Shedding Light on Problems with Hyperbolic Graph Learning

• URL: http://arxiv.org/abs/2411.06688v1
• Date: Mon, 11 Nov 2024 03:12:41 GMT
• Title: Shedding Light on Problems with Hyperbolic Graph Learning
• Authors: Isay Katsman, Anna Gilbert,
• Abstract summary: Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. We take a careful look at the field of hyperbolic graph representation learning as it stands today. We find that a number of papers fail to diligently present baselines, make faulty modelling assumptions when constructing algorithms, and use misleading metrics to quantify geometry of graph datasets.
• Score: 2.3743504594834635
• License:
• 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 papers fail to 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.

Related papers

• Parametric Graph Representations in the Era of Foundation Models: A Survey and Position [69.48708136448694]
  Graphs have been widely used in the past decades of big data and AI to model comprehensive relational data. Identifying meaningful graph laws can significantly enhance the effectiveness of various applications.
  arXiv  Detail & Related papers  (2024-10-16T00:01:31Z)
• Weighted Embeddings for Low-Dimensional Graph Representation [0.13499500088995461]
  We propose embedding a graph into a weighted space, which is closely related to hyperbolic geometry but mathematically simpler. We show that our weighted embeddings heavily outperform state-of-the-art Euclidean embeddings for heterogeneous graphs while using fewer dimensions.
  arXiv  Detail & Related papers  (2024-10-08T13:41:03Z)
• Graph data augmentation with Gromow-Wasserstein Barycenters [0.0]
  It has been proposed a novel augmentation strategy for graphs that operates in a non-Euclidean space. A non-Euclidean distance, specifically the Gromow-Wasserstein distance, results in better approximations of the graphon. This framework also provides a means to validate different graphon estimation approaches.
  arXiv  Detail & Related papers  (2024-04-12T10:22:55Z)
• Neural Scaling Laws on Graphs [54.435688297561015]
  We study neural scaling laws on graphs from both model and data perspectives. For model scaling, we investigate the phenomenon of scaling law collapse and identify overfitting as the potential reason. For data scaling, we suggest that the number of graphs can not effectively metric the graph data volume in scaling law since the sizes of different graphs are highly irregular.
  arXiv  Detail & Related papers  (2024-02-03T06:17:21Z)
• Improving embedding of graphs with missing data by soft manifolds [51.425411400683565]
  The reliability of graph embeddings depends on how much the geometry of the continuous space matches the graph structure. We introduce a new class of manifold, named soft manifold, that can solve this situation. Using soft manifold for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets.
  arXiv  Detail & Related papers  (2023-11-29T12:48:33Z)
• Tight and fast generalization error bound of graph embedding in metric space [54.279425319381374]
  We show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested. Our new upper bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(frac1S)$ at the fastest.
  arXiv  Detail & Related papers  (2023-05-13T17:29:18Z)
• Explanation Graph Generation via Pre-trained Language Models: An Empirical Study with Contrastive Learning [84.35102534158621]
  We study pre-trained language models that generate explanation graphs in an end-to-end manner. We propose simple yet effective ways of graph perturbations via node and edge edit operations. Our methods lead to significant improvements in both structural and semantic accuracy of explanation graphs.
  arXiv  Detail & Related papers  (2022-04-11T00:58:27Z)
• Synthetic Graph Generation to Benchmark Graph Learning [7.914804101579097]
  Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks. One reason is due to the very small number of datasets used in practice to benchmark the performance of graph learning algorithms. We propose to generate synthetic graphs, and study the behaviour of graph learning algorithms in a controlled scenario.
  arXiv  Detail & Related papers  (2022-04-04T10:48:32Z)
• Line Graph Neural Networks for Link Prediction [71.00689542259052]
  We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. In this formalism, a link prediction problem is converted to a graph classification task. We propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task.
  arXiv  Detail & Related papers  (2020-10-20T05:54:31Z)
• Are Hyperbolic Representations in Graphs Created Equal? [1.80476943513092]
  We consider whether non-Euclidean embeddings are always useful for graph learning tasks. We first fix an issue of the existing models associated with the optimization process at zero curvature. We evaluate the approach of embedding graphs into the manifold in several graph representation learning tasks.
  arXiv  Detail & Related papers  (2020-07-15T14:14:14Z)
• Non-Parametric Graph Learning for Bayesian Graph Neural Networks [35.88239188555398]
  We propose a novel non-parametric graph model for constructing the posterior distribution of graph adjacency matrices. We demonstrate the advantages of this model in three different problem settings: node classification, link prediction and recommendation.
  arXiv  Detail & Related papers  (2020-06-23T21:10:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.