SE(3)-Hyena Operator for Scalable Equivariant Learning
This work addresses computational bottlenecks in equivariant learning for fields like biology and chemistry, offering a scalable solution with significant efficiency gains.
The paper tackles the challenge of modeling global geometric context with equivariance in high-dimensional data by introducing the SE(3)-Hyena operator, which matches or outperforms equivariant self-attention in tasks like associative recall and n-body modeling while being 3.5 times faster for 20k tokens and enabling 175 times longer contexts within the same memory budget.
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 x3.5 times faster than the equivariant transformer and allows x175 longer a context within the same memory budget.