FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes

TL;DR

FlexConv introduces a learnable kernel size convolutional operation that models long-term dependencies efficiently, achieving state-of-the-art results on sequential and image datasets while allowing higher resolution deployment.

Contribution

The paper proposes FlexConv, a novel convolutional operation with learnable kernel sizes and a new kernel parameterization, enabling high bandwidth kernels at fixed parameters and improved performance.

Findings

FlexNets outperform recent learned kernel size methods.

FlexNets achieve state-of-the-art on sequential datasets.

FlexNets are competitive with deeper ResNets on image benchmarks.

Abstract

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.