GeoGAE: Scalable Graph-Level Autoencoding via Hyperball Cloud Representations

2026-09-28

AI Summary

This work addresses the scalability bottleneck in whole-graph embedding within Euclidean spaces caused by node ordering and matching. To this end, we propose GeoGAE, a model based on hyperspherical cloud representations that innovatively defines a unique node ordering to overcome the scalability limitations of traditional graph embeddings. Furthermore, GeoGAE employs a Transformer-based autoencoder architecture to achieve efficient, lossless encoding and reconstruction of graph structures while preserving both global topology and local relational patterns. Extensive experiments across multi-domain graph datasets demonstrate that the proposed method significantly improves the ability to accurately recover original graph structures from low-dimensional embeddings, thereby validating its generalizability and superiority over existing approaches.

Abstract

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.

Problem

• graph-level embedding
• graph autoencoding
• scalability
• Euclidean space

Innovation

• Graph-level Autoencoding
• Hyperball Cloud Representation
• Scalability
• Transformer
• Graph Embedding