Low-Rank Approximation of Structural Redundancy for Self-Supervised Learning

We study the data-generating mechanism for reconstructive SSL to shed light on its effectiveness. With an infinite amount of labeled samples, we provide a sufficient and necessary condition for perfect linear approximation. The condition reveals a full-rank component that preserves the label classes of Y, along with a redundant component. Motivated by the condition, we propose to approximate the redundant component by a low-rank factorization and measure the approximation quality by introducing a new quantity $\epsilon_s$, parameterized by the rank …

approximation cs.lg data light linear low redundancy samples self-supervised learning ssl stat.ml study supervised learning