# Multi-Type Point Cloud Autoencoder: A Complete Equivariant Embedding for Molecule Conformation and Pose

arXiv: https://arxiv.org/abs/2405.13791 · HTML: https://mlsanity.com/paper/2405.13791/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 80 references that are in the map.
- First posted on arXiv 22 May 2024.

## Builds on (most cited first, 30 of 35)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [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)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [Pre-training Molecular Graph Representation with 3D Geometry](https://mlsanity.com/paper/2110.07728/) (2021)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (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)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Building powerful and equivariant graph neural networks with structural message-passing](https://mlsanity.com/paper/2006.15107/) (2020)
- [Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matching](https://mlsanity.com/paper/2206.13602/) (2022)
- [Graph-based Molecular Representation Learning](https://mlsanity.com/paper/2207.04869/) (2022)
- [Unified 2D and 3D Pre-Training of Molecular Representations](https://mlsanity.com/paper/2207.08806/) (2022)
- [Comprehensive Review of Deep Learning-Based 3D Point Cloud Completion Processing and Analysis](https://mlsanity.com/paper/2203.03311/) (2022)
- [Rigid Body Flows for Sampling Molecular Crystal Structures](https://mlsanity.com/paper/2301.11355/) (2023)
- [The Expressive Power of Graph Neural Networks: A Survey](https://mlsanity.com/paper/2308.08235/) (2023)
- [Incompleteness of graph neural networks for points clouds in three dimensions](https://mlsanity.com/paper/2201.07136/) (2022)

## Built on by (most cited first, 3 of 3)

- [Learning Permutation-invariant Macroscopic Dynamics](https://mlsanity.com/paper/2605.30812/) (2026)
- [Implicit Neural Representations of Molecular Vector-Valued Functions](https://mlsanity.com/paper/2502.10848/) (2025)
- [MXtalTools: A Toolkit for Machine Learning on Molecular Crystals](https://mlsanity.com/paper/2511.20327/) (2025)

## Abstract (arXiv)

Representations are a foundational component of any modelling protocol, including on molecules and molecular solids. For tasks that depend on knowledge of both molecular conformation and 3D orientation, such as the modelling of molecular dimers, clusters, or condensed phases, we desire a rotatable representation that is provably complete in the types and positions of atomic nuclei and roto-inversion equivariant with respect to the input point cloud. In this paper, we develop, train, and evaluate a new type of autoencoder, molecular O(3) encoding net (Mo3ENet), for multi-type point clouds, for which we propose a new reconstruction loss, capitalizing on a Gaussian mixture representation of the input and output point clouds. Mo3ENet is end-to-end equivariant, meaning the learned representation can be manipulated on O(3), a practical bonus. An appropriately trained Mo3ENet latent space comprises a universal embedding for scalar and vector molecule property prediction tasks, as well as other downstream tasks incorporating the 3D molecular pose, and we demonstrate its fitness on several such tasks.