---
title: "Euclidean Crowding-Driven Adaptive Euclidean-Hyperbolic Graph Learning"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.37373v1"
permalink: "https://feed.astralor.com/items/itm_2d93709fe00c3cb34864720c"
published: "2026-10-27T15:04:50.000Z"
score: 55
channel: "tech"
tags: ["Euclidean Crowding-Driven Adaptive","Euclidean-Hyperbolic Graph Learning","Hyperbolic","Unlike Euclidean","Euclidean","Despite"]
---

# Euclidean Crowding-Driven Adaptive Euclidean-Hyperbolic Graph Learning

## 速览

Hyperbolic graph representation learning has emerged as a powerful paradigm for modeling hierarchical data. Unlike Euclidean space, which exhibits polynomial volume growth, hyperbolic space grows exponentially with radi…

## 关键点

- Hyperbolic graph representation learning has emerged as a powerful paradigm for modeling hierarchical data.
- Unlike Euclidean space, which exhibits polynomial volume growth, hyperbolic space grows exponentially with radius, naturally accommodating tree-like structures without the geometric distortion known as Euclidean crowdin…
- Despite strong empirical performance, the theoretical mechanisms underlying hyperbolic embeddings remain poorly understood.

## 全文

Hyperbolic graph representation learning has emerged as a powerful paradigm for modeling hierarchical data. Unlike Euclidean space, which exhibits polynomial volume growth, hyperbolic space grows exponentially with radius, naturally accommodating tree-like structures without the geometric distortion known as Euclidean crowding. Despite strong empirical performance, the theoretical mechanisms underlying hyperbolic embeddings remain poorly understood. In this work, we provide a geometric quantifcation research for Euclidean crowding, a generalization-theoretic explanation for the superiority of hyperbolic space on hierarchical data, and further develop an adaptive Euclidean-hyperbolic fusion learning framework toward bridging this gap. Specifically, we \textbf{first} establish a geometric quantification of Euclidean crowding by analyzing layer-wise minimum separation in node embeddings, proving that fixed-dimensional Euclidean embeddings of tree-like graphs inevitably exhibit layer-wise crowding that leads to weaker margin-based generalization bounds. \textbf{Second}, we provide a generalization-bound for the superiority of hyperbolic geometry on hierarchical data. \textbf{Third}, we propose EH-Fusion, a geometry-adaptive framework that lifts Euclidean GNN representations into hyperbolic space via exponential mapping and adaptively fuses both geometries based on node-level neighborhood expansion patterns. Extensive experiments validate our theoretical insights and demonstrate the effectiveness of EH-Fusion on benchmark datasets.

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