SE(3)-Hyena Operator for Scalable Equivariant Learning

Modeling global geometric context while maintaining equivariance is crucial for accurate predictions in many fields such as biology, chemistry, or vision. Yet, this is challenging due to the computational demands of processing high-dimensional data at scale. Existing approaches such as equivariant self-attention or distance-based message passing, suffer from quadratic complexity with respect to sequence length, while localized methods sacrifice global information. Inspired by the recent success of state-space and long-convolutional models, in this work, we introduce SE(3)-Hyena operator, an equivariant long-convolutional model based on the Hyena operator. The SE(3)-Hyena captures global geometric context at sub-quadratic complexity while maintaining equivariance to rotations and translations. Evaluated on equivariant associative recall and n-body modeling, SE(3)-Hyena matches or outperforms equivariant self-attention while requiring significantly less memory and computational resources for long sequences. Our model processes the geometric context of $20k$ tokens $\times3.5$ faster than the equivariant transformer and allows $\times175$ longer a context within the same memory budget.