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A Depth-Aware Comparative Study of Euclidean and Hyperbolic Graph Neural Networks on Bitcoin Transaction Systems

arXiv:2603.16080v1 Announce Type: new Abstract: Bitcoin transaction networks are large scale socio- technical systems in which activities are represented through multi-hop interaction patterns. Graph Neural Networks(GNNs) have become a widely adopted tool for analyzing such systems, supporting tasks such as entity detection and transaction classification. Large-scale datasets like Elliptic have allowed for a rise in the analysis of these systems and in tasks such as fraud detection. In these settings, the amount of transactional context available to each node is determined by the neighborhood aggregation and sampling strategies, yet the interaction between these receptive fields and embedding geometry has received limited attention. In this work, we conduct a controlled comparison of Euclidean and tangent-space hyperbolic GNNs for node classification on a large Bitcoin transaction graph. By explicitly varying the neighborhood while keeping the model architecture and dimensionality fix

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Ankit Ghimire, Saydul Akbar Murad, Nick Rahimi · · 1 min read · 31 views
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arXiv:2603.16080v1 Announce Type: new Abstract: Bitcoin transaction networks are large scale socio- technical systems in which activities are represented through multi-hop interaction patterns. Graph Neural Networks(GNNs) have become a widely adopted tool for analyzing such systems, supporting tasks such as entity detection and transaction classification. Large-scale datasets like Elliptic have allowed for a rise in the analysis of these systems and in tasks such as fraud detection. In these settings, the amount of transactional context available to each node is determined by the neighborhood aggregation and sampling strategies, yet the interaction between these receptive fields and embedding geometry has received limited attention. In this work, we conduct a controlled comparison of Euclidean and tangent-space hyperbolic GNNs for node classification on a large Bitcoin transaction graph. By explicitly varying the neighborhood while keeping the model architecture and dimensionality fixed, we analyze the differences in two embedding spaces. We further examine optimization behavior and observe that joint selection of learning rate and curvature plays a critical role in stabilizing high-dimensional hyperbolic embeddings. Overall, our findings provide practical insights into the role of embedding geometry and neighborhood depth when modeling large-scale transaction networks, informing the deployment of hyperbolic GNNs for computational social systems.

Executive Summary

This article presents a comprehensive comparative study of Euclidean and hyperbolic Graph Neural Networks (GNNs) in the context of Bitcoin transaction systems. The researchers conduct a controlled experiment, varying neighborhood aggregation strategies while keeping the model architecture and dimensionality fixed. Their findings highlight the importance of embedding geometry and neighborhood depth in modeling large-scale transaction networks. The study also investigates the optimization behavior of hyperbolic GNNs, demonstrating the critical role of joint learning rate and curvature selection in stabilizing high-dimensional embeddings. The research provides valuable insights for the deployment of hyperbolic GNNs in computational social systems, particularly in the analysis of socio-technical systems like Bitcoin transaction networks.

Key Points

  • ▸ The study provides a controlled comparison of Euclidean and hyperbolic GNNs on a large Bitcoin transaction graph.
  • ▸ The researchers investigate the impact of neighborhood aggregation strategies on node classification performance.
  • ▸ The study highlights the importance of embedding geometry and neighborhood depth in modeling large-scale transaction networks.

Merits

Strength in Methodology

The study's controlled experimental design and fixed model architecture allow for a comprehensive comparison of Euclidean and hyperbolic GNNs.

Insightful Findings

The researchers provide practical insights into the role of embedding geometry and neighborhood depth in modeling large-scale transaction networks.

Demerits

Limited Scope

The study focuses on a specific application (Bitcoin transaction networks) and may not be generalizable to other domains.

Hyperparameter Sensitivity

The study highlights the importance of joint learning rate and curvature selection, but does not fully explore the sensitivity of hyperbolic GNNs to other hyperparameters.

Expert Commentary

The study presents a well-designed comparative analysis of Euclidean and hyperbolic GNNs in the context of Bitcoin transaction systems. The researchers' findings provide valuable insights into the role of embedding geometry and neighborhood depth in modeling large-scale transaction networks. However, the study's limited scope and focus on a specific application may limit its generalizability to other domains. Nevertheless, the study's contributions to the growing body of research on GNNs and hyperbolic geometry make it a significant contribution to the field.

Recommendations

  • ✓ Future studies should explore the application of hyperbolic GNNs in other domains, such as social network analysis or recommender systems.
  • ✓ Researchers should investigate the sensitivity of hyperbolic GNNs to other hyperparameters, such as the number of layers or the activation function.

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