Geometric Prediction: Moving Beyond Scalars
This work addresses the data inefficiency in predicting geometric tensors for applications in 3D vision, robotics, and molecular biology, representing a novel formulation rather than an incremental improvement.
The paper tackles the problem of predicting geometric tensors in real-world scenarios, demonstrating that equivariant networks can predict these tensors without approximations, leading to improved state-of-the-art structural candidates in biomolecular refinement and generalization to unseen systems with small training sets.
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them through scalar predictions, leading to losses in data efficiency. In this work, we demonstrate that equivariant networks have the capability to predict real-world geometric tensors without the need for such approximations. We show the applicability of this method to the prediction of force fields and then propose a novel formulation of an important task, biomolecular structure refinement, as a geometric prediction problem, improving state-of-the-art structural candidates. In both settings, we find that our equivariant network is able to generalize to unseen systems, despite having been trained on small sets of examples. This novel and data-efficient ability to predict real-world geometric tensors opens the door to addressing many problems through the lens of geometric prediction, in areas such as 3D vision, robotics, and molecular and structural biology.