提出4个全局通用的欧式不变量，提升分子动力学预测精度。
Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
- 构建4个独立且完备的欧式不变量集合，覆盖整个位置-方向空间
- 在PONITA模型上验证，使用通用不变量使预测准确率显著提升
- 适用于需要高精度对称性保持的分子模拟任务
基于位置-方向空间M(3)上的标量场的欧氏E(3)协变神经网络已成功应用于分子动力学与性质预测。为在这些架构中实现类卷积的协变操作，需在M(3) × M(3)上定义欧氏不变核。实践中常人工选择一组不变量，并通过多层感知机参数化核函数。本文严格构造出一个在M(3) × M(3)全空间上最优的4个光滑标量不变量集合，其“最优”指具有独立性与普遍性：所有不变量均相关，且任意不变核均可表示为它们的函数。我们在PONITA神经网络架构下评估了两组不变量集合（一组通用，一组非通用），实验表明采用通用不变量集合可显著提升模型精度。
原文摘要 · Abstract (English)
Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied to tasks such as predicting molecular dynamics and properties. To perform equivariant convolutional-like operations in these architectures one needs Euclidean invariant kernels on M(3) x M(3). In practice, a handcrafted collection of invariants is selected, and this collection is then fed into multilayer perceptrons to parametrize the kernels. We rigorously describe an optimal collection of 4 smooth scalar invariants on the whole of M(3) x M(3). With optimal we mean that the collection is independent and universal, meaning that all invariants are pertinent, and any invariant kernel is a function of them. We evaluate two collections of invariants, one universal and one not, using the PONITA neural network architecture. Our experiments show that using a collection of invariants that is universal positively impacts the accuracy of PONITA significantly.
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