  When designing Convolutional Neural Networks (CNNs), one must select the
size\break of the convolutional kernels before training. Recent works show CNNs
benefit from different kernel sizes at different layers, but exploring all
possible combinations is unfeasible in practice. A more efficient approach is
to learn the kernel size during training. However, existing works that learn
the kernel size have a limited bandwidth. These approaches scale kernels by
dilation, and thus the detail they can describe is limited. In this work, we
propose FlexConv, a novel convolutional operation with which high bandwidth
convolutional kernels of learnable kernel size can be learned at a fixed
parameter cost. FlexNets model long-term dependencies without the use of
pooling, achieve state-of-the-art performance on several sequential datasets,
outperform recent works with learned kernel sizes, and are competitive with
much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be
deployed at higher resolutions than those seen during training. To avoid
aliasing, we propose a novel kernel parameterization with which the frequency
of the kernels can be analytically controlled. Our novel kernel
parameterization shows higher descriptive power and faster convergence speed
than existing parameterizations. This leads to important improvements in
classification accuracy.
