# Global graph features unveiled by unsupervised geometric deep learning

arXiv: https://arxiv.org/abs/2503.05560 · HTML: https://mlsanity.com/paper/2503.05560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Eliciting Structural and Semantic Global Knowledge in Unsupervised Graph Contrastive Learning](https://mlsanity.com/paper/2202.08480/) (2022)
- [Geometric deep learning reveals the spatiotemporal fingerprint of microscopic motion](https://mlsanity.com/paper/2202.06355/) (2022)
- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
- [Graph-Based Modeling and Simulation of Complex Systems](https://mlsanity.com/paper/1812.04983/) (2018)

## Abstract (arXiv)

Graphs provide a powerful framework for modeling complex systems, but their structural variability poses significant challenges for analysis and classification. To address these challenges, we introduce GAUDI (Graph Autoencoder Uncovering Descriptive Information), a novel unsupervised geometric deep learning framework designed to capture both local details and global structure. GAUDI employs an innovative hourglass architecture with hierarchical pooling and upsampling layers linked through skip connections, which preserve essential connectivity information throughout the encoding-decoding process. Even though identical or highly similar underlying parameters describing a system's state can lead to significant variability in graph realizations, GAUDI consistently maps them into nearby regions of a structured and continuous latent space, effectively disentangling invariant process-level features from stochastic noise. We demonstrate GAUDI's versatility across multiple applications, including small-world networks modeling, characterization of protein assemblies from super-resolution microscopy, analysis of collective motion in the Vicsek model, and identification of age-related changes in brain connectivity. Comparison with related approaches highlights GAUDI's superior performance in analyzing complex graphs, providing new insights into emergent phenomena across diverse scientific domains.