# Beyond Atoms: Evaluating Electron Density Representation for 3D Molecular Learning

arXiv: https://arxiv.org/abs/2511.21900 · HTML: https://mlsanity.com/paper/2511.21900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [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)
- [Protein-Ligand Scoring with Convolutional Neural Networks](https://mlsanity.com/paper/1612.02751/) (2016)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery](https://mlsanity.com/paper/1510.02855/) (2015)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)

## Built on by (most cited first, 1 of 1)

- [Blending experimental electron density information to protein-ligand interaction](https://mlsanity.com/paper/2610.14862/) (2026)

## Abstract (arXiv)

Machine learning models for 3D molecular property prediction typically rely on atom-based representations, which may overlook subtle physical information. Electron density maps -- the direct output of X-ray crystallography and cryo-electron microscopy -- offer a continuous, physically grounded alternative. We compare three voxel-based input types for 3D convolutional neural networks (CNNs): atom types, raw electron density, and density gradient magnitude, across two molecular tasks -- protein-ligand binding affinity prediction (PDBbind) and quantum property prediction (QM9). We focus on voxel-based CNNs because electron density is inherently volumetric, and voxel grids provide the most natural representation for both experimental and computed densities. On PDBbind, all representations perform similarly with full data, but in low-data regimes, density-based inputs outperform atom types, while a shape-based baseline performs comparably -- suggesting that spatial occupancy dominates this task. On QM9, where labels are derived from Density Functional Theory (DFT) but input densities from a lower-level method (XTB), density-based inputs still outperform atom-based ones at scale, reflecting the rich structural and electronic information encoded in density. Overall, these results highlight the task- and regime-dependent strengths of density-derived inputs, improving data efficiency in affinity prediction and accuracy in quantum property modeling.