Graph Autoencoder Uncovering Descriptive Information (GAUDI), an unsupervised graph deep learning framework designed to capture both local details and global structure, is introduced, providing new insights into emergent phenomena across diverse scientific domains.
Abstract
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 Graph Autoencoder Uncovering Descriptive Information (GAUDI), an unsupervised graph deep learning framework designed to capture both local details and global structure. GAUDI employs an 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.
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Graph convolutional networks (GCNs) have shown promising performance in real-world applications involving graph-structured data. To enhance the model’s ability to integrate information from neighbor nodes, GCNs typically expand the receptive field by stacking more layers, which can lead to the problem of over-smoothing. To address this limitation, high-order graph convolutional networks (HGCNs) such as Mixhop have been proposed. These high-order models, however, introduce the risk of overfitting due to the increased number of parameters required for designing different order convolutions, which in turn can degrade classification performance. To overcome these issues, we first provide a theoretical analysis of the bottlenecks in conventional GCNs and establish that an effective graph convolutional model should integrate multi-hop neighborhood information in a unified manner. Inspired by this, we propose a novel broad graph convolutional network (BGCN) paradigm, which completely eliminates hidden layers and instead expands the receptive field through network width. We introduce four specific BGCN architectures and provide a detailed analysis of their computational complexity and parameter efficiency. A number of experiments on citation networks demonstrate that the proposed methods achieve state-of-the-art performance in terms of both classification accuracy and stability. In particular, our BGCN with simple attention mechanism (
$$\text {BGCN}_{\text {SA}}$$
BGCN
SA
) achieves top performance on the Citeseer, Cora, and Pubmed datasets, with accuracies of 73.3%, 83.5%, and 81.1%, respectively. The main advantage of this work lies in offering a robust, efficient, and scalable alternative for graph representation learning, effectively circumventing the inherent limitations of over-smoothing and overfitting in existing deep and high-order GCN models.
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