Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks

TL;DR

This paper introduces JSGNN, a graph neural network that adaptively selects Euclidean or hyperbolic space for each node based on local geometric hyperbolicity, improving representation learning.

Contribution

It proposes a novel method for node-specific space selection in GNNs using local hyperbolicity measures, enabling adaptive embedding in Euclidean or hyperbolic spaces.

Findings

Promising performance on node classification tasks

Effective alignment of hyperbolicity distributions using Wasserstein metric

Enhanced flexibility in graph representation learning

Abstract

Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries at different regions of the graph. Thus, it is sub-optimal to indifferently embed an entire graph into a single space. In this paper, we explore and analyze two notions of local hyperbolicity, describing the underlying local geometry: geometric (Gromov) and model-based, to determine the preferred space of embedding for each node. The two hyperbolicities' distributions are aligned using the Wasserstein metric such that the calculated geometric hyperbolicity guides the choice of the learned model hyperbolicity. As such our model Joint Space Graph Neural Network (JSGNN) can leverage both Euclidean and hyperbolic spaces during learning by allowing node-specific geometry space selection. We evaluate our model on both node classification and link prediction tasks and observe promising performance compared to baseline models.