The field of geometric deep learning has had a profound impact on the development of innovative and powerful graph neural network architectures. Disciplines such as computer vision and computational biology have benefited significantly from such methodological advances, which has led to breakthroughs in scientific domains such as protein structure prediction and design. In this work, we introduce GCPNet, a new geometry-complete, SE(3)-equivariant graph neural network designed for 3D molecular graph representation learning. Rigorous experiments across four distinct geometric tasks demonstrate that GCPNet's predictions (1) for protein-ligand binding affinity achieve a statistically significant correlation of 0.608, more than 5% greater than current state-of-the-art methods; (2) for protein structure ranking achieve statistically significant target-local and dataset-global correlations of 0.616 and 0.871, respectively; (3) for Newtownian many-body systems modeling achieve a task-averaged mean squared error less than 0.01, more than 15% better than current methods; and (4) for molecular chirality recognition achieve a state-of-the-art prediction accuracy of 98.7%, better than any other machine learning method to date. The source code, data, and instructions to train new models or reproduce our results are freely available at https://github.com/BioinfoMachineLearning/GCPNet.

Generalized CP-nets (GCP-nets) allow a succinct representation of preferences over multi-attribute domains. As a consequence of their succinct representation, many GCP-net related tasks are computationally hard. Even finding the more preferable of two outcomes is PSPACE-complete. In this work, we employ the framework of parameterized complexity to achieve two goals: First, we want to gain a deeper understanding of the complexity of GCP-nets. Second, we search for efficient fixed-parameter tractable algorithms.