Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

翻译：连续卷积因其处理非均匀采样数据和建模长程依赖关系的能力而近期备受关注。同时，使用大卷积核所取得的优异实验结果进一步推动了连续卷积的发展，因为连续卷积能够极其高效地构建大卷积核。利用神经网络，特别是多层感知机（MLPs），是目前实现连续卷积最主流的方法。然而，该方法存在一些缺点，例如计算成本高、超参数调优复杂以及滤波器描述能力有限。本文提出了一种替代方法，无需使用神经网络即可构建连续卷积，从而实现了更高的计算效率和性能提升。我们提出了自移动点表示，其中权重参数可自由移动，并通过插值方案来实现连续函数。当将其应用于构建卷积核时，实验结果表明，在现有框架中进行即插即用替换即可提升性能。由于其轻量级结构，我们是首个在大型数据集（如ImageNet）上展示连续卷积有效性的团队，并相比于现有技术取得了性能提升。我们的代码可在 https://github.com/sangnekim/SMPConv 获取。