  In recent years, deep learning has achieved great success in many computer
vision applications. Convolutional neural networks (CNNs) have lately emerged
as a major approach to image classification. Most research on CNNs thus far has
focused on developing architectures such as the Inception and residual
networks. The convolution layer is the core of the CNN, but few studies have
addressed the convolution unit itself. In this paper, we introduce a
convolution unit called the active convolution unit (ACU). A new convolution
has no fixed shape, because of which we can define any form of convolution. Its
shape can be learned through backpropagation during training. Our proposed unit
has a few advantages. First, the ACU is a generalization of convolution; it can
define not only all conventional convolutions, but also convolutions with
fractional pixel coordinates. We can freely change the shape of the
convolution, which provides greater freedom to form CNN structures. Second, the
shape of the convolution is learned while training and there is no need to tune
it by hand. Third, the ACU can learn better than a conventional unit, where we
obtained the improvement simply by changing the conventional convolution to an
ACU. We tested our proposed method on plain and residual networks, and the
results showed significant improvement using our method on various datasets and
architectures in comparison with the baseline.
