Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance

TL;DR

This paper introduces EIGN, a novel graph neural network architecture that models both directed and undirected edge signals, addressing limitations of previous methods by incorporating orientation equivariance and invariance.

Contribution

The paper proposes a new GNN architecture, EIGN, with direction-aware operators that can handle both directed and undirected edge signals, a first in topological graph learning.

Findings

EIGN outperforms prior methods in edge-level tasks.

Improves RMSE on flow simulation by up to 23.5%.

Successfully models both directed and undirected edge signals.

Abstract

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the diameter of a pipe. Topological methods model edge signals with inherent direction by representing them relative to a so-called orientation assigned to each edge. These approaches can neither model undirected edge signals nor distinguish if an edge itself is directed or undirected. We address these shortcomings by (i) revising the notion of orientation equivariance to enable edge direction-aware topological models, (ii) proposing orientation invariance as an additional requirement to describe signals without inherent direction, and (iii) developing EIGN, an architecture composed of novel direction-aware edge-level graph shift operators, that provably fulfills the aforementioned desiderata. It is the first general-purpose topological GNN for edge-level signals that can model directed and undirected signals while distinguishing between directed and undirected edges. A comprehensive evaluation shows that EIGN outperforms prior work in edge-level tasks, for example, improving in RMSE on flow simulation tasks by up to 23.5%.