# Directional Message Passing on Molecular Graphs via Synthetic Coordinates

arXiv: https://arxiv.org/abs/2111.04718 · HTML: https://mlsanity.com/paper/2111.04718/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 81 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [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)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)

## Built on by (most cited first, 24 of 24)

- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [Graph-based Molecular Representation Learning](https://mlsanity.com/paper/2207.04869/) (2022)
- [Towards Multi-Layered 3D Garments Animation](https://mlsanity.com/paper/2305.10418/) (2023)
- [Long-range Brain Graph Transformer](https://mlsanity.com/paper/2501.01100/) (2025)
- [Spatial Attention Kinetic Networks with E(n)-Equivariance](https://mlsanity.com/paper/2301.08893/) (2023)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Space](https://mlsanity.com/paper/2406.10513/) (2024)
- [Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems](https://mlsanity.com/paper/2504.06087/) (2025)
- [Invariance-Aware Randomized Smoothing Certificates](https://mlsanity.com/paper/2211.14207/) (2022)
- [Knowledge-augmented Graph Machine Learning for Drug Discovery: A Survey](https://mlsanity.com/paper/2302.08261/) (2023)
- [Learning Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamics](https://mlsanity.com/paper/2205.07852/) (2022)
- [Domain-informed graph neural networks: a quantum chemistry case study](https://mlsanity.com/paper/2208.11934/) (2022)
- [DuEqNet: Dual-Equivariance Network in Outdoor 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2302.13577/) (2023)
- [AI for Scientific Discovery is a Social Problem](https://mlsanity.com/paper/2509.06580/) (2025)
- [3D Molecular Geometry Analysis with 2D Graphs](https://mlsanity.com/paper/2305.13315/) (2023)
- [Enhancing Molecular Property Prediction with Auxiliary Learning and Task-Specific Adaptation](https://mlsanity.com/paper/2401.16299/) (2024)
- [Dumpling GNN: Hybrid GNN Enables Better ADC Payload Activity Prediction Based on Chemical Structure](https://mlsanity.com/paper/2410.05278/) (2024)
- [Grothendieck Graph Neural Networks Framework: An Algebraic Platform for Crafting Topology-Aware GNNs](https://mlsanity.com/paper/2412.08835/) (2024)
- [On the Interplay of Subset Selection and Informed Graph Neural Networks](https://mlsanity.com/paper/2306.10066/) (2023)
- [Differentially Private Graph Neural Network with Importance-Grained Noise Adaption](https://mlsanity.com/paper/2308.04943/) (2023)
- [HEroBM: a deep equivariant graph neural network for universal backmapping from coarse-grained to all-atom representations](https://mlsanity.com/paper/2404.16911/) (2024)
- [Hybrid Quantum--Classical Machine Learning Potential with Variational Quantum Circuits](https://mlsanity.com/paper/2508.04098/) (2025)
- [Scalar-pathway fidelity improves physical accuracy in short-range equivariant interatomic potentials](https://mlsanity.com/paper/2606.15892/) (2026)

## Abstract (arXiv)

Graph neural networks that leverage coordinates via directional message passing have recently set the state of the art on multiple molecular property prediction tasks. However, they rely on atom position information that is often unavailable, and obtaining it is usually prohibitively expensive or even impossible. In this paper we propose synthetic coordinates that enable the use of advanced GNNs without requiring the true molecular configuration. We propose two distances as synthetic coordinates: Distance bounds that specify the rough range of molecular configurations, and graph-based distances using a symmetric variant of personalized PageRank. To leverage both distance and angular information we propose a method of transforming normal graph neural networks into directional MPNNs. We show that with this transformation we can reduce the error of a normal graph neural network by 55% on the ZINC benchmark. We furthermore set the state of the art on ZINC and coordinate-free QM9 by incorporating synthetic coordinates in the SMP and DimeNet++ models. Our implementation is available online.