perform. They tested their method on many open-source models and found it useful for managing and understanding big collections of language models.
Large Language ModelsSpectral ShapeEmpirical Spectral DensityHeavy-Tailed Self-RegularizationModel LineageUnsupervised ClusteringModel EvaluationScale-InvarianceData-Free Metrics
Authors
Zhuoying Zhang, Ishan V. Prasad, Yuanzhe Hu, Zihang Liu, Hengrui Luo, Pu Ren, Yaoqing Yang
Abstract
The rapidly growing repository of publicly available large language models (LLMs) presents significant challenges for systematic management and quantification at scale, such as model lineage tracing, licensing, and evaluation. However, task-specific benchmarks are insufficient for this setting, as LLMs differ widely in architectures, scales, and training procedures. To address this challenge, we adopt spectral shape-based metrics for managing and quantifying LLMs based on Heavy-Tailed Self-Regularization theory. Our approach uses the shape information of the weight empirical spectral density as a compact spectral signature of each model. This signature captures intrinsic properties of pretrained models and remains robust during post-training, making it suitable for model-level analysis. In addition, this metric is data-free, computationally-efficient, and scale-invariant, enabling large-scale analysis in practice. Moreover, we curate a large and diverse model corpus consisting of major open-source LLM families, and use it to systematically benchmark spectral and non-spectral metrics across models and downstream tasks. We show that our spectral signature supports the tracking of the model lineage, the unsupervised clustering of similar models, and the quantification of the model performance. Overall, the proposed spectral signature provides a meaningful proxy for broad performance trends across LLMs, enabling efficient organization, comparison, and analysis of large model collections.