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
this https URL

本文提出了一种不需要神经网络的连续卷积建模方法，通过自动移动的点表示和插值方案实现连续函数，从而构建卷积核，其计算效率更高、性能更好，并在 ImageNet 等大规模数据集上得到了验证。

SMPConv: 连续卷积自动移动点表示

SMPConv: Self-moving Point Representations for Continuous Convolution

We present a new convolution layer for deep learning architectures which we
call QuadConv -- an approximation to continuous convolution via quadrature. Our
operator is developed explicitly for use on non-uniform, mesh-based data, and
accomplishes this by learning a continuous kernel that can be sampled at
arbitrary locations. Moreover, the construction of our operator admits an
efficient implementation which we detail and construct. In the setting of
compressing data arising from partial differential equation (PDE) simulations,
we show that QuadConv can match the performance of standard discrete
convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to
a standard convolutional autoencoder (CAE). Further, we show that the QCAE can
maintain this accuracy even on non-uniform data.

本文介绍了一种新的卷积层 ——QuadConv，可以对基于网格的非均匀数据进行连续卷积的近似，并通过学习连续核在任意位置进行采样，从而比较标准离散卷积和 QuadConv 制造的数据上压缩数据的性能，并且表明 QCAE 模型可以即使在非均匀数据上也可以保持该准确性。