On Linear Separation Capacity of Self-Supervised Representation Learning

TL;DR

This paper investigates how self-supervised learning with data augmentation enhances the linear separability of complex data manifolds, providing theoretical insights into its advantages over unsupervised methods and its effectiveness with limited labeled data.

Contribution

It offers a theoretical framework explaining how data augmentation improves linear separation capacity in self-supervised learning, especially for multi-manifold data structures.

Findings

Data augmentation increases information-theoretic linear separation rates.

Self-supervised learning achieves separation with smaller manifold distances than unsupervised learning.

Linear classifier performance depends more on data representation separability than on labeled data size.

Abstract

Recent advances in self-supervised learning have highlighted the efficacy of data augmentation in learning data representation from unlabeled data. Training a linear model atop these enhanced representations can yield an adept classifier. Despite the remarkable empirical performance, the underlying mechanisms that enable data augmentation to unravel nonlinear data structures into linearly separable representations remain elusive. This paper seeks to bridge this gap by investigating under what conditions learned representations can linearly separate manifolds when data is drawn from a multi-manifold model. Our investigation reveals that data augmentation offers additional information beyond observed data and can thus improve the information-theoretic optimal rate of linear separation capacity. In particular, we show that self-supervised learning can linearly separate manifolds with a smaller distance than unsupervised learning, underscoring the additional benefits of data augmentation. Our theoretical analysis further underscores that the performance of downstream linear classifiers primarily hinges on the linear separability of data representations rather than the size of the labeled data set, reaffirming the viability of constructing efficient classifiers with limited labeled data amid an expansive unlabeled data set.