Provable Benefits of Unsupervised Pre-training and Transfer Learning via Single-Index Models

TL;DR

This paper demonstrates that unsupervised pre-training and transfer learning significantly reduce the sample complexity for training single-layer neural networks, sometimes exponentially, especially under concept shift.

Contribution

It provides theoretical evidence that pre-training and transfer learning can drastically improve sample efficiency in high-dimensional neural network training.

Findings

Pre-training reduces sample complexity polynomially in dimension.

Transfer learning can lead to exponential improvements in sample complexity.

Benefits hold under very general assumptions, including concept shift.

Abstract

Unsupervised pre-training and transfer learning are commonly used techniques to initialize training algorithms for neural networks, particularly in settings with limited labeled data. In this paper, we study the effects of unsupervised pre-training and transfer learning on the sample complexity of high-dimensional supervised learning. Specifically, we consider the problem of training a single-layer neural network via online stochastic gradient descent. We establish that pre-training and transfer learning (under concept shift) reduce sample complexity by polynomial factors (in the dimension) under very general assumptions. We also uncover some surprising settings where pre-training grants exponential improvement over random initialization in terms of sample complexity.