  We present a multigrid-in-channels (MGIC) approach that tackles the quadratic
growth of the number of parameters with respect to the number of channels in
standard convolutional neural networks (CNNs). Thereby our approach addresses
the redundancy in CNNs that is also exposed by the recent success of
lightweight CNNs. Lightweight CNNs can achieve comparable accuracy to standard
CNNs with fewer parameters; however, the number of weights still scales
quadratically with the CNN's width. Our MGIC architectures replace each CNN
block with an MGIC counterpart that utilizes a hierarchy of nested grouped
convolutions of small group size to address this.
  Hence, our proposed architectures scale linearly with respect to the
network's width while retaining full coupling of the channels as in standard
CNNs.
  Our extensive experiments on image classification, segmentation, and point
cloud classification show that applying this strategy to different
architectures like ResNet and MobileNetV3 reduces the number of parameters
while obtaining similar or better accuracy.
