Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph neural networks (GNNs) based on Clifford multivectors, structured similarly to other prevalent equivariant models in geometric deep learning. Our approach leverages efficient invariant scalar features while simultaneously performing expressive learning on multivector representations, particularly through the use of the equivariant geometric product operator. By integrating these elements, our methods outperform established efficient baseline models on an N-Body simulation task and protein denoising task while maintaining a high efficiency. In particular, we push the state-of-the-art error on the N-body dataset to 0.0035 (averaged over 3 runs); an 8% improvement over recent methods. Our implementation is available on Github.

翻译：目前大多数对$O(n)$或$SO(n)$具有等变性的深度学习模型，要么主要考虑距离和角度等标量信息，要么具有极高的计算复杂度。本工作中，我们测试了几种基于克利福德多向量的新型消息传递图神经网络（GNN），其结构与几何深度学习中其他主流等变模型相似。我们的方法在利用高效不变标量特征的同时，通过等变几何积算子的运用，在多向量表示上执行富有表现力的学习。通过整合这些要素，我们的方法在N体模拟任务和蛋白质去噪任务上超越了现有高效基线模型，同时保持了较高的计算效率。特别地，我们将N体数据集上的最先进误差推进至0.0035（3次运行平均值）；相较于近期方法提升了8%。我们的实现代码已在Github上开源。