Graph Autoencoders

Traditional autoencoders rely on static network architectures to learn latent representations. Recently we suggested a dynamic architecture inspired by Hebbian plasticity, enabling topological self-organization among convolutional feature maps (R. Koç et al., Proceedings of the SIU, 2026). Early implementations of this paradigm infer relationships among feature maps using global average pooling and model their interactions through scalar-valued connections. This approach falls short to fully exploit the underlying spatial information, embedded in input images. Furthermore, abrupt transitions between different loss functions and training dynamics can introduce representation shocks, leading to unstable feature learning. In this paper, we introduce a Spatially-Aware Self-Organizing Graph Autoencoder (S-LooM) to address these structural bottlenecks. By using spatial cross-correlation, and spatial kernels, S-LooM establishes dynamic connections among feature maps. We replace static scalar message passing of autoencoders with learnable spatial kernels and eliminate high-frequency deconvolutional artifacts observed in decoders using nearest-neighbor upsampling. Via a soft-blending training curriculum, the latent topology aligns smoothly during training. Our experiments show that S-LooM yields a more stable topology, compared to the state of the art dynamic architectures. Meaning, the graph structure that emerge has more resistance to feature entanglement and noise. It forms functional communities responsible for visual attributes, such as illumination, shape and texture even under high connection densities.

Graphs play a crucial role in many applications, ranging from drug discovery to social network modeling and astronomy. Generative models for graphs have substantially advanced in recent years, but we identify relatively simple scenarios where state-of-the-art models struggle to converge within a standard compute budget, or exhibit prohibitively slow generation times. We propose a generative architecture that achieves quality competitive with state-of-the-art models and is orders of magnitude faster at generation. Our approach is inspired by the Aldous-Hoover theorem, a classic representation theorem that characterizes any probability distribution of graphs that is invariant to permutations of node indices or exchangeable. This theorem establishes that three ingredients suffice: a graph-level latent variable, a set of exchangeable node-specific latent variables, and a so-called graphon function that maps graph- and node-level variables to the probability of an edge between any node pair. Given a training set of graphs, our exchangeable Variational Graph AutoEncoder (xVGAE) learns an approximation to their underlying graphons, as well as graph- and node-level latent variables. We show that our xVGAE encodes latent representations that correlate with graph- and node-level properties, and can (quickly, in one shot) generate new graphs that closely match key training set statistics.

Knowledge graph embedding (KGE) models encode the entities and relations of a knowledge graph into a low-dimensional latent space, enabling tasks such as classification or link prediction. Most KGE models follow an autoencoder architecture, in which an encoder projects the knowledge graph into the latent space and a decoder reconstruct it. Combining both encoder and decoder components is increasingly needed, yet existing libraries rarely support complete autoencoders, are often unmaintained, rely on undocumented default hyperparameters, and produce results that cannot be compared across libraries. Here we present KGATE (Knowledge Graph Autoencoder Training Environment), a modular Python library built on PyTorch Geometric and TorchKGE. KGATE lets users assemble initializers, encoders, decoders, losses, negative samplers, and evaluation metrics as building blocks, or plug in their own block. KGATE includes a preprocessing procedure that controls data leakage, a builtin training pipeline, and reproducibility by design. Benchmarks against six existing KGE libraries show that KGATE training time is comparable with the fastest libraries while offering a broader set of features.

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.

The variational graph autoencoder (VGAE) regularizes its posterior toward the prior with the Kullback-Leibler divergence, a choice inherited from the variational autoencoder rather than argued for. We introduce the generalized graph variational autoencoder (GGVA), which replaces that term with any member of the Rényi-Tsallis family of order $q$ while leaving every other part of the model untouched. Both members admit closed forms for diagonal Gaussians and both recover the KL exactly as $q \to 1$, so the VGAE is the $q=1$ arm of our own model rather than a separate baseline, and any measured difference is attributable to a single scalar. Our analysis identifies boundedness, not the order, as the operative property: for $q<1$ the Tsallis divergence is bounded above by $1/(1-q)$, independently of the latent width, whereas the KL and the Rényi divergence of the same order are unbounded. On ten graphs spanning three synthetic families, a social network, three citation networks, a connectome, a power grid and a road network, $q$ moves the retained posterior information by up to $49\times$ relative to the VGAE, while the Rényi arm at the same order stays within $1.02$-$1.30\times$ of it on all six larger real graphs (isolating the bound as the cause). The retained information is usable: probing the frozen embedding for node class, a label absent from the objective, gives GGVA up to $+0.14$ macro-F1 over the VGAE on CiteSeer, with the Rényi control again tracking the VGAE. We also report what the design was built to expose: none of this reaches held-out link-prediction accuracy on any of the six larger real graphs, and boundedness delays posterior collapse rather than preventing it.

