# Geometric Prediction: Moving Beyond Scalars

arXiv: https://arxiv.org/abs/2006.14163 · HTML: https://mlsanity.com/paper/2006.14163/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fields](https://mlsanity.com/paper/2403.09549/) (2024)
- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [3DReact: Geometric deep learning for chemical reactions](https://mlsanity.com/paper/2312.08307/) (2023)
- [Machine-learning force-field models for dynamical simulations of metallic magnets](https://mlsanity.com/paper/2602.18213/) (2026)
- [6DCNN with roto-translational convolution filters for volumetric data processing](https://mlsanity.com/paper/2107.12078/) (2021)
- [Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems](https://mlsanity.com/paper/2604.11513/) (2026)
- [HEroBM: a deep equivariant graph neural network for universal backmapping from coarse-grained to all-atom representations](https://mlsanity.com/paper/2404.16911/) (2024)

## Abstract (arXiv)

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.