Complexity-Guided Component-wise Initialization for Language Model Pretraining

Jul 16, 2026

Pretrained language models exhibit recurring structured weight spectra, indicating repeated layerwise and component-wise organization during training. The work tests whether such recurring spectral patterns can serve as an initialization signal for GPT-2-style language-model pretraining. Eleven pretrained GPT-2-style checkpoints are analyzed with Frobenius norm and effective-rank entropy across layers and Transformer subcomponents. Initialization schemes imitate component magnitudes and spectral profiles, and evaluations show no consistent performance gains; pretrained-weight reuse stays competitive.

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CategoryResearch & Report

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Pages8

Reading Time20 min

Introduction

Research Questions and Answers

Spectral Patterns in Pre-trained LLMs

Complexity-Guided Component-wise Initialization for Language Model Pretraining Konstantin Garbers∗ Peking University Beijing, China [konstantin.garbers25@stu.pku.edu.cn](konstantin.garbers25@stu.pku.edu.cn) Nicholas Oh∗ Peking University Beijing, China [2501213380@stu.pku.edu.cn](2501213380@stu.pku.edu.cn) arXiv :2607 .09204v 1 [ cs .CL] 10 Jul 2026 Abstract Pretrained language models often exhibit structured weight spectra, suggesting that training may repeatedly produce similar layerwise and component-wise organization. We ask whether these recurring spectral patterns can be reused as an initialization signal for GPT-2-style language-model pretraining. First, we analyze eleven pretrained GPT-2-style checkpoints that vary in size, language, tokenizer, and training corpus, measuring Frobenius normand effective-rank entropy across layers and Transformer subcomponents. The checkpoints show shared depth trends, especially increasing scale and stronger spectral concentration in residualwriting matrices. We then construct initialization schemes that imitate the component-wise magnitudes and spectral profiles of pretrained models, and compare them with several weight initialization methods. These initializers visibly change the model’s structural spectral patterns, but the evaluation results do not show a corresponding performance advantage. Pretrained-weight reuse remains competitive, while coarse spectral matching alone is not a reliable optimization strategy. Our results suggest that pretrained spectra are useful diagnostics of trained model structure, but that effective reuse likely requires preserving richer information than component-wise scale and singular-value shape. Keywords language model pretraining, transformer initialization, layerwise diagnostics, memorization, training dynamics 1 Introduction Large language models are typically trained from randomly initialized weights, often drawn from Gaussian or related distributions. This choice is robust and architecture-agnostic: it does not assume prior knowledge about the data, the model size, or the internal structure that training will eventually produce. However, it also ignores a growing body of evidence suggesting that trained language models are not arbitrary points in parameter space. Across models, layers, and components, pre-trained transformers often exhibit recurring structural regularities, including characteristic spectral properties of their weight matrices [16, 29, 33] . These regularities raise a natural question: if trained models repeatedly develop similar patterns, can some of these patterns be used before training begins? In principle, an initialization that already reflects common structure found in pre-trained models could reduce the burden on optimization. Instead of learning all structural properties from scratch, the model would start from weights whose scale, rank structure, or spectral shape better resembles those ∗ Both authors contributed equally to this research. of trained transformers. At the same time, it is unclear whether such coarse spectral information is actually useful for pre-training. Spectral similarity may capture meaningful structure, but it may also discard the specific directions, correlations, and feature-level organization that make pre-trained weights effective. In this paper, we study this question for GPT-2-style language models. We analyze the weight matrices of several pre-trained models using spectral tools, including the Frobenius norm and effective rank entropy [16] . Our goal is first to determine whether consistent spectral patterns appear across models that differ in size, language, tokenizer, and training corpus. We then test whether these patterns can be transferred into the initialization of a new model and whether such initialization improves pre-training dynamics. Research questions and answers. Specifically, we ask the following questions. | | Research question | Answer | | --

FAQs

What recurring property of pretrained language models is studied in this paper?

The paper investigates structured weight spectra that appear across layers and Transformer components in pretrained GPT-2-style models.

How are spectral patterns measured in the analyzed checkpoints?

Spectral tools are used, including Frobenius norm and effective-rank entropy across layers and Transformer subcomponents.

Do spectral-pattern-based initializers improve pretraining performance?

The initialization methods change the model’s structural spectral patterns, but evaluation does not show a corresponding performance advantage over baselines.

Jul 16, 2026

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