Predicting What You Already Know Helps: Provable Self-Supervised Learning

Jason D. Lee, Qi Lei, Nikunj Saunshi, Jiacheng Zhuo

Keywords: theory, self-supervised learning, representation learning, unsupervised learning, conditional independence

Abstract: Self-supervised representation learning solves auxiliary prediction tasks (known as pretext tasks), that do not require labeled data, to learn semantic representations. These pretext tasks are created solely using the input features, such as predicting a missing image patch, recovering the color channels of an image from context, or predicting missing words, yet predicting this \textit{known} information helps in learning representations effective for downstream prediction tasks. This paper posits a mechanism based on approximate conditional independence to formalize how solving certain pretext tasks can learn representations that provably decrease the sample complexity of downstream supervised tasks. Formally, we quantify how the approximate independence between the components of the pretext task (conditional on the label and latent variables) allows us to learn representations that can solve the downstream task with drastically reduced sample complexity by just training a linear layer on top of the learned representation.

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One-sentence Summary: We prove the sample efficiency of representations learned using reconstruction-based self-supervised learning on downstream tasks under an approximate conditional independence assumption.

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