The Clebsch-Gordan Transform (CG transform) effectively encodes many-body interactions. Many studies have proven its accuracy in depicting atomic environments, although this comes with high computational needs. The computational burden of this challenge is hard to reduce due to the need for permutation equivariance, which limits the design space of the CG transform layer. We show that, implementing the CG transform layer on permutation-invariant inputs allows complete freedom in the design of this layer without affecting symmetry. Developing further on this premise, our idea is to create a CG transform layer that operates on permutation-invariant abstract edges generated from real edge information. We bring in group CG transform with sparse path, abstract edges shuffling, and attention enhancer to form a powerful and efficient CG transform layer. Our method, known as FreeCG, achieves State-of-The-Art (SoTA) results in force prediction for MD17, rMD17, MD22, and property prediction in QM9 datasets with notable enhancement. The extensibility to other models is also examined. Molecular dynamics simulations are carried out on MD17 and other periodic systems, including water and LiPS, showcasing the capacity for real-world applications of FreeCG. It introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric neural network designs.

翻译：Clebsch-Gordan变换能有效编码多体相互作用。多项研究已证明其在描述原子环境方面具有高精度，但这也伴随着高昂的计算需求。由于需要满足置换等变性，其计算负担难以降低，这限制了CG变换层的设计空间。我们证明，在置换不变的输入上实现CG变换层，可以在不影响对称性的前提下完全自由地设计该层。基于此前提进一步拓展，我们的核心思想是构建一个作用于从真实边信息生成的置换不变抽象边上的CG变换层。我们引入了具有稀疏路径的群CG变换、抽象边重排机制和注意力增强器，从而形成一个强大且高效的CG变换层。我们的方法——FreeCG——在MD17、rMD17、MD22数据集的力预测以及QM9数据集的性质预测中取得了最先进的结果，且性能提升显著。本文还验证了该方法对其他模型的扩展性。在MD17及其他周期性体系（包括水和LiPS）上进行的分子动力学模拟，展示了FreeCG在实际应用中的潜力。这项工作为未来几何神经网络设计中实现高效且富有表达力的CG变换提供了一种新颖的范式。