Enhancing Distance-Based Graph Autoencoders with Structural Penalties for Dynamic Graph Embedding

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.

Dynamic graph learning aims to capture evolving structural and semantic patterns in real-world systems, such as fraud detection and recommender systems. Due to the scarcity of labeled data in real-world dynamic graphs, recent studies have introduced generative or contrastive paradigms (e.g., masked graph autoencoders or graph contrastive learning) to generate task-agnostic graph embeddings. However, these methods typically rely on complex edge-level reconstruction objectives and tailored graph augmentation strategies. This incurs substantial computational overhead when scaling to large-scale dynamic graphs. In this paper, we propose SG-JEPA, a joint spiking embedding predictive architecture for large-scale dynamic graphs. In contrast to existing self-supervised methods, SG-JEPA partitions nodes into context and target sets along the temporal dimension to learn embeddings that are predictive of each other via additional spatial-temporal information. Furthermore, through encoding sequential inputs into coarse-to-fine spike count embeddings, spiking neurons enable SG-JEPA to adapt to the varying computational constraints of downstream tasks. Extensive experiments demonstrate that SG-JEPA achieves competitive or even superior performance over discriminative baselines on node classification, while effectively scaling to the dynamic graph with 13 million edges. SG-JEPA avoids the complex machinery (negative sampling, graph augmentations, edge-level reconstruction, etc.), resulting in superior training efficiency and memory scalability compared with prior self-supervised dynamic graph baselines.

We propose MABLE (Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning), a self-supervised framework for learning node and graph embeddings from large, heterogeneous graphs, demonstrated here on geospatial mineral-exploration data. MABLE combines masked reconstruction with fixed cosine-similarity losses that align matched augmented views while keeping unpaired embeddings well spread. A bi-Lipschitz feature decoder ties a low-dimensional reconstruction component of each node embedding to feature similarity, while matched-node consistency shapes the remaining context used by graph pooling. Lipschitz-controlled pooling helps stabilize graph-level representations under perturbations of retained node embeddings, while augmentation alignment trains robustness to masking, node dropping, and sampling variation. Across local copper and regional Arabian Shield studies, MABLE embeddings provide complementary downstream signal and produce coherent embedding-derived layers for hypothesis generation without learned discriminators or hard-negative selection.