  Despite their ability to represent highly expressive functions, deep learning
models seem to find simple solutions that generalize surprisingly well.
Spectral bias -- the tendency of neural networks to prioritize learning low
frequency functions -- is one possible explanation for this phenomenon, but so
far spectral bias has primarily been observed in theoretical models and
simplified experiments. In this work, we propose methodologies for measuring
spectral bias in modern image classification networks on CIFAR-10 and ImageNet.
We find that these networks indeed exhibit spectral bias, and that
interventions that improve test accuracy on CIFAR-10 tend to produce learned
functions that have higher frequencies overall but lower frequencies in the
vicinity of examples from each class. This trend holds across variation in
training time, model architecture, number of training examples, data
augmentation, and self-distillation. We also explore the connections between
function frequency and image frequency and find that spectral bias is sensitive
to the low frequencies prevalent in natural images. On ImageNet, we find that
learned function frequency also varies with internal class diversity, with
higher frequencies on more diverse classes. Our work enables measuring and
ultimately influencing the spectral behavior of neural networks used for image
classification, and is a step towards understanding why deep models generalize
well.
