# GeoMFormer: A General Architecture for Geometric Molecular Representation Learning

arXiv: https://arxiv.org/abs/2406.16853 · HTML: https://mlsanity.com/paper/2406.16853/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 77 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 30 of 60)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Stacked Cross Attention for Image-Text Matching](https://mlsanity.com/paper/1803.08024/) (2018)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)

## Built on by (most cited first, 6 of 6)

- [Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity](https://mlsanity.com/paper/2502.01171/) (2025)
- [Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learning](https://mlsanity.com/paper/2410.10118/) (2024)
- [Bridging Geometric States via Geometric Diffusion Bridge](https://mlsanity.com/paper/2410.24220/) (2024)
- [Enhancing Materials Discovery with Valence Constrained Design in Generative Modeling](https://mlsanity.com/paper/2507.19799/) (2025)
- [ModuLM: Enabling Modular and Multimodal Molecular Relational Learning with Large Language Models](https://mlsanity.com/paper/2506.00880/) (2025)
- [Learning 3D Anisotropic Noise Distributions Improves Molecular Force Field Modeling](https://mlsanity.com/paper/2510.22123/) (2025)

## Abstract (arXiv)

Molecular modeling, a central topic in quantum mechanics, aims to accurately calculate the properties and simulate the behaviors of molecular systems. The molecular model is governed by physical laws, which impose geometric constraints such as invariance and equivariance to coordinate rotation and translation. While numerous deep learning approaches have been developed to learn molecular representations under these constraints, most of them are built upon heuristic and costly modules. We argue that there is a strong need for a general and flexible framework for learning both invariant and equivariant features. In this work, we introduce a novel Transformer-based molecular model called GeoMFormer to achieve this goal. Using the standard Transformer modules, two separate streams are developed to maintain and learn invariant and equivariant representations. Carefully designed cross-attention modules bridge the two streams, allowing information fusion and enhancing geometric modeling in each stream. As a general and flexible architecture, we show that many previous architectures can be viewed as special instantiations of GeoMFormer. Extensive experiments are conducted to demonstrate the power of GeoMFormer. All empirical results show that GeoMFormer achieves strong performance on both invariant and equivariant tasks of different types and scales. Code and models will be made publicly available at https://github.com/c-tl/GeoMFormer.