Graph autoencoders (GAEs) are widely used for learning representations of dynamic graphs. However, their optimisation objectives typically do not take structural heterogeneity across nodes into account. We propose three distance-based GAE variants that incorporate structural penalties into the reconstruction loss. All variants share a two-layer Graph Convolutional Network encoder and a Euclidean-distance decoder trained with distance-based reconstruction objectives. We extend sparsity-corrected loss with two node-level regularization terms: (i) a hub penalty based on degree centrality, and (ii) a penalty based on Natural Community Local Intrinsic Dimensionality (NC-LID). The paper is motivated by prior evidence linking high NC-LID to reduced embedding quality. The proposed methods are designed to emphasize reconstruction errors for structurally ambiguous nodes. Experiments on multiple dynamic graph data sets show that incorporating NC-LID-based regularization consistently improves reconstruction performance over the baseline without structural regularization and the method using hub-aware regularization. These findings highlight NC-LID as a useful structural signal for enhancing distance-based graph autoencoders in dynamic settings.

Unsupervised graph representation learning aims to derive meaningful node embeddings by capturing both structural and attribute information without relying on labeled data. Existing methods, such as GAEs, have demonstrated effectiveness but typically rely on message-passing mechanisms that assume homophily, leading to performance degradation on heterophilous graphs, where connected nodes exhibit dissimilar features. This homophily bias results in the loss of critical high-frequency components that are essential for identifying heterophilous patterns. To address these challenges, we propose AlignGAE, a novel extension of MaskGAE that preserves the full frequency spectrum through complementary view alignment. Our framework introduces a dual-encoder architecture that separately processes structural and attribute information, incorporates node positional encoding to approximate Neighborhood Identity Distribution (NID), and employs dual reconstruction tasks for both edges and node attributes. We further propose theoretically grounded NID alignment strategies that ensure semantic consistency across views while preserving their distinct characteristics. Through comprehensive spectral analysis, we demonstrate that AlignGAE achieves optimal representation properties when the alignment loss converges. Extensive experiments across 12 benchmark datasets validate our approach, showing that AlignGAE outperforms state-of-the-art methods by up to 18.7% on heterophilous graphs in node classification, while maintaining competitive performance on homophilous graphs. Our results establish a new paradigm for frequency-aware graph representation learning.

Defending Graph Neural Networks (GNNs) against adversarial attacks requires balancing accuracy and robustness, a trade-off often mishandled by traditional methods like adversarial training that intertwine these conflicting objectives within a single classifier. To overcome this limitation, we propose a self-supervised adversarial purification framework. We separate robustness from the classifier by introducing a dedicated purifier, which cleanses the input data before classification. In contrast to prior adversarial purification methods, we propose GPR-GAE, a novel graph auto-encoder (GAE), as a specialized purifier trained with a self-supervised strategy, adapting to diverse graph structures in a data-driven manner. Utilizing multiple Generalized PageRank (GPR) filters, GPR-GAE captures diverse structural representations for robust and effective purification. Our multi-step purification process further facilitates GPR-GAE to achieve precise graph recovery and robust defense against structural perturbations. Experiments across diverse datasets and attack scenarios demonstrate the state-of-the-art robustness of GPR-GAE, showcasing it as an independent plug-and-play purifier for GNN classifiers.

