Provable Target Sample Complexity Improvements as Pre-Trained Models Scale

2026-02-04

AI Summary

Existing theoretical frameworks struggle to explain why larger-scale pre-trained models substantially reduce sample complexity on downstream tasks. This work proposes a novel theoretical framework—termed “caulking”—inspired by parameter-efficient fine-tuning methods such as adapters, low-rank adaptation, and partial fine-tuning. It establishes, for the first time, a provable relationship between the scale of pre-trained models and the sample complexity of downstream tasks. By rigorously linking stronger pre-training capabilities to reduced data requirements in transfer learning, this study not only addresses a critical gap in current theoretical understanding but also provides a solid foundation for empirically observed scaling laws, demonstrating that enhanced pre-training capacity can significantly decrease the number of samples needed for effective downstream adaptation.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Pre-trained models have become indispensable for efficiently building models across a broad spectrum of downstream tasks. The advantages of pre-trained models have been highlighted by empirical studies on scaling laws, which demonstrate that larger pre-trained models can significantly reduce the sample complexity of downstream learning. However, existing theoretical investigations of pre-trained models lack the capability to explain this phenomenon. In this paper, we provide a theoretical investigation by introducing a novel framework, caulking, inspired by parameter-efficient fine-tuning (PEFT) methods such as adapter-based fine-tuning, low-rank adaptation, and partial fine-tuning. Our analysis establishes that improved pre-trained models provably decrease the sample complexity of downstream tasks, thereby offering theoretical justification for the empirically observed scaling laws relating pre-trained model size to downstream performance, a relationship not covered by existing results.

Problem

• pre-trained models
• sample complexity
• scaling laws
• downstream tasks
• theoretical justification

Innovation

• pre-trained models
• sample complexity
• scaling laws
• parameter-efficient fine-tuning
• theoretical analysis