Recent SO(3)-equivariant models embedded a molecule as a set of single atoms
fixed in the three-dimensional space, which is analogous to a ball-and-stick
view. This perspective provides a concise view of atom arrangements, however,
the surrounding electron density cannot be represented and its polarization
effects may be underestimated. To overcome this limitation, we propose
\textit{Neural Polarization}, a novel method extending equivariant network by
embedding each atom as a pair of fixed and moving points. Motivated by density
functional theory, Neural Polarization represents molecules as a space-filling
view which includes an electron density, in contrast with a ball-and-stick
view. Neural Polarization can flexibly be applied to most type of existing
equivariant models. We showed that Neural Polarization can improve prediction
performances of existing models over a wide range of targets. Finally, we
verified that our method can improve the expressiveness and equivariance in
terms of mathematical aspects.

最近的 SO (3) 等变模型以分子作为一组固定在三维空间中的单原子的形式进行嵌入，类似于球杆观点。然而，这种观点虽然提供了原子排列的简洁视图，但不能表示周围的电子密度，其极化效应可能被低估。为了克服这个限制，我们提出了 “神经极化”，一种通过将每个原子嵌入为一对固定和移动点来扩展等变网络的新方法。受密度泛函理论的启发，神经极化将分子表示为一种填充空间的视图，其中包括电子密度，与球杆视图形成对比。神经极化可以灵活应用于大多数现有的等变模型。我们证明了神经极化可以提高对各种目标的预测性能。最后，我们验证了我们的方法在数学方面的表达能力和等变性。