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Lorentzian Logic: Visualizing High-Fidelity Graph Hierarchies in Hyperbolic Space

Written by @hyperbole | Published on 2026/2/19
TL;DR —
Explore the visualized hyperbolic partitioning trees of the Cora dataset using LSEnet. Discover how Differentiable Structural Information (DSI) and the Lorentz model identify optimal cluster structures without predefined group numbers (K).

Abstract and 1. Introduction

  1. Related Work

  2. Preliminaries and Notations

  3. Differentiable Structural Information

    4.1. A New Formulation

    4.2. Properties

    4.3. Differentiability & Deep Graph Clustering

  4. LSEnet

    5.1. Embedding Leaf Nodes

    5.2. Learning Parent Nodes

    5.3. Hyperbolic Partitioning Tree

  5. Experiments

    6.1. Graph Clustering

    6.2. Discussion on Structural Entropy

  6. Conclusion, Broader Impact, and References Appendix

A. Proofs

B. Hyperbolic Space

C. Technical Details

D. Additional Results

D. Additional Results

The hyperbolic partitioning trees of Cora is visualized in Fig. 6, where different clusters are distinguished by colors.

Table 4. The notation descriptions.

Table 5. The statistics of the datasets.

Figure 6. Visualization of hyperbolic partitioning trees of Cora.

Authors:

(1) Li Sun, North China Electric Power University, Beijing 102206, China (ccesunli@ncepu.edu);

(2) Zhenhao Huang, North China Electric Power University, Beijing 102206, China;

(3) Hao Peng, Beihang University, Beijing 100191, China;

(4) Yujie Wang, North China Electric Power University, Beijing 102206, China;

(5) Chunyang Liu, Didi Chuxing, Beijing, China;

(6) Philip S. Yu, University of Illinois at Chicago, IL, USA.

This paper is available on arxiv under CC BY-NC-SA 4.0 Deed (Attribution-Noncommercial-Sharelike 4.0 International) license.

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Written by
@hyperbole
Amplifying words and ideas to separate the ordinary from the extraordinary, making the mundane majestic.
Topics and
tags
deep-learning|lorentzian-graph-visualization|hyperbolic-partitioning-tree|cora-dataset-clustering|dsi|lsenet-neural-architecture|minkowski-inner-product|non-euclidean-deep-learning
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