多向量神经元：更优更快的O(n)等变Clifford图神经网络
Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networks
AI总结：
针对现有O(n)/SO(n)等变深度学习模型的局限，提出基于Clifford多向量的新型消息传递GNN，结合不变标量特征与等变几何积算子，在N体模拟和蛋白质去噪任务上实现性能提升与高效率。
摘要：
当前大多数对$O(n)$或$SO(n)$等变的深度学习模型，要么主要处理距离、角度等标量信息，要么计算复杂度极高。本研究测试了几种基于Clifford多向量的新型消息传递图神经网络（GNNs），其结构与几何深度学习中其他主流等变模型类似。该方法在利用高效不变标量特征的同时，尤其通过等变几何积算子，对多向量表示进行富有表现力的学习。结合这些要素后，我们的方法在N体模拟任务和蛋白质去噪任务上优于已有的高效基线模型，同时保持了高效率。具体而言，我们将N体数据集的当前最优误差推至0.0035（3次运行的平均值），较近期方法提升了8%。我们的实现代码已在Github上公开。
英文摘要：
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.
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