Spectral Batch Normalization: Normalization in the Frequency Domain
Rinor Cakaj Jens Mehnert Bin Yang
Regularization is a set of techniques that are used to improve the
generalization ability of deep neural networks. In this paper, we introduce
spectral batch normalization (SBN), a novel effective method to improve
generalization by normalizing feature maps in the frequency (spectral) domain.
The activations of residual networks without batch normalization (BN) tend to
explode exponentially in the depth of the network at initialization. This leads
to extremely large feature map norms even though the parameters are relatively
small. These explosive dynamics can be very detrimental to learning. BN makes
weight decay regularization on the scaling factors $\gamma, \beta$
approximately equivalent to an additive penalty on the norm of the feature
maps, which prevents extremely large feature map norms to a certain degree.
However, we show experimentally that, despite the approximate additive penalty
of BN, feature maps in deep neural networks (DNNs) tend to explode at the
beginning of the network and that feature maps of DNNs contain large values
during the whole training. This phenomenon also occurs in a weakened form in
non-residual networks. SBN addresses large feature maps by normalizing them in
the frequency domain. In our experiments, we empirically show that SBN prevents
exploding feature maps at initialization and large feature map values during
the training. Moreover, the normalization of feature maps in the frequency
domain leads to more uniform distributed frequency components. This discourages
the DNNs to rely on single frequency components of feature maps. These,
together with other effects of SBN, have a regularizing effect on the training
of residual and non-residual networks. We show experimentally that using SBN in
addition to standard regularization methods improves the performance of DNNs by
a relevant margin, e.g. ResNet50 on ImageNet by 0.71%.