mlsanityData to 7 Oct 2026

Learning Harmonic Molecular Representations on Riemannian Manifold

arXiv 2303.15520 ↗First posted 27 Mar 2023cs.LG cs.AI q-bio.QMcited by 8

Not on the map. Why?

Abstract (arXiv)

Molecular representation learning plays a crucial role in AI-assisted drug discovery research. Encoding 3D molecular structures through Euclidean neural networks has become the prevailing method in the geometric deep learning community. However, the equivariance constraints and message passing in Euclidean space may limit the network expressive power. In this work, we propose a Harmonic Molecular Representation learning (HMR) framework, which represents a molecule using the Laplace-Beltrami eigenfunctions of its molecular surface. HMR offers a multi-resolution representation of molecular geometric and chemical features on 2D Riemannian manifold. We also introduce a harmonic message passing method to realize efficient spectral message passing over the surface manifold for better molecular encoding. Our proposed method shows comparable predictive power to current models in small molecule property prediction, and outperforms the state-of-the-art deep learning models for ligand-binding protein pocket classification and the rigid protein docking challenge, demonstrating its versatility in molecular representation learning.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 28 of its 75 references that are in the map. First posted on arXiv 27 Mar 2023.

Builds on

28 of 75 references.

References · 28

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  6. 2021E(n) Equivariant Graph Neural Networkscited by 951
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  9. 2020Directional Message Passing for Molecular Graphscited by 556
  10. 2020PointContrast: Unsupervised Pre-training for 3D Point Cloud Understandingcited by 502
  11. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  12. 2018Spherical CNNscited by 452
16 more
  1. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  2. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  3. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  4. 2020Networks beyond pairwise interactions: structure and dynamicscited by 127
  5. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  6. 2021Geometric Deep Learning on Molecular Representationscited by 113
  7. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  8. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  9. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  10. 2020A Rotation-Invariant Framework for Deep Point Cloud Analysiscited by 62
  11. 2021DPFM: Deep Partial Functional Mapscited by 58
  12. 2022Multi-Scale Representation Learning on Proteinscited by 52
  13. 2022Structure-based drug design with geometric deep learningcited by 40
  14. 2018End-to-End Learning on 3D Protein Structure for Interface Predictioncited by 32
  15. 2020Network Geometrycited by 31
  16. 2020DeepSurf: A surface-based deep learning approach for the prediction of ligand binding sites on proteinscited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 1; 2026: 1.

8 papers.

  1. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  2. 2025MolSpectra: Pre-training 3D Molecular Representation with Multi-modal Energy Spectracited by 8
  3. 2023AtomSurf : Surface Representation for Learning on Protein Structurescited by 5
  4. 2024Effective Protein-Protein Interaction Exploration with PPIretrievalcited by 5
  5. 2024Deep Reinforcement Learning for Modelling Protein Complexescited by 5
  6. 2024Manifold-Constrained Nucleus-Level Denoising Diffusion Model for Structure-Based Drug Designcited by 1
  7. 2024Recent advances in interpretable machine learning using structure-based protein representationscited by 1
  8. 2026From Surfaces to Volumes: Registered Geometry for Protein Representation Learningcited by 0