FreeCG: Free the Design Space of Clebsch-Gordan Transform for Machine Learning Force Fields

Machine Learning Force Fields (MLFFs) are of great importance for chemistry, physics, materials science, and many other related fields. The Clebsch–Gordan transform (CG transform) effectively encodes many-body interactions and is thus an important building block for many models of MLFFs. However, the permutation-equivariance requirement of MLFFs limits the design space of CG transform, that is, intensive CG transform has to be conducted for each neighboring edge and the operations should be performed in the same manner for all edges. Freeing up the design space can greatly improve the model's expressiveness while simultaneously decreasing computational demands. To reach this goal, we utilize a mathematical proposition, invariance transitivity, to show that implementing the CG transform layer on the permutation-invariant abstract edges allows complete freedom in the design of the layer without compromising the overall permutation equivariance. Developing on this free design space, we further propose 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 is well extended to property prediction in QM9 datasets with several improvements greater than 15% and the maximum beyond 20%. The extensive real-world applications showcase high practicality. FreeCG introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric network designs. To demonstrate this, the recent SOTA, QuinNet, is also enhanced under our paradigm. Code: https://github.com/ShihaoShao-GH/FreeCG.