Oversquashing in Hypergraph Neural Networks

Naganand Yadati

Keywords: Graph Neural Networks, Hypergraphs, Oversquashing

TL;DR: We investigate the oversquashing phenomenon in Hypergraph Neural Networks.

Abstract:

Message Passing Neural Networks (MPNNs) are a type of Graph Neural Networks (GNNs) that utilise the graph structure to facilitate the exchange of messages along the edges.
On the one hand, the inductive bias gives rise to a phenomenon termed "over-squashing," where a node's hidden feature becomes insensitive to information present in distant nodes.
On the other hand, there has been a recent wave of innovations involving the adaptation of MPNNs and GNNs to hypergraphs, which relax the notion of an edge to a hyperedge containing a subset of nodes.
In recent times, MPNNs and GNNs have found application in web datasets, spanning both graph and hypergraph scenarios.
However, there exists a research gap regarding the investigation of over-squashing within hypergraph neural networks.
Our paper contributes to bridging this precise research gap by investigating several methods each belonging to one of two distinct classes of hypergraph neural networks.
To begin with, we introduce three novel problems termed HyperEdgeSingle, HyperEdgePath, and HyperEdgeRing designed specifically for assessing the phenomenon of over-squashing within hypergraph neural networks.
Through theoretical and experimental analyses, we reveal a counter-intuitive and significant finding: advanced state-of-the-art hypergraph neural networks are more susceptible to over-squashing than their predecessors.
Validation of the findings is reinforced through experiments conducted on real-world datasets.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 50