Beyond Local Linearity: Scale-Resolved Geometry of Learned Image Encoders
Understanding how learned representations respond to finite input changes is important for characterizing their sensitivity, invariances, and robustness. Yet existing geometric analyses are predominantly local and describe only infinitesimal perturbations. We introduce a scale-resolved statistic that compares an encoder's measured feature displacement with its local linear prediction as the perturbation magnitude increases....
Understanding how learned representations respond to finite input changes is important for characterizing their sensitivity, invariances, and robustness. Yet existing geometric analyses are predominantly local and describe only infinitesimal perturbations. We introduce a scale-resolved statistic that compares an encoder's measured feature displacement with its local linear prediction as the perturbation magnitude increases....