A key challenge in designing convolutional network models is sizing them
appropriately. Many factors are involved in these decisions, including number
of layers, feature maps, kernel sizes, etc. Complicating this further is the
fact that each of these influence not only the numbers and dimensions of the
activation units, but also the total number of parameters. In this paper we
focus on assessing the independent contributions of three of these linked
variables: The numbers of layers, feature maps, and parameters. To accomplish
this, we employ a recursive convolutional network whose weights are tied
between layers; this allows us to vary each of the three factors in a
controlled setting. We find that while increasing the numbers of layers and
parameters each have clear benefit, the number of feature maps (and hence
dimensionality of the representation) appears ancillary, and finds most of its
benefit through the introduction of more weights. Our results (i) empirically
confirm the notion that adding layers alone increases computational power,
within the context of convolutional layers, and (ii) suggest that precise
sizing of convolutional feature map dimensions is itself of little concern;
more attention should be paid to the number of parameters in these layers
instead