Relative stability toward diffeomorphisms indicates performance in deep nets*

Abstract Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support it is often not the case. We revisit this question defining maximum-entropy distribution on allows study typical diffeomorphisms of given norm. confirm stability toward does strongly correlate performance benchmark sets images. By contrast, we find relative generic transformations R f correlates remarkably with test error ? t . order unity at initialization but decreases several decades during training for state-of-the-art architectures. For CIFAR10 and 15 known architectures ? t ? 0.2 R f , suggesting obtaining small important achieve good performance. how depends size set compare simple model invariant learning.