The role of invariance in spectral complexity-based generalization bounds

Understand

Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels.

• Describing CNN capacity through a posteriori measures of complexity has been recently proposed to tackle this apparent paradox.
• These complexity measures are usually validated by showing that they correlate empirically with GE; being empirically larger for networks trained on random vs normal labels.
• Focusing on the case of spectral complexity we investigate theoretically and empirically the insensitivity of the complexity measure to invariances relevant to CNNs, and show several limitations of spectral complexity that occur as a result.