Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networks

• URL: http://arxiv.org/abs/2406.04052v2
• Date: Wed, 10 Jul 2024 11:24:42 GMT
• Title: Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networks
• Authors: Cong Liu, David Ruhe, Patrick Forré,
• Abstract summary: In this work, we test a few novel message passing graph neural networks (GNNs) based on Clifford multivectors. We push the state-of-the-art error on the N-body dataset to 0.0035; an 8% improvement over recent methods.
• Score: 17.716680490388306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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