Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNs
This work provides insights into the role of affine transformations in deep learning, characterizing the expressive power of networks built from shifted and rescaled random features, which is incremental but clarifies a specific bottleneck in feature normalization techniques.
The paper investigates the expressive power of affine parameters in BatchNorm by training only these parameters while freezing all other network weights at random initializations, achieving surprisingly high accuracy of 82% on CIFAR-10 and 32% top-5 on ImageNet with deep ResNets, partly due to BatchNorm learning to disable around a third of random features.
A wide variety of deep learning techniques from style transfer to multitask learning rely on training affine transformations of features. Most prominent among these is the popular feature normalization technique BatchNorm, which normalizes activations and then subsequently applies a learned affine transform. In this paper, we aim to understand the role and expressive power of affine parameters used to transform features in this way. To isolate the contribution of these parameters from that of the learned features they transform, we investigate the performance achieved when training only these parameters in BatchNorm and freezing all weights at their random initializations. Doing so leads to surprisingly high performance considering the significant limitations that this style of training imposes. For example, sufficiently deep ResNets reach 82% (CIFAR-10) and 32% (ImageNet, top-5) accuracy in this configuration, far higher than when training an equivalent number of randomly chosen parameters elsewhere in the network. BatchNorm achieves this performance in part by naturally learning to disable around a third of the random features. Not only do these results highlight the expressive power of affine parameters in deep learning, but - in a broader sense - they characterize the expressive power of neural networks constructed simply by shifting and rescaling random features.