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

arXiv: https://arxiv.org/abs/2603.16080 · HTML: https://mlsanity.com/paper/2603.16080/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Anti-Money Laundering in Bitcoin: Experimenting with Graph Convolutional Networks for Financial Forensics](https://mlsanity.com/paper/1908.02591/) (2019)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [A Hyperbolic-to-Hyperbolic Graph Convolutional Network](https://mlsanity.com/paper/2104.06942/) (2021)
- [Demystifying Fraudulent Transactions and Illicit Nodes in the Bitcoin Network for Financial Forensics](https://mlsanity.com/paper/2306.06108/) (2023)
- [Inspection-L: Self-Supervised GNN Node Embeddings for Money Laundering Detection in Bitcoin](https://mlsanity.com/paper/2203.10465/) (2022)
- [BitcoinHeist: Topological Data Analysis for Ransomware Detection on the Bitcoin Blockchain](https://mlsanity.com/paper/1906.07852/) (2019)
- [The Shape of Money Laundering: Subgraph Representation Learning on the Blockchain with the Elliptic2 Dataset](https://mlsanity.com/paper/2404.19109/) (2024)
- [Bitcoin Research with a Transaction Graph Dataset](https://mlsanity.com/paper/2411.10325/) (2024)
- [Topological Analysis of Mixer Activities in the Bitcoin Network](https://mlsanity.com/paper/2504.11924/) (2025)
- [Pattern Analysis of Money Flow in the Bitcoin Blockchain](https://mlsanity.com/paper/2207.07315/) (2022)
- [Demystifying Bitcoin Address Behavior via Graph Neural Networks](https://mlsanity.com/paper/2211.14582/) (2022)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [ORBITAAL: A Temporal Graph Dataset of Bitcoin Entity-Entity Transactions](https://mlsanity.com/paper/2408.14147/) (2024)

## Abstract (arXiv)

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.