Provable Target Sample Complexity Improvements as Pre-Trained Models Scale

Kazuto Fukuchi, Ryuichiro Hataya, Kota Matsui
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1720-1728, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-fukuchi26a, title = { Provable Target Sample Complexity Improvements as Pre-Trained Models Scale }, author = {Fukuchi, Kazuto and Hataya, Ryuichiro and Matsui, Kota}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1720--1728}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/fukuchi26a/fukuchi26a.pdf}, url = {https://proceedings.mlr.press/v300/fukuchi26a.html}, 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. } }
Endnote
%0 Conference Paper %T Provable Target Sample Complexity Improvements as Pre-Trained Models Scale %A Kazuto Fukuchi %A Ryuichiro Hataya %A Kota Matsui %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-fukuchi26a %I PMLR %P 1720--1728 %U https://proceedings.mlr.press/v300/fukuchi26a.html %V 300 %X 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.
APA
Fukuchi, K., Hataya, R. & Matsui, K.. (2026). Provable Target Sample Complexity Improvements as Pre-Trained Models Scale . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1720-1728 Available from https://proceedings.mlr.press/v300/fukuchi26a.html.

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