We propose a general architecture that combines the coefficient learning
scheme with a residual operator layer for learning mappings between continuous
functions in the 3D Euclidean space. Our proposed model is guaranteed to
achieve SE(3)-equivariance by design. From the graph spectrum view, our method
can be interpreted as convolution on graphons (dense graphs with infinitely
many nodes), which we term InfGCN. By leveraging both the continuous graphon
structure and the discrete graph structure of the input data, our model can
effectively capture the geometric information while preserving equivariance.
Through extensive experiments on large-scale electron density datasets, we
observed that our model significantly outperformed the current state-of-the-art
architectures. Multiple ablation studies were also carried out to demonstrate
the effectiveness of the proposed architecture.

我们提出了一种将系数学习方案与残差操作器层结合起来的通用架构，用于在三维欧几里得空间中学习连续函数之间的映射。通过设计，我们的模型可以保证实现 SE (3)- 等变性。从图谱的观点来看，我们的方法可以被解释为在图上（具有无限多个节点的稠密图）上进行卷积，我们将其称为 InfGCN。通过利用输入数据的连续图结构和离散图结构，我们的模型可以有效地捕捉几何信息并保持等变性。通过在大规模电子密度数据集上进行广泛的实验证明，我们的模型明显优于当前最先进的架构。我们还进行了多项消融研究，以证明所提出的架构的有效性。