Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networks
This work addresses the need for more efficient and expressive equivariant models in geometric deep learning, with applications in tasks like N-body simulations and protein denoising, though it appears incremental as it builds on existing equivariant frameworks.
The authors tackled the problem of high computational complexity and limited expressiveness in O(n)-equivariant deep learning models by introducing multivector-based graph neural networks that leverage Clifford algebra. Their approach achieved an 8% improvement, reducing the state-of-the-art error on the N-body dataset to 0.0035, while maintaining high efficiency.
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.