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

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19 Feb 2026

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 ([email protected]);

(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.