We introduce GraViti, a transformer-based graph-level variational autoencoder that encodes entire graphs into single, fixed-dimensional latent vectors rather than per-node embeddings, yielding a graph-level latent space that supports smooth interpolation, property-guided search, and other downstream tasks beyond the reach of node-level approaches. GraViti achieves state-of-the-art reconstruction accuracy on large molecular graph datasets while offering competitive single-step generative performance. Our central finding concerns where permutation invariance is needed in such a model, and where it is not. The encoder remains permutation-invariant throughout, ensuring the model generalizes to graphs regardless of input order. The reconstruction loss, however, does not need to be: when training data is provided in a consistent node order, comparing predictions to targets directly in that order, without a graph-matching step, is sufficient. Relaxing invariance in the loss alone lets GraViti avoid the cubic-cost matching step required by prior graph-level autoencoders, reducing complexity to quadratic while improving reconstruction fidelity. We show the resulting latent space is chemically meaningful, supporting controlled molecular editing and property optimization, recovering established chemical trends, and enabling direct regression of graph-level properties from latent embeddings.

Graph self-supervised learning can reduce the need for labeled graph data and has been widely used in recommendation, social networks, and other web applications. However, existing methods often underuse high-frequency signals and may overfit to specific local patterns, which limits representation quality and generalization. We propose Frequency-Corrupt Based Graph Self-Supervised Learning (FC-GSSL), a method that builds corrupted graphs biased toward high-frequency information by corrupting nodes and edges according to their low-frequency contributions. These corrupted graphs are used as inputs to an autoencoder, while low-frequency and general features are reconstructed as supervision targets, forcing the model to fuse information from multiple frequency bands. We further design multiple sampling strategies and generate diverse corrupted graphs from the intersections and unions of the sampling results. By aligning node representations from these views, the model can discover useful frequency combinations, reduce reliance on specific high-frequency components, and improve robustness. Experiments on 14 datasets across node classification, graph prediction, and transfer learning show that FC-GSSL consistently improves performance and generalization.

Prime Video regularly conducts load tests to simulate the viewer traffic spikes seen during live events such as Thursday Night Football as well as video-on-demand (VOD) events such as Rings of Power. While these stress tests validate system capacity, they can sometimes miss service behaviors unique to real event traffic. We present a graph-based anomaly detection system that identifies under-represented services using unsupervised node-level graph embeddings. Built on a GCN-GAE, our approach learns structural representations from directed, weighted service graphs at minute-level resolution and flags anomalies based on cosine similarity between load test and event embeddings. The system identifies incident-related services that are documented and demonstrates early detection capability. We also introduce a preliminary synthetic anomaly injection framework for controlled evaluation that show promising precision (96%) and low false positive rate (0.08%), though recall (58%) remains limited under conservative propagation assumptions. This framework demonstrates practical utility within Prime Video while also surfacing methodological lessons and directions, providing a foundation for broader application across microservice ecosystems.

Phishing remains the most pervasive threat to the Web, enabling large-scale credential theft and financial fraud through deceptive webpages. While recent reference-based and generative-AI-driven phishing detectors achieve strong accuracy, their reliance on external knowledge bases, cloud services, and complex multimodal pipelines fundamentally limits practicality, scalability, and reproducibility. In contrast, conventional deep learning approaches often fail to generalize to evolving phishing campaigns. We introduce SpecularNet, a novel lightweight framework for reference-free web phishing detection that demonstrates how carefully designed compact architectures can rival heavyweight systems. SpecularNet operates solely on the domain name and HTML structure, modeling the Document Object Model (DOM) as a tree and leveraging a hierarchical graph autoencoding architecture with directional, level-wise message passing. This design captures higher-order structural invariants of phishing webpages while enabling fast, end-to-end inference on standard CPUs. Extensive evaluation against 13 state of the art phishing detectors, including leading reference-based systems, shows that SpecularNet achieves competitive detection performance with dramatically lower computational cost. On benchmark datasets, it reaches an F1 score of 93.9%, trailing the best reference-based method slightly while reducing inference time from several seconds to approximately 20 milliseconds per webpage. Field and robustness evaluations further validate SpecularNet in real-world deployments, on a newly collected 2026 open-world dataset, and against adversarial attacks.