Spin-Weighted Spherical Harmonics Enable Complete and Scalable $\mathrm{E}(3)$-Equivariant Networks
arXiv:2607.01408v1 Announce Type: new Abstract: $\mathrm{E}(3)$-equivariant networks are promising for 3D atomistic system modeling, yet their scalability is limited by the $O(L^6)$ complexity of the Clebsch-Gordan Tensor Product (CGTP). The recently proposed Gaunt Tensor Product (GTP) reduces the complexity but is unable to capture the antisymmetric paths, resulting in incomplete expressivity. In this work, we present SpinGTP, an approach to overcome the GTP incompleteness by generalizing from scalar functions to Spin-Weighted Spherical Harmonics (SWSH). By relying on the algebraic properties
The continuous push for more efficient and expressive AI models, particularly in 3D applications, drives research into overcoming current computational bottlenecks.
This breakthrough addresses a fundamental limitation in E(3)-equivariant networks, potentially enabling more scalable and accurate AI models for atomistic systems, which are crucial for materials science and drug discovery.
The proposed SpinGTP method improves both the scalability and expressivity of 3D equivariant networks, moving beyond the limitations of prior techniques and opening new avenues for complex molecular simulations.
- · AI researchers
- · Materials science
- · Drug discovery
- · Deep learning hardware developers
- · Inefficient E(3)-equivariant network architectures
More accurate and scalable simulations of molecular structures will accelerate research in related scientific fields.
Reduced computational costs for complex 3D simulations could decentralize access to advanced material design capabilities.
New classes of AI-designed materials or drugs could emerge, profoundly impacting various industries and human health.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG