# Cormorant: Covariant Molecular Neural Networks

arXiv: https://arxiv.org/abs/1906.04015 · HTML: https://mlsanity.com/paper/1906.04015/

## Key facts

- Cited by 263 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 30 of 263)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Nested Graph Neural Networks](https://mlsanity.com/paper/2110.13197/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [One Transformer Can Understand Both 2D & 3D Molecular Data](https://mlsanity.com/paper/2210.01765/) (2022)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)

## Abstract (arXiv)

We propose Cormorant, a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems. We apply these networks to molecular systems with two goals: learning atomic potential energy surfaces for use in Molecular Dynamics simulations, and learning ground state properties of molecules calculated by Density Functional Theory. Some of the key features of our network are that (a) each neuron explicitly corresponds to a subset of atoms; (b) the activation of each neuron is covariant to rotations, ensuring that overall the network is fully rotationally invariant. Furthermore, the non-linearity in our network is based upon tensor products and the Clebsch-Gordan decomposition, allowing the network to operate entirely in Fourier space. Cormorant significantly outperforms competing algorithms in learning molecular Potential Energy Surfaces from conformational geometries in the MD-17 dataset, and is competitive with other methods at learning geometric, energetic, electronic, and thermodynamic properties of molecules on the GDB-9 dataset.