E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Products

TL;DR

E2Former is a new equivariant transformer that significantly reduces computational costs in modeling microscale systems by shifting tensor operations from edges to nodes, enabling scalable and efficient molecular modeling.

Contribution

It introduces Wigner 6j convolution into transformers, reducing complexity from edge-based to node-based, maintaining expressiveness and equivariance while achieving substantial speedups.

Findings

Achieves 7x-30x speedup over traditional SO(3) convolutions.

Maintains model's ability to capture detailed geometric information.

Mitigates computational challenges in large-scale microscale system modeling.

Abstract

Equivariant Graph Neural Networks (EGNNs) have demonstrated significant success in modeling microscale systems, including those in chemistry, biology and materials science. However, EGNNs face substantial computational challenges due to the high cost of constructing edge features via spherical tensor products, making them impractical for large-scale systems. To address this limitation, we introduce E2Former, an equivariant and efficient transformer architecture that incorporates the Wigner $6j$ convolution (Wigner $6j$ Conv). By shifting the computational burden from edges to nodes, the Wigner $6j$ Conv reduces the complexity from $O(|\mathcal{E}|)$ to $ O(| \mathcal{V}|)$ while preserving both the model's expressive power and rotational equivariance. We show that this approach achieves a 7x-30x speedup compared to conventional $\mathrm{SO}(3)$ convolutions. Furthermore, our empirical results demonstrate that the derived E2Former mitigates the computational challenges of existing approaches without compromising the ability to capture detailed geometric information. This development could suggest a promising direction for scalable and efficient molecular modeling.