Saddle-to-Saddle Dynamics in Self-Supervised Shortcut Learning

Although the mechanics of eigenvalue bias of self-supervised learning (SSL) in linear networks are well-understood, they remain theoretically disconnected from empirical shortcut learning, offering little guidance or intuition. In this paper, we present a theoretical analysis of this shortcut learning phenomenon through the lens of extent bias and amplitude bias, two forms of eigenvalue bias. By investigating the relations among extent bias, amplitude bias, and learning priorities in SSL, we demonstrate that SSL prioritizes features based on dimensionality (object to image ratio) and amplitude (backdoor attack intensity), not their semantic importance. Our analysis reveals how the eigenvalues of the feature cross-correlation matrix influence which features are learned earlier, providing insights into why models preferentially learn shortcut features over more generalizable features.