Pretrained weights reduce data needed for fine-tuning tasks
Statistical Benefits of Fine-Tuning from Pretrained Initialization in Diagonal Linear Networks
Machine Learning
Summary
Fine-tuning pretrained deep learning models on small new datasets usually works well in practice, but it's not clear why. The authors studied this by looking at simple linear models where pretrained weights contain clues about which features matter. They showed that starting from good pretrained weights helps the model focus on the right parts, needing less data to learn the new task. Their math explains how gradient-based fine-tuning implicitly uses this prior information to be more sample-efficient.
What this means in practice
- •For machine learning engineers: Design fine-tuning schemes that reduce labeled data needs by exploiting pretrained weight information.
- •For data scientists: Develop more sample-efficient downstream models by implicitly using pretrained supports in high-dimensional tasks.
A theory result. No direct application yet.
Authors
Alexandre Declèves, Etienne Boursier, Nicolas Flammarion
Abstract
Adapting pretrained models to downstream tasks with limited data has become a central paradigm in modern deep learning. Yet, despite its widespread practical success, how fine-tuning leverages information from pretraining remains poorly understood theoretically. We study fine-tuning from pretrained weights through the lens of sparse linear regression and two-layer diagonal linear networks. In our setting, pretraining provides information through the support (and signs) of the initialization predictor, which may contain coordinates relevant to the downstream task. We show how pretrained information reshapes the implicit bias and training dynamics, and can thereby reduce the sample complexity of recovering the target parameters and support. In particular, for a clean initialization with correctly inherited signs, we show that the required sample size is comparable to that of a weighted Lasso estimator that explicitly exploits the pretrained support through a suitably chosen regularizer. Our results thus show how information encoded in pretrained weights can be implicitly exploited by gradient-based fine-tuning, reducing the amount of data needed to recover a downstream task.