  Modern convolutional neural networks (CNNs) have massive identical
convolution blocks, and, hence, recursive sharing of parameters across these
blocks has been proposed to reduce the amount of parameters. However, naive
sharing of parameters poses many challenges such as limited representational
power and the vanishing/exploding gradients problem of recursively shared
parameters. In this paper, we present a recursive convolution block design and
training method, in which a recursively shareable part, or a filter basis, is
separated and learned while effectively avoiding the vanishing/exploding
gradients problem during training. We show that the unwieldy
vanishing/exploding gradients problem can be controlled by enforcing the
elements of the filter basis orthonormal, and empirically demonstrate that the
proposed orthogonality regularization improves the flow of gradients during
training. Experimental results on image classification and object detection
show that our approach, unlike previous parameter-sharing approaches, does not
trade performance to save parameters and consistently outperforms
overparameterized counterpart networks. This superior performance demonstrates
that the proposed recursive convolution block design and the orthogonality
regularization not only prevent performance degradation, but also consistently
improve the representation capability while a significant amount of parameters
are recursively shared.
