Shedding Light on Problems with Hyperbolic Graph Learning

2024-11-11

arXiv.org

AI Summary

This work challenges the prevailing assumption in hyperbolic graph representation learning that “hyperbolic is superior to Euclidean.” Through systematic reproduction and fair empirical comparison, the authors identify methodological flaws in prior studies—specifically, inconsistent baseline configurations, unjustified modeling assumptions, and inadequate geometric quantification. They formally articulate three critical issues, introduce a controllable family of tree-structured benchmark datasets, and propose a novel evaluation paradigm grounded in Gromov δ-hyperbolicity and geometric suitability. Under rigorously controlled training frameworks and hyperparameters, they compare mainstream hyperbolic models (e.g., HGCN, HypER) against their Euclidean GNN counterparts. Results demonstrate that, on highly δ-hyperbolic data (e.g., perfect trees), properly tuned Euclidean models match or even surpass hyperbolic models in performance—thereby undermining foundational theoretical premises and widely held practical consensus in the field.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Humans and AI: Other Foundations of Human Computation & AI

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link prediction included. Claims have also been made about the geometric suitability of particular hierarchical graph datasets to representation in hyperbolic space. Despite these claims, our work makes a surprising discovery: when simple Euclidean models with comparable numbers of parameters are properly trained in the same environment, in most cases, they perform as well, if not better, than all introduced hyperbolic graph representation learning models, even on graph datasets previously claimed to be the most hyperbolic as measured by Gromov $delta$-hyperbolicity (i.e., perfect trees). This observation gives rise to a simple question: how can this be? We answer this question by taking a careful look at the field of hyperbolic graph representation learning as it stands today, and find that a number of results do not diligently present baselines, make faulty modelling assumptions when constructing algorithms, and use misleading metrics to quantify geometry of graph datasets. We take a closer look at each of these three problems, elucidate the issues, perform an analysis of methods, and introduce a parametric family of benchmark datasets to ascertain the applicability of (hyperbolic) graph neural networks.

Problem

• Evaluating hyperbolic vs. Euclidean graph learning models
• Challenging hyperbolic model superiority claims
• Identifying flaws in hyperbolic graph representation metrics

Innovation

• Euclidean models outperform hyperbolic
• Analyzes hyperbolic graph learning issues
• Introduces parametric benchmark datasets