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[2602.13942] A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization
Summary
This article presents a theoretical framework for fine-tuning large language models (LLMs) using early stopping and non-random initialization, providing insights into convergence rates and task performance.
Why It Matters
As LLMs become increasingly prevalent in various applications, understanding the theoretical foundations of their fine-tuning processes is crucial. This research addresses the gap in knowledge regarding why minimal epochs can yield strong performance, offering a structured approach that can enhance model efficiency and effectiveness.
Key Takeaways
- Develops a statistical framework combining early stopping theory with Neural Tangent Kernel for LLMs.
- Provides a convergence guarantee for attention-based fine-tuning with non-random initializations.
- Links convergence rates to the eigenvalue decay rate of the empirical kernel matrix.
- Explains task vectors for multiple tasks in LLMs through the proposed framework.
- Empirical evidence supports the theoretical insights, enhancing understanding of fine-tuning practices.
Statistics > Machine Learning arXiv:2602.13942 (stat) [Submitted on 15 Feb 2026] Title:A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization Authors:Zexuan Sun, Garvesh Raskutti View a PDF of the paper titled A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization, by Zexuan Sun and Garvesh Raskutti View PDF HTML (experimental) Abstract:In the era of large language models (LLMs), fine-tuning pretrained models has become ubiquitous. Yet the theoretical underpinning remains an open question. A central question is why only a few epochs of fine-tuning are typically sufficient to achieve strong performance on many different tasks. In this work, we approach this question by developing a statistical framework, combining rigorous early stopping theory with the attention-based Neural Tangent Kernel (NTK) for LLMs, offering new theoretical insights on fine-tuning practices. Specifically, we formally extend classical NTK theory [Jacot et al., 2018] to non-random (i.e., pretrained) initializations and provide a convergence guarantee for attention-based fine-tuning. One key insight provided by the theory is that the convergence rate with respect to sample size is closely linked to the eigenvalue decay rate of the empirical kernel matrix induced by the NTK. We also demonstrate how the framework can be used to explain task vectors for multiple tasks in LLMs. Finally, experiments with modern language models on...
