  Self-supervised representation learning solves auxiliary prediction tasks
(known as pretext tasks) without requiring labeled data to learn useful
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 in text; yet
predicting this \textit{known} information helps in learning representations
effective for downstream prediction tasks. We posit a mechanism exploiting the
statistical connections between certain {\em reconstruction-based} pretext
tasks that guarantee to learn a good representation. 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 by just training a linear
layer on top of the learned representation. We prove the linear layer yields
small approximation error even for complex ground truth function class and will
drastically reduce labeled sample complexity. Next, we show a simple
modification of our method leads to nonlinear CCA, analogous to the popular
SimSiam algorithm, and show similar guarantees for nonlinear CCA.
