Provable Target Sample Complexity Improvements as Pre-Trained Models Scale

• URL: http://arxiv.org/abs/2602.04233v1
• Date: Wed, 04 Feb 2026 05:51:56 GMT
• Title: Provable Target Sample Complexity Improvements as Pre-Trained Models Scale
• Abstract summary: The advantages of pre-trained models have been highlighted by empirical studies on scaling laws.<n>We provide a theoretical investigation by introducing a novel framework, caulking.<n>Our analysis establishes that improved pre-trained models provably decrease the sample complexity of downstream tasks.
• Score: 6.964881957695288
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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