# GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations

arXiv: https://arxiv.org/abs/2609.35527 · HTML: https://mlsanity.com/paper/2609.35527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 53 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## 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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Learning Graph-Level Representation for Drug Discovery](https://mlsanity.com/paper/1709.03741/) (2017)
- [3DLinker: An E(3) Equivariant Variational Autoencoder for Molecular Linker Design](https://mlsanity.com/paper/2205.07309/) (2022)
- [Graph convolutions that can finally model local structure](https://mlsanity.com/paper/2011.15069/) (2020)
- [Minimum-Distortion Embedding](https://mlsanity.com/paper/2103.02559/) (2021)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning](https://mlsanity.com/paper/2104.09856/) (2021)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [Unified Guidance for Geometry-Conditioned Molecular Generation](https://mlsanity.com/paper/2501.02526/) (2025)
- [Series2Vec: Similarity-based Self-supervised Representation Learning for Time Series Classification](https://mlsanity.com/paper/2312.03998/) (2023)
- [Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Space](https://mlsanity.com/paper/2406.10513/) (2024)

## Abstract (arXiv)

Embedding structured objects into Euclidean spaces has enabled a wide range of successful machine learning applications. Such objects include words, documents, image patches, time series, and graph nodes. In contrast, embedding entire graphs remains a challenging problem. Existing methods either sustain the original order of the graph nodes or match the output nodes to the input ones, both of which create scalability issues. In this work, we propose a graph representation as a cloud of hyperballs, which allows us to define a specific, typically unique, node ordering. Based on this representation, we propose GeoGAE, an autoencoder, in which the Transformer encoder translates a hyperball cloud into a graph-level embedding, and the Transformer decoder translates the graph-level embedding back into the graph. This formulation enables the model to capture both the global graph structure and local relational patterns. We evaluate our method on multiple graph datasets, spanning various domains. The results demonstrate effectiveness of our method in encoding and reconstructing graphs from their embeddings.